sensors Article
Analysis of the Dynamic Sensitivity of Hemisphere-Shaped Electrostatic Sensors’ Circular Array for Charged Particle Monitoring Xin Tang, Zhong-Sheng Chen *, Yue Li, Zheng Hu and Yong-Min Yang Science and Technology on Integrated Logistics Support Laboratory, National University of Defense Technology, Changsha 410073, China; [email protected] (X.T.); [email protected] (Y.L.); [email protected] (Z.H.); [email protected] (Y.-M.Y.) * Correspondence: [email protected]; Tel.: +86-139-7580-3247 Academic Editor: Vittorio M. N. Passaro Received: 1 July 2016; Accepted: 27 August 2016; Published: 31 August 2016
Abstract: Electrostatic sensor arrays (ESAs) are promising in industrial applications related to charged particle monitoring. Sensitivity is a fundamental and commonly-used sensing characteristic of an ESA. However, the usually used spatial sensitivity, which is called static sensitivity here, is not proper for moving particles or capable of reflecting array signal processing algorithms integrated in an ESA. Besides, reports on ESAs for intermittent particles are scarce yet, especially lacking suitable array signal processing algorithms. To solve the problems, the dynamic sensitivity of ESA is proposed, and a hemisphere-shaped electrostatic sensors’ circular array (HSESCA) along with its application in intermittent particle monitoring are taken as an example. In detail, a sensing model of the HSESCA is built. On this basis, its array signals are analyzed; the dynamic sensitivity is thereupon defined by analyzing the processing of the array signals. Besides, a component extraction-based array signal processing algorithm for intermittent particles is proposed, and the corresponding dynamic sensitivity is analyzed quantitatively. Moreover, simulated and experimental results are discussed, which validate the accuracy of the models and the effectiveness of the relevant approaches. The proposed dynamic sensitivity of ESA, as well as the array signal processing algorithm are expected to provide references in modeling, designing and using ESAs. Keywords: electrostatic sensor array; dynamic sensitivity; hemisphere-shaped electrostatic sensor; circular array; array signal processing algorithm
1. Introduction Electrostatic monitoring systems (EMSs) are featured with the advantages of robustness and low cost [1,2], making them very promising in parameter monitoring of gas-solid flows [3–5], exhaust debris monitoring-based PHM of gas turbines [1,6,7], etc. Electrostatic sensors are key components of EMSs. Among them, hemisphere-shaped electrostatic sensors were proposed by us as a trade-off between intrusive and non-intrusive electrostatic sensors. They combine the advantages of relatively high sensitivity, easy installation, flexible layout, accuracy in theoretical modeling and cause very little disturbance to flows [8,9]. The sensing principle of an electrostatic sensor is electrostatic induction. It determines that even if a particle carries a constant charge, the corresponding induced charge on an electrostatic sensor probe will reduce sharply when the distance between the particle and the probe gets larger. As a result, a near particle with quite weak charge can generate similar signals as a far particle with great charge. That is to say, the charge quantity of a particle can hardly be accurately monitored by a single electrostatic sensor if the position of the particle is not provided. In view of the sensitivity, this means that most
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electrostatic sensors have the drawback of inhomogeneous and quite localized sensitivity; thus, only particles near the probe can be effectively detected [8,10]. In a word, as for the applications that need the accurate particle charge (e.g., particle size monitoring or gas-solid flow density monitoring), an EMS that contains a single electrostatic sensor is usually of poor monitoring accuracy. Moreover, a total failure of the whole system will occur if only the sensor breaks down. Therefore, in order to obtain better monitoring accuracy and reliability, EMSs composed of multiple electrostatic sensors have become the trend [5,11,12]. They are usually called electrostatic sensor arrays (ESAs), and the electrostatic sensors are called the sensor unit. Two aspects are of high concern in relevant research: the first is the hardware design and related sensing characteristics analysis; the second is the application and related array signal processing algorithms. Circular ESA is a kind of representative hardware structure, which is made up by placing some identical electrostatic sensors uniformly around a circular pipeline in one cross-section [12–18]. Xu et al. used arc-sharped electrostatic sensors to construct circular ESAs and used the finite element method to study the sensing characteristics of the sensor units. Some geometric and material influence factors on the sensing characteristics were also analyzed [18]. Thuku et al. studied circular ESAs composed of rod-shaped electrostatic sensors [5,19]. A sensing model of the sensor units was built, and a comparison between four and 16 sensor systems was made [17]. In addition, differently-sized circularplate-shaped and rectangular plate-shaped electrostatic sensors were modeled and analyzed [20]; they are also suitable for circular ESAs. However, existing works on the sensing characteristics were generally focused on individual electrostatic sensors, thus lacking descriptions and models for the sensing characteristics of a whole ESA. In addition, as a fundamental and the most commonly-used sensing characteristic, sensitivity should reflect the monitoring accuracy of an EMS directly. As for an ESA, this means that a proper sensitivity definition should build a direct relationship between the monitored particles and the monitoring parameters of the whole ESA. However, the usually used spatial sensitivity only builds a basic relationship between static charged particles and corresponding induced charge on a sensor probe [10,18,21]; thus, it is called static sensitivity here. In practice, particles to be monitored are always moving. Furthermore, as a three-dimensionally-defined parameter, static sensitivity is difficult to accurately model when real boundary conditions are considered [9]. More importantly, follow-up processing of the induced charge is not considered in the definition, such as charge-voltage transformation and array signal processing algorithms. In a word, in order to build a direct relationship between the monitored particles and the monitoring parameters of a whole ESA, thus reflecting its monitoring accuracy directly, a more practical sensitivity definition needs to be defined in a systemic perspective. In the aspect of application, a circular ESA is usually used to detect the particle distribution over the cross-section of a pipeline and further infer gas-solid flow parameters, such as particle density and flow regime. In these cases, the particles to be monitored are continuous in the time domain. That is to say, there are always numerous particles passing a cross-section simultaneously, thus forming an obvious profile of the solid-phase, which can be imaged by tomography-based methods [5,11,14]. ESAs with arc-shaped sensor units usually adopt array signal processing algorithms based on electrical capacitance tomography [11,12,16,22,23]. They are suitable for dense gas-solid flows. There are also reports on volume tomography using multi-circular ESAs with arc-shaped sensor units [24–26]. ESAs with rod-shaped sensor units usually adopt algorithms based on electrostatic tomography [5,14,18]. They are suitable for both dense and dilute gas-solid flows. However, because of the limited number of sensor units, the tomography-based algorithms are faced with tough ill-conditioned problems, which lead to poor image resolution [11,16]. Improvements can be made by increasing the unit number [17] and adopting some iterative regularization methods, filtering methods, error minimization protocols, etc., which will increase the computation time [11,12,16]. As a result, the tomography-based algorithms only indicate approximate areas where particles concentrate, but they cannot accurately confirm where discrete particles are located. Moreover, the algorithms are more suitable for relatively stable flows, because the monitoring accuracy can be improved by making a compromise on the computation time.
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contrast, particles to be monitored could be quite intermittent in some applications. That is to say, there are only one or just a few particles passing a cross-section simultaneously. One representative application exhausttodebris monitoring-based PHM of gas turbines In this In contrast, is particles be monitored could be quite intermittent in some[7,17–29]. applications. Thatcase, is tothe say, occurrences of one fault-related particles arepassing accidental and instantaneous. In otherOne words, first, the there are only or just a few particles a cross-section simultaneously. representative particles to beis monitored are quite intermittent. Second, a fast signal processing algorithm is application exhaust debris monitoring-based PHM of gas array turbines [7,17–29]. In this case, the needed to avoid missing the fast-passing particles. Besides, the size and charge quantity of the occurrences of fault-related particles are accidental and instantaneous. In other words, first, the particles, rather than the distribution, are concerned. A ameasurement technique was algorithm studied byis particles to be monitored are quite intermittent. Second, fast array signal processing Addabbo et al. to estimate the trajectory position, charge and velocity of a moving needed to avoid missing the fast-passing particles. Besides, the size and charge quantity of the charged particles, particle. It was based on a small array whose electrostatic technique sensors have rather than the distribution, are concerned. A measurement wasimproved studied bylow-frequency Addabbo et al. response [30,31]. However, relevant studies scarce As for a circular ESA, arraybased signal to estimate the trajectory position, charge and are velocity of ayet. moving charged particle. It was on processing algorithms remain to be designed for the intermittent particle monitoring. a small array whose electrostatic sensors have improved low-frequency response [30,31]. However, To solve theare problems above, dynamic sensitivity of ESA is proposed to describe relevant studies scarce yet. As forthe a circular ESA, array signal processing algorithms remain tothe be sensitivity of ESAs in a systemic perspective. An ESA called the hemisphere-shaped electrostatic designed for the intermittent particle monitoring. sensors’ circular (HSESCA) along with its application in intermittent particle monitoring are To solve thearray problems above, the dynamic sensitivity of ESA is proposed to describe the sensitivity taken as an detail, a sensing model thehemisphere-shaped HSESCA, as well as that of thesensors’ sensor units is of ESAs in aexample. systemicIn perspective. An ESA calledofthe electrostatic circular built in Section 2. On this basis, array signals of the HSESCA are analyzed, and the dynamic array (HSESCA) along with its application in intermittent particle monitoring are taken as an example. sensitivity ESA is thereupon defined in Section 3. A extraction-based array signal In detail, a of sensing model of the HSESCA, as well as that of component the sensor units is built in Section 2. On this processing algorithm for discrete particle monitoring is designed in Section 4. Numerical basis, array signals of the HSESCA are analyzed, and the dynamic sensitivity of ESA is thereupon simulations and experiments are done for validations array in Section The main results are for concluded defined in Section 3. A component extraction-based signal5.processing algorithm discrete in Sectionmonitoring 6. particle is designed in Section 4. Numerical simulations and experiments are done for validations in Section 5. The main results are concluded in Section 6. 2. Sensing Model of an HSESCA 2. Sensing Model of an HSESCA This section builds a quantitative relationship between a charged particle and the induced chargeThis of an HSESCA, providesrelationship a theoreticalbetween foundation for thisparticle paper. and the induced charge section buildswhich a quantitative a charged of an HSESCA, which provides a theoretical foundation for this paper. 2.1. Basic Structure of an HSESCA 2.1. Basic Structure of an HSESCA An HSESCA with eight sensor units is installed on a grounded pipeline, as shown in Figure 1. An HSESCA with eight sensor units ishemispherical installed on a probes, grounded pipeline, as shown in Figure 1. It is It is mainly composed of eight identical a multi-channel signal conditioner mainly composed eight identical hemispherical probes, a multi-channel signal conditioner and an and an array signalof analyzer. Compared to a “flat head” probe leaning inward toward the pipeline, array signal analyzer. Compared to a “flat head” probe leaning inward toward the pipeline, it is it is much easier to build a theoretical sensing model for a hemispherical probe, because it much only easier to abuild a theoretical sensing model a hemispherical probe, because it onlybe contains a simple contains simple hemispheric surface. In for addition, a hemispherical probe should more durable hemispheric surface. In addition, a hemispherical probe should more durablesurface than a “flat head” than a “flat head” probe under severe working conditions, as be a hemispheric is free of probe under severe working conditions, as a hemispheric surface is free of damageable edges. damageable edges.
Figure Figure1.1.Schematic Schematicofofaagrounded groundedpipeline-installed pipeline-installedHSESCA. HSESCA.
The hemispherical probes are uniformly installed in a cross-section around the pipeline. It is The hemispherical probes are uniformly installed in a cross-section around the pipeline. It is called called the observation cross-section. Once the charged particles pass, the induced charge will be the observation cross-section. Once the charged particles pass, the induced charge will be generated generated on each probe and then converted into voltage array signals immediately by the on each probe and then converted into voltage array signals immediately by the multi-channel multi-channel signal conditioner for post-processing. Every channel of the conditioner is designed
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as an identical proportional two-stage amplifier as in Figure 2 [9]. The induced charge is proportionally intotwo-stage voltage inamplifier the first as stage and then amplified in theis as anconditioner identicaltransformed proportional in Figure 2 negatively [9]. The induced signal for post-processing. Every channel of the conditioner is designed as an charge identical second stage. Therefore, theinto total function each channel is isrepresented by transformed a negative proportionally transformed in2 the first stage and then negatively amplified in the proportional two-stage amplifier asvoltage in Figure [9].ofThe induced charge proportionally amplification coefficient K whose unit is V/C. A hemispherical probe and its signal conditioner second stage. Therefore, function of each channel is represented by a the negative into voltage in the first stagethe and total then negatively amplified in the second stage. Therefore, total channel compose an independent sensor unit Aofhemispherical the HSESCA.probe The and arrayits analyzer is amplification coefficient whose unit is aV/C. signalunit conditioner function of each channel isKrepresented by negative amplification coefficient K signal whose is V/C. composed of a signal acquisition card andunit a computer. Some specially-designed array signal channel compose an and independent sensor of the HSESCA. The array signal analyzer A hemispherical probe its signal conditioner channel compose an independent sensor unit ofis processing algorithms usually integrated in the to calculate the aarray monitoring composed of a signal acquisition card a computer. Someacquisition specially-designed signal the HSESCA. The array are signal analyzer isand composed of acomputer signal card and computer. parameters (denoted as M) of the whole HSESCA. processing algorithms are usually integrated in the computer calculate thecomputer monitoring Some specially-designed array signal processing algorithms are usually to integrated in the to parameters as M) of the whole HSESCA. calculate the (denoted monitoring parameters (denoted as M) of the whole HSESCA.
Figure 2. Schematic of a proportional two-stage signal conditioner channel. Figure2.2.Schematic Schematicof ofaaproportional proportionaltwo-stage two-stagesignal signalconditioner conditionerchannel. channel. Figure
As the sensitivity characteristics of an electrostatic sensor are quite localized [8–10] and the radiusAsofthe thesensitivity probes is much smaller than distances sensor between between characteristics of anthe electrostatic arethem, quiteinteractions localized [8–10] and the the As the sensitivity characteristics of an electrostatic sensor are quite localized [8–10] and the radius probes can be ignored. Thus, a sensor unit is firstly modeled to lay a foundation for the radius of the probes is much smaller than the distances between them, interactions between the of the probes is much smaller than the distances between them, interactions between the probes can be whole probesHSESCA. can be ignored. Thus, a sensor unit is firstly modeled to lay a foundation for the ignored. Thus, a sensor unit is firstly modeled to lay a foundation for the whole HSESCA. whole HSESCA. 2.2. Theoretical Modeling of a Hemisphere-Shaped Electrostatic Sensor Unit 2.2. Theoretical Modeling of a Hemisphere-Shaped Electrostatic Sensor Unit 2.2. Theoretical Hemisphere-Shaped Electrostatic Sensorcoordinate Unit As shown Modeling in Figureof3,aone sensor unit is kept. A Descartes system is built with the As shown in Figure 3, one sensor unit is kept. A Descartes coordinate system is built with the centerAs of shown the probe’s bottom face set as the origin. The axial direction of the pipeline that of the in Figure 3, one unitorigin. is kept. A axial Descartes coordinate system isand built with the center of the probe’s bottom facesensor set as the The direction of the pipeline and that of the probe are setprobe’s as the bottom x-axis and the as z-axis, respectively. Then, the y-axis is determined byofthe center of the face set the origin. The axial direction of the pipeline and that the probe are set as the x-axis and the z-axis, respectively. Then, the y-axis is determined by the right-hand right-hand rule automatically. Accordingly, a point in the pipeline isthe denoted as P(x, y, z). probe are set as the x-axis and the z-axis, respectively. Then, y-axis is determined by the rule automatically. Accordingly, a point in the pipeline is denoted as P(x, y, z). right-hand rule automatically. Accordingly, a point in the pipeline is denoted as P(x, y, z).
Figure 3. 3. Schematic Schematic of of aa grounded grounded pipeline-installed pipeline-installed sensor Figure sensor unit unit of of the the HSESCA. HSESCA.
Figure 3. Schematic of a grounded pipeline-installed sensor unit of the HSESCA.
19 s), states are are reached reached instantaneously instantaneously (10 (10−−19 Because electrostatic equilibrium states s), the interaction −19 the in by between probe and charged particles the pipeline can be described a Because electrostatic equilibrium states are reached instantaneously (10 pure s), theelectrostatic interaction is determined by Poisson equation and boundary conditions as: field [18,21]. Itprobe is uniquely uniquely determined bythe thein Poisson equation and Dirichlet boundary conditions as: between theIt and charged particles the pipeline can beDirichlet described by a pure electrostatic field [18,21]. It is uniquely determined by the Poisson equation and Dirichlet boundary conditions as: 2 ∈ Γ t Pϕt ( P0,) P=0,ΓP 2 ρt (Pt )P 2 P 0, P Γ 2 ϕ P = const t , P 2 ( ) ( ) ∇ ϕt( P) = (1) P−= ε , s.t. , s. t. ttt P const t , P Γ∈1 Γ1 (1) t P lim ϕt ( P) = 0 t 2 , s.t. lim t PP → t P = (1) P∞const 0 t , P Γ1 P t limΓ2t isPthe 0inner wall of the pipeline. ρt (P) is the where Γ1 is the hemispherical surface of the probe P and where Γ 1 is the hemispherical surface of the probe and Γ2 is the inner wall of the pipeline. ρt(P) is the volume charge density in the pipeline at time t, and ϕt (P) is the corresponding potential distribution. volume in the pipeline at time t, andand φt(P) potential distribution. where Γcharge 1 is thedensity hemispherical surface of the probe Γ2 isis the the corresponding inner wall of the pipeline. ρt(P) is the volume charge density in the pipeline at time t, and φt(P) is the corresponding potential distribution.
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Sensors 2016, 16, 1403 of 23 Besides, const(t) is a constant function of t, describing the equipotential surface of the probe. ε is5the 2 permittivity of free space, and is the Laplace operator. On account of the pipeline being much bigger than the probe, the electrostatic field on the Besides, const(t) is a constant function of t, describing the equipotential surface of the probe. ε is the inner wall is simplified as that on2 one infinite plane [2,6,17]. In this case, when a charged particle is permittivity of free space, and ∇ is the Laplace operator. simplified as a point charge q [8,10], φt(P) is firstly solved using the Green function and the method On account of the pipeline being much bigger than the probe, the electrostatic field on the inner of image charges. Then, the sensing model at P(x, y, z) is obtained according to the relationship wall is simplified as that on one infinite plane [2,6,17]. In this case, when a charged particle is simplified between the induced charge and the potential distribution on a conductor surface [8,9]. That is: as a point charge q [8,10], ϕt (P) is firstly solved using the Green function and the method of image 3 2π y, z) a is obtained according to therelationship between the qa at qzP(x, charges. Then, the sensing model Q x, y , z = d r 2 b2 2 xy cos 2 yr sin 2 rdr 0 on a conductor surface [8,9]. That is: induced charge and the potential 2 0 b distribution 3 4 2 (2) 3 qa z 2πR a R2 a 2a xr cos yr sin 2 3 −2 + qa 3 qz d2π r a+ 2 rdr 2 Q ( x, y, z) = − 2bb− 2π − 2yrsinθ rdr 0 b2 0 0dθ 0h r + b − 2xycosθ i− 32 (2) R R 3 4 2 a qa z 2π a −2a ( xrcosθ +yrsinθ ) rdr + 2πb dθ 0 r2 + 3 0 b2 where Q is the total induced charge on the probe, a is the radius of the probe and b = x 2 y 2 z 2 p iswhere the distance the point charge and the origin. Q is thebetween total induced charge on the probe, a is the radius of the probe and b = x2 + y2 + z2 is the distance between the point charge and the origin. 2.3. Theoretical Modeling of an HSESCA 2.3. Theoretical Modeling of an HSESCA In order to build a sensing model for all of the sensor units in the same coordinate system, order to build sensing model all ofEquation the sensor(2) units in the sameinto: coordinate system, firstly, firstly,Inaccording to theasymmetry of thefor probe, is transformed according to the symmetry of the probe, Equation (2) is transformed into: 3 a qa qb cos 2 Q x, y , z = d r 2 b 2 2br sin sin 2 rdr − 23 bqa qbcosβ 2 R 02π R0 a 2 3 2 Q ( x, y, z) = − rdr (3) 2 b − 2brsinβsinθ 2 b − 0a dθ a04 r 2 + 2 qa 3 cos 2π a r sin sin 2 3 −rdr (3) R R 3 2 + d r + 4 2 2π a qa2 cosβ 0 dθ0 rb22 + a2 − 2ab rsinβsinθ rdr + 2 b2πb 2 b 0 0 b
= arccos( z /) bis) the is included the included between the linethe from the pointtocharge to the where where ββ = arccos(z/b angleangle between the line from point charge the origin and origin and of the probe. Then, a new coordinate Descartes coordinate system is built by translating the axis ofthe theaxis probe. Then, a new Descartes system is built by translating the originalthe one original one 2) (see 2) to of the cross-section. observation cross-section. Meanwhile, theare sensor units (see Figure to Figure the center ofthe thecenter observation Meanwhile, the sensor units numbered are numbered anticlockwise, withof coordinates of the i-th probe as (0, yi, zof i) and those of the anticlockwise, with coordinates the i-th probe denoted as (0,denoted yi , zi ) and those the point charge point charge denoted asthe P(x,new y, z)coordinate in the newsystem; coordinate system; shown denoted as P(x, y, z) in as shown in as Figure 4. in Figure 4.
Figure βi in the new Descartes coordinate system. Figure4.4.Schematic Schematicofofbiband i and βi in the new Descartes coordinate system.
Thereupon, the sensing model of the i-th sensor unit is derived from Equation (3) as: Thereupon, the sensing model of the i-th sensor unit is derived from Equation (3) as: − 3 Ra 2 dθ 0 r2 + bi 2 − 2bi rsinβ i sinθ rdr i 3 −2 R 2π R a 2 a4 3 2a2 i rsinβ i sinθ i + qa cosβ rdr 2 b 0 dθ 0 r + 2 − qa
Qi ( x, y, z) = − b −
qbi cosβ i R 2π 2π 0
2πbi
bi
i
(4)
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where bi is the distance from the charged particle to the i-th probe and βi is the included angle between the point charge and the axis of the i-th probe. They are determined by geometrical relationships: q
bi =
x 2 + ( y − y i )2 + ( z − z i )2
(5)
h i β i = arccos (yi 2 + zi 2 − yyi − zzi )/lbi
(6)
p
where l = yi 2 + zi 2 is the distance between the origin O and the bottom face of a probe. Further, the sensing model of the HSESCA is obtained by making a superposition of sensing models of all of the sensor units. That is: Q A ( x, y, z) = ∑ Qi ( x, y, z) = −∑ i
i
+ ∑ qa i
3 cosβ
2πbi
2
qa bi i
−∑ i
R 2π 0
dθ
qbi cosβ i R 2π 2π 0
Ra 0
r2 +
dθ
a4 bi 2
Ra
−
0
r2 + bi 2 − 2bi rsinβ i sinθ
2a2 i rsinβ i sinθ bi
− 23
− 3
2
rdr (7)
rdr
In addition, an FEM-based calibration method was proposed as a supplement to consider the actual boundary conditions [9]. It is used to improve the accuracy of the sensing models when a charged particle is in the observation cross-section. The main steps are as follows: First, an FEM model of a grounded pipeline-installed probe is built. The model provides simulated induced charge with high fidelity. Then, the relative error between the simulated and the theoretical induced charge is analyzed. On this basis, a calibration item calculated by using fitting methods is added to eliminate the relative error. When the inner radius of the pipeline is 200 mm and the button face of a probe is 2 mm apart away from the inner wall, Equation (4) is calibrated as: ( 0 Qi,x =0 ( y, z )
=
Qi,x=0 (y, z) ( p1 bi p2 + p3 ) Qi,x=0 (y, z)
, if bi ≥ D , if bi < D
(8)
where D = −0.0188 βi + 0.0444 is the calibration boundary that is determined according to the variation trend of the relative error [10]. In the area of bi < D, the relative error is negligible; thus, the sensing model is only calibrated where bi ≥ D. The calibration parameters are obtained using fitting methods; they are: 2 2 p1 = −5.7311 × 10−8 e8.7639βi − 6.103e0.5724βi 2 2 (9) p2 = −43.9996e0.1261βi + 45.9113e0.113βi − 2 2 7.0643×10 β i 4.4059β2i − 4 p3 = 1.0479e + 1.2218 × 10 e 0 It is obvious that Equation (7) is calibrated as Q0A,x=0 (y, z) = ∑ Qi,x =0 ( y, z ). i
3. Definition of the Dynamic Sensitivity of ESA 3.1. Definition of the Static Sensitivity of ESA In order to make a comparison with the dynamic sensitivity of ESA, the static sensitivity of ESA is defined here. The static sensitivity of an electrostatic sensor is defined as the absolute induced charge on the probe generated by a unit charge [7,8,21]. Analogously, the static sensitivity of ESA is defined as the absolute induced charge on all of the probes of an ESA generated by a unit charge. That is: S A ( x, y, z) = −
Q A ( x, y, z) q
(10)
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The minus indicates that the induced charge and the point charge q are of opposite signs. As for an HSESCA, its static sensitivity model is derived from Equations (9) and (10): SA ( x, y, z) = ∑ i
a bi
i + ∑ bi cosβ 2π
R 2π
i
R 2π 3 − ∑ a cosβ2 i 0 2πb i i
dθ
0
dθ
Ra 0
Ra
r2
0
+
r2 + bi 2 − 2bi rsinβ i sinθ
a4 bi 2
−
2a2 i rsinβ i sinθ bi
− 32
− 3
2
rdr (11)
rdr
When actual boundary conditions are considered, the model in the observation cross-section can also be calibrated in a similar way as Equation (8), that is S0A,x=0 (y, z) = − Q0A,x=0 (y, z) /q. 3.2. Theoretical Array Signals of an HSESCA Array signal processing algorithms are included in the definition of the dynamic sensitivity of ESA. In order to find effective array signal processing algorithms for an HSESCA, the characteristics of its array signal shave to be analyzed. It is assumed that a charged particle moves along the pipeline’s axial direction at a constant velocity [10,32]. In this case, the x-coordinates of the particle are denoted with velocity v and time t, while the y-coordinates and z-coordinates are regarded as constants. In this way, induced charge on the i-th probe is expressed by Qi (x0 + vt, y, z), where x0 is the initial x-coordinate. After that, the induced charge is transformed and amplified into voltage according to the amplification coefficient K of the signal conditioner (see Figure 4), thus obtaining the out-put signal of the i-th sensor unit. That is: ui (t) = KQi ( x0 + vt, y, z)
(12)
Then, by combining Equations (4) and (12), one can get: ui ( t ) = −
− 3 Ra 2 rdr dθ 0 r2 + bi 2 − 2bi rsinβ i sinθ 3 − R R 3 2 2 2π a 2a i rsinβ i sinθ a4 2 i + qKa cosβ rdr 2 b 0 dθ 0 r + 2 −
qKa bi
−
qKbi cosβ i R 2π 2π 0
2πbi
q
bi
(13)
i
where bi = ( x0 + vt)2 + (y − yi )2 + (z − zi )2 . In order to provide a visualized view of the array signals, here, we set K = −1, q = 1C, and the time when the particle reaches the observation cross-section is set as the zero time (i.e., x0 = 0). The radius of the hemispherical probes is set to 12 mm, and the motion path is set to y = 100 mm and z = 70 mm (see Figure 3). Besides, the velocities of the charged particle are set to 1 m/s, 2 m/s and 3 m/s, respectively. Then, the array signals of the HSESCA are calculated by using Equation (13), as shown in Figure 5. This shows that all of the signal peaks umax,i appear when the charged particle reaches the observation cross-section; when q is set as a constant, the i-th peak is just determined by the relative position between the motion path and the i-th sensor unit, but has nothing to do with the particle’s velocity. Moreover, it is obvious that the peaks will change if the position of the charged particle changes. In a word, different combinations of peaks of the array signals indicate different position information of the charged particle in the observation cross-section. In order to build a quantitative and direct relationship between a charged particle and the out-put signal peaks of a single electrostatic sensor, the dynamic sensitivity of the electrostatic sensor was proposed by us. It is defined as the absolute value of the out-put signal peak of an electrostatic sensor when a unit point charge passes [9]. As for the i-th sensor unit, the relationship is built by its dynamic sensitivity model as: 0 KQi,x umax,i =0 ( y, z ) SD,i (y, z) = = (14) q q 0 where Qi,x =0 ( y, z ) is shown as Equation (8).
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It is worth noting that in many applications, the monitoring parameters are reflected by the charge quantity of the monitored particles directly or indirectly, such as the particle size, concentration, flow rate, etc. [4,33]. Therefore, it is significant to ensure that the charge quantity of any particle can be accurately monitored no matter where it crosses the observation cross-section. Accordingly, a reasonable way of processing the array signals is as follows: first, obtaining the position information of the monitored particles from the array signals; then, weighting the signal components induced by particles in the less sensitive area according to the position information. In this way, the charge quantity of 16, any particle can be effectively reflected. Sensors 2016, 1403 8 of 22
Figure5.5.(a–h) (a–h)Theoretical Theoreticalarray arraysignals signalsof ofthe theHSESCA HSESCAfrom fromNo. No.1–No. 1–No.88sensor sensorunits. units. Figure
In orderand to build a quantitative and direct relationship 3.3. Definition Interpretation of the Dynamic Sensitivity of ESA between a charged particle and the out-put signal peaks of a single electrostatic sensor, the dynamic sensitivity of the electrostatic Thewas aimproposed of proposing theItdynamic sensitivity of ESA isvalue to build a direct relationship between sensor by us. is defined as the absolute of the out-put signal peak of an moving charged particles thepoint monitoring parameters offor an the ESA, thus reflecting its monitoring electrostatic sensor when and a unit charge passes [9]. As i-th sensor unit, the relationship accuracy “Dynamic” heremodel has two is built bydirectly. its dynamic sensitivity as:implications: the first is making a distinction from static sensitivity, that is dynamic sensitivity is proposed for moving charged particles; the second is that the uESA KQi, x 0 ( y , z ) according to different array signal ,i is changeable specific expression of the dynamic sensitivity SD ,i y , z =of max (14) q q processing algorithms. More detailed interpretations are provided by taking intermittent particle monitoring, for example, as follows. where Qi, x 0 ( y , z ) is shown as Equation (8). In some applications, the particles to be monitored are intermittent. One representative application It is worth noting that in many applications, the monitoring parameters are reflected by the is exhaust debris monitoring-based PHM of gas turbines. When faults (e.g., fatigue or carbon charge quantity of the monitored particles directly or indirectly, such as the particle size, deposition) occur on gas path components of gas turbines, some fault-related particles will be concentration, flow rate, etc. [4,33]. Therefore, it is significant to ensure that the charge quantity of produced and charged. Thus, the condition information of the gas path components can be obtained any particle can be accurately monitored no matter where it crosses the observation cross-section. by monitoring the particles [1,6,7,28]. In general, the fault-related particles are intermittent. Moreover, Accordingly, a reasonable way of processing the array signals is as follows: first, obtaining the it is considered that larger particles carry greater charge, which indicates more serious faults [1,7]. position information of the monitored particles from the array signals; then, weighting the signal Therefore, the charge quantity of any fault-related particle should be accurately monitored. components induced by particles in the less sensitive area according to the position information. In As for a single electrostatic sensor, for example the i-th sensor unit of the HSESCA, its dynamic this way, the charge quantity of any particle can be effectively reflected. sensitivity model builds a relationship between moving charged particles and its out-put voltage signals, as Equation (14). This is expressed by Figure 6. 3.3. Definition and Interpretation of the Dynamic Sensitivity of ESA The aim of proposing the dynamic sensitivity of ESA is to build a direct relationship between moving charged particles and the monitoring parameters of an ESA, thus reflecting its monitoring accuracy directly. “Dynamic” here has two implications: the first is making a distinction from static sensitivity, that is dynamic sensitivity is proposed for moving charged particles; the second is that the specific expression of the dynamic sensitivity of ESA is changeable according to different array signal processing algorithms. More detailed interpretations are provided by taking intermittent particle monitoring, for example, as follows. In some applications, the particles to be monitored are intermittent. One representative
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faults [1,7]. Therefore, the charge quantity of any fault-related particle should be accurately faults [1,7]. Therefore, the charge quantity of any fault-related particle should be accurately monitored. monitored. As for a single electrostatic sensor, for example the i-th sensor unit of the HSESCA, its dynamic As formodel a singlebuilds electrostatic sensor, for example the i-th sensor particles unit of the HSESCA, its dynamic sensitivity a relationship between moving charged and its out-put voltage Sensors 2016, 16, 1403 9 of 23 sensitivity model builds a relationship between moving charged particles and its out-put voltage signals, as Equation (14). This is expressed by Figure 6. signals, as Equation (14). This is expressed by Figure 6.
qS D,i ( y, z ) qS D,i ( y, z )
Figure Figure 6. 6. Signal Signal flow flow diagram diagram of of the the i-th i-th sensor sensor unit unit of of the the HSESCA. HSESCA. Figure 6. Signal flow diagram of the i-th sensor unit of the HSESCA.
This means that a charged particle contains two kinds of information, charge quantity q and This means that a charged contains two kinds of information, charge quantity q and charged particle information, to the unit’s dynamic sensitivity position (y, z). They codetermine the signal peak umax,i according position (y, z). They codetermine the signal peak u according to the unit’s dynamic sensitivity max,i according to (y,(y,z).z), thatcodetermine signal peak umax,i is umax,i = qSthe D,i(y, z). However, the relationship is irreversible in practical model SD,i model SSD,i (y, z), that is = qSD,i (y, z). z). However, However, the the relationship relationship is irreversible irreversible in practical D,i(y, is uumax,i max,i = practical D,i(y, applications. This is because the position information is difficult to is obtain by using a single applications. This is is because the the position information is difficult to obtaintobyobtain using aby single electrostatic applications. This because position information is difficult using a single q electrostatic sensor; thus, the value of SD,i(y, z) is not determined. As a result, the charge quantity sensor; thus, the value of S (y, z) is not determined. As a result, the charge quantity q cannot beq D,i(y, z) is not determined. As a result, the charge quantity electrostatic sensor; thus, the value of S D,i cannot be calculated backward for the lack of position information. This is the basic reason for the calculated for the lack of This is the basic reason for the low monitoring cannot be backward calculated backward forposition the lackinformation. of position low monitoring accuracy of a single electrostatic sensor. information. This is the basic reason for the accuracy of a single electrostatic sensor. low monitoring accuracy of a single electrostatic sensor. It has been mentioned that the array signals of an HSESCA contain the position information of It has been mentioned that the array signals of an contain the position information of an HSESCA HSESCA positionaccuracy a monitored particle (see Section 3.2), which can be used to improve the monitoring of the a monitored particle (see Section 3.2), which can be used to improve the monitoring accuracy of the HSESCA. This is expressed by Figure 7. HSESCA. This is expressed expressed by by Figure Figure 7. 7.
qS D,1 ( y, z ) qS D,1 ( y, z )
qS D,2 ( y, z ) qS D,2 ( y, z )
qS D,3 ( y, z ) qS D,3 ( y, z )
qS D,4 ( y, z ) qS D,4 ( y, z )
qS D,5 ( y, z ) qS D,5 ( y, z )
qS D,6 ( y, z ) qS D,6 ( y, z )
qS DA ( y, z ) qS DA ( y, z )
( y, z ) ( y, z )
Figure 7. Signal flow diagram of the HSESCA. Figure 7. 7. Signal Signal flow flow diagram diagram of of the the HSESCA. HSESCA. Figure
This means that a charged particle contains two kinds of information, charge quantity q and This means that a charged particle contains two kinds of information, charge quantity q and max,i of each sensor unit according to its dynamic position z). They the signal peak utwo This(y, means thatcodetermine a charged particle contains kinds of information, charge quantity q and max,i of each sensor unit according to its dynamic position (y, z). They codetermine the signal peak u (y, z). Then,the the peaks areu processed by a certain array signal processing sensitivity SD,i position (y, model z). They codetermine signal peak max,i of each sensor unit according to its dynamic D,i(y, z). Then, the peaks are processed by a certain array signal processing sensitivity model S algorithm to calculate monitoring M.byIn this process, the processing estimatedalgorithm position sensitivity model SD,i (y, z).the Then, the peaks parameter are processed a certain array signal algorithm to(y’,calculate the monitoring parameter M.and In used. this Therefore, process, the estimated position D,i(y, z) are information z’) of the particle is usually obtained valves of S to calculate the monitoring parameter M. In this process, the estimated position information (y’, z’) of D,i(y, z) are information (y’, z’) of the particle is usually obtained and used. Therefore, valves of S determined the position making valves it possible the charge quantity q the particle isby usually obtainedinformation, and used. Therefore, of S to (y, calculate z) are determined by the position determined by the position information, making it possibleD,ito calculate the charge quantity q information, making it possible to calculate the charge quantity q backward. In fact, the monitoring parameters of many applications are just the charge quantity or some derivative values of it. As a
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result, by using an HSESCA and corresponding array signal processing algorithms, the monitoring accuracy can be improved. In order to provide a unified and convenient expression for different array signal processing algorithms, dynamic operator FD is proposed to denote the array signal processing algorithms. It builds the relationship between the array signals and monitoring parameters of an ESA (see Figure 7). Further, the dynamic sensitivity of ESA is defined in the observation cross-section as the absolute value of a monitoring parameter when a unit charge passes. As for intermittent particle monitoring, the dynamic sensitivity model of an HSESCA is expressed as: M FD [Umax (y, z)] FD [qSD (y, z)] = | FD [SD (y, z)]| SDA (y, z) = = = q q q
(15)
where U max (y, z) is the vector of the signal peaks and SD (y, z) is the vector of dynamic sensitivity values of the sensor units. The q is reducible because FD has to be designed as a linear operator of q. It is seen from Equation (15) that the essence of the dynamic sensitivity of ESA is a recombination of the dynamic sensitivity of the sensor units according to a dynamic operator, which builds a direct relationship between moving charged particles and the system monitor values of an ESA. In other words, the dynamic sensitivity of ESA reflects the monitoring accuracy of an ESA directly by taking array signal processing algorithms into consideration. The concept of dynamic sensitivity has been used by Zhou et al. [34], but the physical meaning is quite different. 4. A Component Extraction-Based Array Signal Processing Algorithm for Intermittent Particles A proper array signal processing algorithm is significant to ensuring the monitoring accuracy of an ESA. As for intermittent particle monitoring (e.g., exhaust debris monitoring-based PHM of gas turbines), it has been mentioned that the accurate charge quantity of any monitored particle is desired; thus, the position information of the particle should be used. In addition, the demand for real-time monitoring should be met to avoid missing momentary faults; thus, the corresponding array signal processing algorithms have to be fast enough. To meet the conditions above, a component extraction-based array signal processing algorithm is designed. It is based on a simple idea that a monitored particle is located near the sensor units that produce larger signal peaks. According to this idea, a set of common components is extracted from the peaks of the array signals. The components are considered to be generated by a set of imaginary point charges. They have fixed positions, but their imaginary charge quantities vary with the position of the monitored particle. In this way, the position information of the monitored particle can be used according to different charge quantities of the imaginary point charges. It is worth noting that the accurate position of a particle is not needed in the algorithm, but it is made use of by introducing a component extraction-based method. As a result, the algorithm only contains some simple steps, which are convenient for computer processing. More details are provided as follows. As shown in Figure 8, three main steps and one pre-step are contained in the component extraction-based array signal processing algorithm. The condition in Figure 4 is taken as an example below, that is to say, the HSESCA contains eight sensor units, and a charged particle moves along a motion path of y = 100 mm and z = 70 mm. The first step is re-sorting. When a charged particle passes the observation cross-section, the corresponding signal peaks of the eight sensor units are recorded as a vector U max . Then, U max is re-sorted into U r incrementally according to the absolute values of the signal peaks. That is to say, the i-th absolute smallest peak is denoted as uri ; thus, the new vector is U r {ur1 , ur2 , ur3 , ur4 , ur5 , ur6 , ur7 , ur8 }. For example, the No. 2 probe is the nearest one to the point charge, while the No. 6 probe is the farthest one to the point charge (see Figure 3); thus, according to the fact that nearer probes produce larger signal peaks, one will have ur1 = umax,6 , ur8 = umax,2 .
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W C
Figure 8. Flow diagram of of the component arraysignal signal processing algorithm. Figure 8. Flow diagram the componentextraction-based extraction-based array processing algorithm.
The The second stepstep is component clear that thataamonitored monitored particle is located second is componentextraction. extraction. It It is is clear particle is located nearnear the the sensor units thatthat produce larger if aasignal signalcomponent component is only contained in one sensor units produce largersignal signalpeaks. peaks. Thus, Thus, if is only contained in one signal peak, its value implies how close the particle is to the corresponding sensor probe. Analogously, signal peak, its value implies how close the particle is to the corresponding sensor probe. if a signal component contained in is every signal peak, its value implies howits close the particle to theclose Analogously, if a signaliscomponent contained in every signal peak, value impliesishow central point. Accordingly, a set of common signal components is extracted from U by using Equation r the particle is to the central point. Accordingly, a set of common signal components is extracted (16). In detail, the absolute smallest signal peak u is firstly denoted as c ; it is a common signal as c1; r1 1 from Ur by using Equation (16). In detail, the absolute smallest signal peak ur1 is firstly denoted component contained in every signal peak. Then, the second absolute smallest peak ur2 is denoted as it is a common signal component contained in every signal peak. Then, the second absolute smallest the sum of c1 and c2 . It is obvious that c2 is a common signal component contained in every signal peak ur2 is denoted as the sum of c1 and c2. It is obvious that c2 is a common signal component peak, except ur1 , and so on; a vector of eight common signal components is extracted from U r , that is contained except ur1, and so on; a vector of eight common signal components C{c1 ,c2 ,inc3 every , c4 , c5 , signal c6 , c7 , c8peak, }. is extracted from Ur, that is C{c 1,c2, c3, c4, c5, c6, c7, c8}.
ur1 = c1 ur 1 c1 u u c c r2 = c1 + c2 1 u2 = c + c2 + c3 r2 c 2 r3 c 3 1 ur 3 c1 ur4c = cc1 + cc42 + c3 + c4 ur 4 c 1 2 3 u cur5= c3c+ c4 + c5 c 2 c1 + c 3 c2 c+4 1 5 r5 u = c + c + c +cc54 +cc6 5 + c6 u c c c r6 2 3 1 r6 1 2 3 4 uur 7r7=c 1c c4c+ c5c + c6c 7+ c7 c 2 c2 + c 3 c3 c+4 1+ 5 6 u c c c c c c c 8c8 u r8r 8= c11+ c22 + 33 + c44 + c55 + c6 6 +c 7c7+
(16)
(16)
The The third stepstep is weighting ofall, all,the theextracted extracted signal components third is weightingand andsummation. summation. First First of signal components are are considered to generated be generated setofofimaginary imaginary point based on on the the symmetry of of considered to be byby a aset pointcharges. charges.InIndetail, detail, based symmetry the circular array and the idea that a charged particle is located near the sensor units that produce the circular array and the idea that a charged particle is located near the sensor units that produce larger signal peaks, imaginarypoint pointcharge charge qq11 located located in point is firstly assumed to to inthe thecentral central point is firstly assumed larger signal peaks, an an imaginary generate c1 . Then, because c2 is contained in every signal peak, except that of the No. 6 sensor unit, an generate c1. Then, because c2 is contained in every signal peak, except that of the No. 6 sensor unit, imaginary point charge q is located in the connection line between the origin, and the No. 2 probe an imaginary point charge 2q2 is located in the connection line between the origin, and the No. 2 is assumed to generate c2 . Analogously, as c3 is produced by every sensor unit except the No. 5 probe is assumed to generate c2. Analogously, as c3 is produced by every sensor unit except the No. 5 and No. 6 sensor units, q3 located in the bisector of the No. 1 and the No. 2 probes is assumed to 3 located in the bisector of the No. 1 and the No. 2 probes is assumed to and generate No. 6 sensor c3 , andunits, so on;qeight imaginary point charges are decomposed from the charged particle q, as so 9. on;Among eight them, imaginary point charges are decomposed from the2charged particle q, generate c3,inand shown Figure the point charge q8 should be quite close to the No. probe, because quite of close to the No.point 2 probe, as shown in Figure Among them, point charge q8 should its relevant signal9.component is onlythe produced by that probe. The be positions the imaginary because its are relevant signal component produced that probe. Thetheir positions of the charges considered to be fixed due toistheonly symmetry of theby HSESCA. However, imaginary imaginary point charges are considered to be fixed due to the symmetry of the HSESCA. However, their imaginary charge quantities, which are determined by the values of the extracted components, vary with the position of the monitored particle. In other words, the charge quantities of the imaginary point charges imply the position information of the monitored particle.
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charge quantities, which are determined by the values of the extracted components, vary with the position of the monitored particle. In other words, the charge quantities of the imaginary point charges Sensors 2016,the 16, position 1403 12 of 22 imply information of the monitored particle.
Figure 9. 9. The original particleqqand anditsitsimaginary imaginary point charges. Figure The originalcharged charged particle point charges.
Next, thethecharge quantitiesof of imaginary point charges are calculated, can be Next, charge quantities thethe imaginary point charges are calculated, which can bewhich regarded regarded as a process of weighting the components extracted components the position information. as a process of weighting the extracted according to according the positiontoinformation. According According to the dynamic sensitivity model of the sensor units as Equation (14), the i-th imaginary to the dynamic sensitivity model of the sensor units as Equation (14), the i-th imaginary point charge /sithe , where si issensitivity the dynamic of unit the at No. sensor of unit at point charge is as expressed qi = sci iis is expressed qi = ci /si , as where dynamic of thesensitivity No. 2 sensor the2position qi . By recording: the position of qi. By recording: wi = 1/si
wi = 1/si
(17)
one will have qi = wi ci , where wi is just the weight coefficient of ci . = wmonitoring ici, where w i is just the coefficient of ci.up the imaginary point charges: one will Finally, have qithe parameter M weight is obtained by summing
(17)
Finally, the monitoring parameter M is obtained by summing up the imaginary point charges: M=
∑ qi = W · C
i q W C M i i
(18)
(18)
where W is the vector of the weight coefficients and C is the vector of the extracted signal components. where W q is the vector of thelines weight andcomponents C is the could vectorbeof thebut extracted When is in some symmetric of thecoefficients HSESCA, some zero, it does notsignal affect the computing components. When q isprocess. in some symmetric lines of the HSESCA, some components could be zero, W is determined the pre-stepprocess. (see Figure 8). Firstly, according to the estimated positions of the but it does not affect theincomputing imaginary point charges, an initial value each weight coefficient is set using (17). Then, of W is determined in the pre-step (seeofFigure 8). Firstly, according to theEquation estimated positions the initial values are optimized by numerical simulations to make M and q as close as possible in the (17). the imaginary point charges, an initial value of each weight coefficient is set using Equation whole observation cross-section. In this study, W was finally determined as {238, 232, 208, 122, 119, Then, the initial values are optimized by numerical simulations to make M and q as close as 98, 31, 0.9} when K = −1. As for a certain HSESCA, the pre-step needs to be done only once, then the possible in the whole observation cross-section. In this study, W was finally determined as {238, 232, weight coefficients are regarded as a priori values in calculating M. 208, 122,According 119, 98, 31, 0.9} when K = −1. As for a certain HSESCA, the pre-step needs to be done only to the definition of the dynamic sensitivity of ESA, the dynamic sensitivity in once, then the weight are regarded asarray a priori values in calculating accordance with thecoefficients component extraction-based signal processing algorithmM. is modeled as:
According to the definition of the dynamic of ESA, the dynamic sensitivity in sensitivity M W · C accordance with the component extraction-based = signal processing algorithm is modeled SDA (y, z) = array (19) as: q q M W C S DA of y , the z HSESCA at different positions in the observation (19) This reflects the monitoring accuracy q q cross-section after adopting the algorithm.
This reflects the monitoring accuracy of the HSESCA at different positions in the observation cross-section after adopting the algorithm. It is seen from the steps that the accurate position of the monitored particle was not obtained. However, the position information was made use of by using the component extraction-based method. In addition, even accurate positions of the imaginary point charges were not necessary. As a result, the proposed array signal processing algorithm only contains some simple steps, making it
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It is seen from the steps that the accurate position of the monitored particle was not obtained. SensorsHowever, 2016, 16, 1403 13 of 22 the position information was made use of by using the component extraction-based method.
In addition, even accurate positions of the imaginary point charges were not necessary. As a result, the
5. Numerical Experiment proposedSimulation array signal and processing algorithm only contains some simple steps, making it promising in applications that need fast processing of the array signals.
5.1. Simulated Results and Discussion
5. Numerical Simulation and Experiment
5.1.1. Simulated Dynamic Sensitivity of the Sensor Units 5.1. Simulated Results and Discussion
As mentioned above, an HSESCA with eight sensor units is installed on a grounded pipeline. 5.1.1. Simulated Dynamic Sensitivity of the Sensor Units The pipeline has an inner radius of 200 mm; the hemispherical probes have a radius of 12 mm with As mentioned above, an HSESCA withwall eightof sensor is installed onsake a grounded pipeline.the their button faces 2 mm far from the inner the units pipeline. For the of simplicity, The pipeline has an inner radius of 200 mm; the hemispherical probes have a radius of 12 mm with their the amplification coefficient of the signal conditioner is set to K = −1. Under these conditions, button faces 2 mm the units inner is wall of the pipeline. For the sake of (14) simplicity, amplification dynamic sensitivity of far thefrom sensor calculated by using Equation at the the grid points shown coefficient of the signal conditioner is set to K = − 1. Under these conditions, the dynamic sensitivity of in Figure 10. It is seen that the grid points are representative, as they cover almost the whole the sensor units is calculated by using Equation (14) at the grid points shown in Figure 10. It is seen observation cross-section. that the grid points are representative, as they cover almost the whole observation cross-section.
Figure Grid points theobservation observation cross-section. Figure 10. 10. Grid points ininthe cross-section.
The simulated results shown thesurface surfacediagrams diagrams in Figure that thethe sensor The simulated results are are shown byby the Figure11. 11.ItItisisseen seen that sensor the same dynamic sensitivity becausethey they are are identical identical in except thatthat the the units units have have the same dynamic sensitivity because ingeometry, geometry, except ◦ in turn, according to the positions of the units. In addition, as for any sensor unit, diagrams rotate 45 diagrams rotate 45° in turn, according to the positions of the units. In addition, as for any sensor its dynamic reaches the maximum value value near the probe it decreases unit, its dynamicsensitivity sensitivity reaches the maximum near thesurface, probe and surface, and it sharply decreases as the distance to the probe increases. To make a quantitative view, the contour diagram of the No. 7 sharply as the distance to the probe increases. To make a quantitative view, the contour diagram of sensor unit is provided as Figure 12. It shows that the dynamic sensitivity is greater than 0.9 near the No. 7 sensor unit is provided as Figure 12. It shows that the dynamic sensitivity is greater than the probe surface. However, it decreases to below 0.1 just about 30 mm away and decreases to below 0.9 near theabout probe surface. However, it decreases to below 0.1 just about 30units mm is away and decreases 0.001 150 mm away. In a word, the dynamic sensitivity of the sensor inhomogeneous to below 0.001localized, about 150 mm away. a word, thesensor dynamic sensitivity of thedetect sensor units is and quite which means thatIn a hemispherical unit can only effectively charged inhomogeneous and quite localized, which means that a hemispherical sensor unit can only particles near its probe. Therefore, it is of practical value to overcome this drawback by using ESAs, effectively detect charged particlesaccuracy. near its probe. Therefore, it is of practical value to overcome this thus improving the monitoring drawback by using ESAs, thus improving the monitoring accuracy.
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Figure 11.(a–h) (a–h) Surface diagrams ofofdynamic dynamic sensitivityof ofthe the sensor units from No. 1–No. 8. Figure 11. (a–h) Surface diagrams dynamicsensitivity sensitivity sensor units from No.No. 1–No. 8. 8. Figure 11. Surface diagrams of of the sensor units from 1–No.
Figure Contourdiagram diagramof of dynamic dynamic sensitivity thethe No. 7 sensor unit.unit. Figure 12.12. Contour sensitivityofof No. 7 sensor
Figure 12. Contour diagram of dynamic sensitivity of the No. 7 sensor unit.
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5.1.2. Simulated Static Sensitivity of the HSESCA 5.1.2. Simulated Static Sensitivity of the HSESCA The static sensitivity of the HSESCA in the observation cross-section is calculated by using The static sensitivity of the HSESCA in the observation cross-section is calculated by using Equation (11) and the calibration method. The results are shown in Figure 13. Equation (11) and the calibration method. The results are shown in Figure 13.
Figure 13. 13. (a) (a) Surface Surface and and (b) (b) contour contour diagrams diagrams of of the the static static sensitivity sensitivity of of the the HSESCA. HSESCA. Figure
It is is seen seenfrom fromFigure Figure 13 that, in observation the observation cross-section, thesensitivity static sensitivity of the 13 that, in the cross-section, the static of the HSESCA HSESCA symmetrically in accordance with the distribution of the probes. In addition, distributesdistributes symmetrically in accordance with the distribution of the probes. In addition, just like the just like the dynamicofsensitivity of a certain sensor the static sensitivity ofreaches the HSESCA reaches dynamic sensitivity a certain sensor unit, the staticunit, sensitivity of the HSESCA the maximum the maximum value than 0.9 near probes, and it decreases sharply distance to the value greater than 0.9greater near the probes, and the it decreases sharply as distance to theasprobes increases. probes increases. In most of the central area, the values of static sensitivity are below 0.05. That is to In most of the central area, values of static sensitivity are below 0.05. That is to say, the static say, the static sensitivity HSESCA is inhomogeneous and which quite localized, which means that sensitivity of the HSESCAofisthe inhomogeneous and quite localized, means that an HSESCA will an will onlycharged effectively detect particles near the summation probes if just using the onlyHSESCA effectively detect particles nearcharged the probes if just using of the induced summation of the induced charges to reflect the charge quantity of a monitored particle. Definitely, charges to reflect the charge quantity of a monitored particle. Definitely, the static sensitivity in the the static sensitivity in the center region can improved by increasing size and of center region can be improved by increasing thebesize and number of probes. the However, thisnumber will cause probes. However, this will problems in installation increase the disturbance to to theensure flow. problems in installation andcause increase the disturbance to theand flow. Therefore, it is advisable Therefore, it isaccuracy advisable to center ensureregion the monitoring accuracyarray in the center region algorithms. by using the monitoring in the by using appropriate signal processing appropriate array signal processing algorithms. 5.1.3. Simulated Dynamic Sensitivity of the HSESCA 5.1.3.For Simulated Sensitivity of the the sakeDynamic of simplicity, here, we setHSESCA the amplification coefficient K = −1. Then, by placing a pointFor charge q = 1 of C in turn at each grid shown in Figure coefficient 10, the corresponding signal peaks of the sake simplicity, here, wepoint set the amplification K = −1. Then, by placing a point charge q = 1 C in turn at each grid point shown in Figure 10, the corresponding signal peaks of
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ofsensor the sensor units are calculated using Equation (14). they Next, are processed by the all ofallthe units are calculated using Equation (14). Next, arethey processed by the component component extraction-based array signal processing algorithm (see Section 4) to get the monitoring extraction-based array signal processing algorithm (see Section 4) to get the monitoring parameter parameter value corresponding to each grid point. In this way, the values of dynamic sensitivity at value corresponding to each grid point. In this way, the values of dynamic sensitivity at all of the grid all of the grid points are obtained. The results are shown in Figure 14. points are obtained. The results are shown in Figure 14.
Figure 14. 14. (a)(a) Surface and (b) dynamicsensitivity sensitivityofof the HSESCA. Figure Surface and (b)contour contourdiagrams diagrams of the dynamic the HSESCA.
is seen from Figure that dynamic sensitivityofofthe theHSESCA HSESCAdistributes distributes symmetrically symmetrically in It isItseen from Figure 14 14 that thethe dynamic sensitivity in accordance with the distribution of the probes. In addition, it is obvious that the dynamic accordance with the distribution of the probes. In addition, it is obvious that the dynamic sensitivity sensitivity has relatively high values, not only near the probes, but also in most of the area of the has relatively high values, not only near the probes, but also in most of the area of the observation observation cross-section. By making a comparison between Figures 13 and 14, it is shown that the cross-section. By making a comparison between Figures 13 and 14, it is shown that the dynamic dynamic sensitivity and the static sensitivity have close values near the probes and the inner wall of sensitivity and the static sensitivity close near the probes and the inner wall theof pipeline. the pipeline. However, the meanhave value of values the static sensitivity is only about 0.04 in of most the However, mean value sensitivity is only about 0.04 0.95. in most the central area, while central the area, while thatof ofthe thestatic dynamic sensitivity reaches about Theofsensitivity represents thatcharge of the measurement dynamic sensitivity reaches sensitivity accuracy, that isabout to say0.95. the The closer to one therepresents sensitivitycharge is, the measurement higher the accuracy, that is to say the closer to one the sensitivity is, the higher the accuracy is. Therefore, in the accuracy is. Therefore, in the case of intermittent particle monitoring, the monitoring ability gets caseenhanced of intermittent particle monitoring, the monitoring ability getsthe enhanced by 23 times in most of by 23 times in most of the central area because of using component extraction-based array signal processing algorithm, which implies significantarray improvements in sensitivity the central area because of using the component extraction-based signal processing algorithm, homogeneity and monitoring accuracyinof the HSESCA. Furthermore, it shows that there still which implies significant improvements sensitivity homogeneity and monitoring accuracy of the distribute relatively low values near the inner wall of the pipeline, except where the probes are HSESCA. Furthermore, it shows that there still distribute relatively low values near the inner wall of located. This is unavoidably caused the influence of the pipeline on the field. the pipeline, except where the probes arebylocated. This is unavoidably caused byelectrostatic the influence of the However, using a strategy to optimize the number of sensor units combined with optimizations pipeline on the electrostatic field. However, using a strategy to optimize the number of sensor on units the proposed algorithm is likely to alleviate this drawback, which deserves further studies.
combined with optimizations on the proposed algorithm is likely to alleviate this drawback, which deserves further studies.
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5.2.Experimental ExperimentalResults Resultsand andDiscussion Discussion 5.2. 5.2. Experimental Results 5.2.1.Experiment ExperimentApparatus Apparatus 5.2.1. 5.2.1. Experiment Apparatus Experimentalresults resultswere wereobtained obtainedby byusing usingan aneight-channel eight-channelHSESCA HSESCA experiment apparatus. Experimental obtained by using eight-channel HSESCAexperiment experiment apparatus. Experimental results apparatus. As showninin inFigure Figure15, 15,the theexperiment experimentapparatus apparatusis mainlycomposed composedof ofan anelectrostatic electrostaticgenerator, generator, a As shown generator, As shown Figure 15, the experiment apparatus isismainly mainly composed electrostatic particle release device, pipeline, an HSESCA, HSESCA, Faraday cylinder and aa computer. computer. The particle release device, a pipeline, an HSESCA, a Faraday cylinder cylinder and a computer. The electrostatic aa particle release device, aa pipeline, an aa Faraday and The electrostatic generator produces ionized air in the particle release device by high voltage, which generator produces ionized air inionized the particle devicerelease by highdevice voltage, makes released electrostatic generator produces air inrelease the particle by which high voltage, which makes released released particles particles charged. An HSESCA that has has eight sensor sensor units isis installed installed in the the particles charged. An HSESCA that has eight sensor that units is installed in the midsection of the grounded makes charged. An HSESCA eight units in midsection of the the grounded grounded pipeline. produces array signals when a charged charged particle falls midsection of pipeline. produces array signals when particle falls pipeline. It produces array signals when aItIt charged particle falls through the apipeline. Then, the signals through the pipeline. Then, the signals are processed by using specially-designed software through the by pipeline. Then, the signalssoftware are processed by inusing specially-designed software are processed using specially-designed integrated the computer. The Faraday cylinder integratedwith in the the computer. The Faradaybelow cylinder connected with charge meter placed below below integrated in computer. The cylinder with aa charge meter isis placed connected a charge meter is Faraday placed theconnected pipeline. A charged particle will finally fall into the pipeline. A charged particle will finally fall into the Faraday cylinder; thus, the charge quantity the pipeline. A charged particle will finally fall into the Faraday cylinder; thus, the charge quantity the Faraday cylinder; thus, the charge quantity of the particle is read from the charge meter with a ofthe theparticle particleisisread readfrom fromthe thecharge chargemeter meter withaameasurement measurement resolutionof of11pC. pC.Steel Steelballs ballswith with of measurement resolution of 1 pC. Steel ballswith with a diameter of 2resolution mm are used as the experimental a diameter of 2 mm are used as the experimental particles. To create a consistent condition with the a diameter 2 mmaare used as the experimental particles. To create a consistent condition the particles. Toofcreate consistent condition with the numerical simulation, the pipeline haswith an inner numerical simulation, the pipeline has an inner radius of 200 mm; the hemispherical probes have a numerical simulation, the pipeline has an inner of 200 mm; hemispherical radius of 200 mm; the hemispherical probes haveradius a radius of 12 mmthe with their buttonprobes faces 2have mm afar radiusof of12 12mm mmwith withtheir theirbutton button faces 2 mm far from the inner wall of the pipeline. radius from the inner wall of the pipeline.faces 2 mm far from the inner wall of the pipeline.
Figure Structure of the HSESCA experiment apparatus. apparatus. Figure15. 15.Structure Structureof ofthe theHSESCA HSESCAexperiment experiment Figure 15. apparatus.
Inthe theexperiment, experiment,the the particles were released different test points, as shown shown in Figure Figure 16. In particles were released atatat different test points, asas shown in in Figure 16.16. The In the experiment, the particles were released different test points, The points were set along two typical lines in the observation cross-section. Line 1 is the axis of the points were were set along two typical lines lines in theinobservation cross-section. LineLine 1 is the of the The points set along two typical the observation cross-section. 1 is axis the axis of No. the 1 No. 11unit, sensor unit, and Line the bisector ofand thethe No. and the No. No. sensor units. Each12 line No. sensor 22 isis the the No. 11 and the 88 sensor units. Each line sensor andunit, Lineand 2 is Line the bisector of bisector the No. 1of No. 8 sensor units. Each line contains test contains 12test test points, which areuniformly uniformly spaced by15 15to mm. Inorder order toreduce reduce theposition position error contains 12 which are spaced by mm. In to the error points, which arepoints, uniformly spaced by 15 mm. In order reduce the position error of each release ofeach each releaseand andthe the measurement error ofthe thecharge charge quantity, 10tests tests were doneThen, ateach each point. of release measurement error of quantity, 10 were done at point. and the measurement error of the charge quantity, 10 tests were done at each point. the mean Then, the mean valves of the measured signal peaks and those of the charge quantities were further Then, of thethe mean valves of the measured those of the charge were valves measured signal peaks andsignal those peaks of the and charge quantities were quantities further used to further calculate usedto tocalculate calculatethe thestatic staticsensitivity andthe thedynamic dynamicsensitivity sensitivityof ofthe theHSESCA. HSESCA. used the static sensitivity and thesensitivity dynamic and sensitivity of the HSESCA.
Figure 16.Test Test pointsset set inthe the experiment. Figure Figure 16. 16. Test points points setin in theexperiment. experiment.
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5.2.2. Array Array Signals Signals of of the the HSESCA HSESCA 5.2.2. Five sets sets of of typical typical array array signals signals with Five with aa sample sample frequency frequency of of 4096 4096 Hz Hz are are shown shown in in Figure Figure 17. 17. P44 and They were were acquired acquiredwhen whenparticles particleswere werereleased releasedatatPP11,,PP22,, PP33,, P They and P P55,,respectively respectively (see (see Figure Figure 16). 16). Among them, them,PP1 1isisthe theorigin; origin; 2 and 4 are away the origin; P3 Pand P5 are 120 mm Among P2Pand P4 Pare 60 60 mmmm away fromfrom the origin; P3 and 5 are 120 mm away away from the origin. Besides, the charge quantities of the particles were measured be − −32 from the origin. Besides, the charge quantities of the particles were measured to be −32topC, 20 pC, pC, -20 and −29respectively. pC, respectively. − 46pC, pC,−46 −25pC, pC−25 andpC −29 pC,
17. Array signals signals of of the the HSESCA. HSESCA. (a) (a) Released Released at atPP11 with with − −32 released at at PP22 Figure 17. 32 pC charge; (b) released with − -20 −46 at PP44 with with − −25 with 20 pC pC charge; charge; (c) (c) released at P33 with − 46 pC pC charge; charge; (d) released at 25 pC charge; −29 (e) released released at at PP55 with − (e) 29pC pCcharge. charge.
Figure 17 17 shows shows that that the the measured measured signals signals are are similar similar in in shape shape as as those those obtained obtained by by numerical numerical Figure simulations (see Figure 5), except the sign symbol. The measured ones are minus because of the simulations (see Figure 5), except the sign symbol. The measured ones are minus because of the minus minus charge quantities of the particles. Besides, a signal variation trend versus the positions in charge quantities of the particles. Besides, a signal variation trend versus the positions in Line 1 can be Line 1 can be observed from Figure 17a–c. In detail, the signals of all of the sensor units are almost observed from Figure 17a–c. In detail, the signals of all of the sensor units are almost coincident at P1 , coincident at P1, which is explained by the same distance from P1 to every probe. However, with the which is explained by the same distance from P1 to every probe. However, with the release position release position moving from P1 to P3, the signal peak of the No. 1 sensor unit gets larger and larger. moving from P1 to P3 , the signal peak of the No. 1 sensor unit gets larger and larger. Conversely, other Conversely, other signal peaks decrease with respect to that of the No. 1 sensor unit; among them, signal peaks decrease with respect to that of the No. 1 sensor unit; among them, that of the No. 5 that of the No. 5 sensor unit decreases the most. In addition, two symmetric sensor units about sensor unit decreases the most. In addition, two symmetric sensor units about Line 1 have the same Line 1 have the same decrease scale in their signal peaks. A similar trend can also be observed when decrease scale in their signal peaks. A similar trend can also be observed when the release position the release position moves from P1 to P5 along Line 2. This is because a charged particle induces moves from P1 to P5 along Line 2. This is because a charged particle induces greater charge on closer greater charge on closer probes, and vice versa. In a word, the measured array signals have probes, and vice versa. In a word, the measured array signals have validated the theoretical ones in validated the theoretical ones in form. Moreover, it is validated that different combinations of peaks form. Moreover, it is validated that different combinations of peaks of the array signals imply different of the array signals imply different position information of the particles. This agrees with the position information of the particles. This agrees with the theoretical analysis and is the precondition theoretical analysis and is the precondition of the proposed array signal processing algorithm. of the proposed array signal processing algorithm. Ten tests were done at the release positions of P1, P2, P3, P4 and P5, respectively. The absolute charge quantities of the particles and the absolute signal peaks of the No. 1 sensor unit were measured. Their relationships are shown in Figure 18.
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Ten tests were done at the release positions of P1 , P2 , P3 , P4 and P5 , respectively. The absolute charge quantities of the particles and the absolute signal peaks of the No. 1 sensor unit were measured. Sensors 2016, 16, 1403 19 of 22 Their relationships are shown in Figure 18.
Figure 18. Relationships between the absolute charge quantities and the absolute peak voltages of the No. 1 sensor unit. Figure 18. Relationships between the absolute charge quantities and the absolute peak voltages of the Figure 18. Relationships between the absolute charge quantities and the absolute peak voltages of 1 sensor ThisNo. shows anunit. obvious proportional relationship between the absolute charge quantities the No. 1 sensor unit.
and the absolute peak voltages at each position. The different slopes indicate different values of shows obvious proportional relationship between thethe absolute charge quantities and and the This showsan an obvious proportional relationship between absolute charge quantities dynamicThis sensitivity with respect to different positions, and greater slopes represent greater values absolute peak voltages at each position. The different slopes indicate different values of dynamic the absolute peak voltages at each position. The different slopes indicate different values of dynamic sensitivity. The errors are acceptable and can be explained by the position error ofofeach sensitivity with respect to different and greaterand slopes represent greater values of dynamic dynamic with respecterror topositions, different greater slopes greater values release and sensitivity the measurement of thepositions, charge quantity. As a represent result, the proportional sensitivity. errors are acceptable can be explained byexplained the position error of eacherror release and of dynamicThe sensitivity. The errors areand acceptable and can be by the position of each characteristic of the signal conditioner is validated. the measurement of the charge quantity. As charge a result, quantity. the proportional of the signal release and the error measurement error of the As a characteristic result, the proportional conditioner is of validated. characteristic the signal conditioner is validated.
5.2.3. Static Sensitivity Test of the HSESCA
5.2.3. Static Test of 5.2.3. StaticaSensitivity Sensitivity Testbetween ofthe theHSESCA HSESCA To make comparison the theoretical and experimental results of the static sensitivity
of the HSESCA, the theoretical values in Line and 1 and and Line 2 were firstly calculated by of using To between the experimental results of of thethe static sensitivity Tomake makeaacomparison comparison between thetheoretical theoretical experimental results static sensitivity the HSESCA, the theoretical values in Line 1 and Line 2 were firstly calculated by using Equation (11) Equation and the when −1. Then, to the definition of static of the (11) HSESCA, thecalibration theoreticalmethod values in LineK1= and Line 2according were firstly calculated by using and the as calibration method when K = −1. when Then, to the definition of static sensitivity as the sensitivity Equation (10), the experimental value each test point was by dividing Equation (11) and the calibration method Kaccording =at−1. Then, according to obtained the definition of static Equation (10), the experimental value at each test point was obtained by dividing the summation of sensitivity (10), the experimental valuequantity at each test point was obtained by dividing the summation ofas allEquation of the signal peaks by the charge of the corresponding particle, followed all of the signal peaks by the charge quantity of the corresponding particle, followed by a scaling to the all of the peaks by theare charge quantity of the19, corresponding particle,represent followed by asummation scaling to of suppose K signal = −1. The results shown in Figure where the curves suppose K=− The results shown in Figure 19, where the curves represent theoretical values by a scaling to1.and suppose K = are −1. represent The results areexperimental shown in Figure 19, where thethe curves represent the theoretical values the points the values. and the points represent the experimental theoretical values and the points representvalues. the experimental values.
Figure 19. Experimental and theoretical values of static sensitivity (a) in Line 1 and (b) in Line 2.
Figure Experimental and theoreticalvalues values of of static static sensitivity 1 and (b)(b) in Line 2. 2. Figure 19. 19. Experimental and theoretical sensitivity(a) (a)ininLine Line 1 and in Line
It can be seen that the experimental values show fine consistencies with the theoretical ones. It can be seen that the experimental values show fine consistencies with the theoretical ones. Further analysis shows that the mean absolute value of relative error from all of the test points in Further analysis shows that the mean absolute value of relative error from all of the test points in Line 1 is 2.2544%, and that in Line 2 is 1.3516%. The errors are acceptable and can be explained by Line 1 is 2.2544%, and that in Line 2 is 1.3516%. The errors are acceptable and can be explained by the errors in controlling the particles’ falling positions and measuring their charge quantities. the Therefore, errors in the controlling the particles’ falling measuring their charge quantities. sensing model of the HSESCA, as positions well as thatand of the sensor units are validated.
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It can be seen that the experimental values show fine consistencies with the theoretical ones. Further analysis shows that the mean absolute value of relative error from all of the test points in Line 1 is 2.2544%, and that in Line 2 is 1.3516%. The errors are acceptable and can be explained by the Sensors 16, 1403 20 of 22 errors 2016, in controlling the particles’ falling positions and measuring their charge quantities. Therefore, the sensing model of the HSESCA, as well as that of the sensor units are validated. 5.2.4. Dynamic Sensitivity Test of the HSESCA 5.2.4.Theoretical Dynamic Sensitivity Test of theresults HSESCA and experimental of the dynamic sensitivity of the HSESCA were also
compared. Whenand the amplification to K = −1, the theoretical in Line and Theoretical experimental coefficient results of was the set dynamic sensitivity of the values HSESCA were1 also Line 2 were firstly calculated (see Section 5.1.3). After that, the measured signal peaks were compared. When the amplification coefficient was set to K = −1, the theoretical values in Line 1 and processed the calculated component extraction-based array signal processing algorithm to obtain the Line 2 wereby firstly (see Section 5.1.3). After that, the measured signal peaks were processed experimental values. In detail, the peaks decomposed, summated to obtain the by the component extraction-based arraywere signal processing weighted algorithmand to obtain the experimental values of monitoring Then, the corresponding values of are values. In the detail, the peaksparameter. were decomposed, weighted and summated to dynamic obtain thesensitivity values of the calculated using Equation (19), followed by avalues scaling supposesensitivity K = −1. The are shown in monitoringby parameter. Then, the corresponding ofto dynamic areresults calculated by using Figure where the by curves represent the Ktheoretical valuesare and the in points Equation20, (19), followed a scaling to suppose = −1. The results shown Figurerepresent 20, where the experimental values. curves represent the theoretical values and the points represent the experimental values.
Figure (a) in in Line Line 11 and and (b) (b) in in Line Line 2. 2. Figure 20. 20. Experimental Experimental and and theoretical theoretical values values of of dynamic dynamic sensitivity sensitivity (a)
It is observed that the experimental values match well with the theoretical ones. Further It is observed that the experimental values match well with the theoretical ones. Further analysis analysis shows that the mean absolute value of relative error from all of the test points in Line 1 is shows that the mean absolute value of relative error from all of the test points in Line 1 is 3.3233%, and 3.3233%, and that in Line 2 is 0.5936%. Just as the results in the static sensitivity test, the errors here that in Line 2 is 0.5936%. Just as the results in the static sensitivity test, the errors here are acceptable and are acceptable and can be explained by the errors in controlling the particles’ falling positions and can be explained by the errors in controlling the particles’ falling positions and measuring their charge measuring their charge quantities. In addition, by making a comparison between Figures 19 and 20, quantities. In addition, by making a comparison between Figures 19 and 20, it is seen that the values it is seen that the values of dynamic sensitivity are larger than 0.8 in most of the section of Line 1 of dynamic sensitivity are larger than 0.8 in most of the section of Line 1 and Line 2, but those of the and Line 2, but those of the static sensitivity are almost below 0.1. This demonstrates that the static sensitivity are almost below 0.1. This demonstrates that the monitoring accuracy of the HSESCA monitoring accuracy of the HSESCA for intermittent particles has been improved significantly by for intermittent particles has been improved significantly by using the component extraction-based using the component extraction-based signal processing algorithm, which agrees with the signal processing algorithm, which agrees with the theoretical analysis above. Therefore, the proposed theoretical analysis above. Therefore, the proposed algorithm is proven to be effective in actual algorithm is proven to be effective in actual measurements. More details can be found in Sections 5.1.2 measurements. More details can be found in Sections 5.1.2 and 5.1.3. and 5.1.3. 6. 6. Conclusions Conclusions
By the array array signals signals into consideration, the By taking taking the the processing processing of of the into consideration, the dynamic dynamic sensitivity sensitivity of of ESA ESA has beendefined definedtotodescribe describe sensitivity characteristics of ESAs in a systemic perspective. It has been thethe sensitivity characteristics of ESAs in a systemic perspective. It builds builds a direct relationship between the monitored particles and the monitoring parameters of a a direct relationship between the monitored particles and the monitoring parameters of a whole whole ESA, thus reflecting the monitoring accuracy directly. An HSESCA along with its application ESA, thus reflecting the monitoring accuracy directly. An HSESCA along with its application in in intermittent particle monitoring has taken been as taken as an example. Its sensitivity dynamic in sensitivity in intermittent particle monitoring has been an example. Its dynamic accordance accordance with a proposed component extraction-based array signal processing algorithm has with a proposed component extraction-based array signal processing algorithm has been analyzed been analyzed Relevant quantitatively. Relevant numerical been made, and experimental quantitatively. numerical simulations havesimulations been made,have and experimental validations have validations have been carried out on an eight-channel HSESCA experiment apparatus. Detailed been carried out on an eight-channel HSESCA experiment apparatus. Detailed results have been results have been provided, compared andare discussed, whichasare summarized as follows: provided, compared and discussed, which summarized follows: 1. 2.
The experimental results match well with the theoretical ones, which has validated the accuracy of the theoretical models and effectiveness of the corresponding methods. Compared with static sensitivity, the dynamic sensitivity of the HSESCA has much greater values in most of the observation cross-section. This demonstrates that the component extraction-based array signal processing algorithm is effective at overcoming the defect of
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The experimental results match well with the theoretical ones, which has validated the accuracy of the theoretical models and effectiveness of the corresponding methods. Compared with static sensitivity, the dynamic sensitivity of the HSESCA has much greater values in most of the observation cross-section. This demonstrates that the component extraction-based array signal processing algorithm is effective at overcoming the defect of inhomogeneous and localized static sensitivity, thus making a significant improvement on the monitoring accuracy for intermittent particles. There still exist relatively less sensitive zones near the inner wall of the pipeline after adopting the proposed algorithm. This is caused by the influence of the pipeline on the electrostatic field. A strategy to optimize the number of sensor units combined with optimizations on the proposed algorithm is likely to alleviate the drawback, which deserves further studies. Ill-conditioning and noise may impact the results of the proposed array signal processing algorithm. This is of great significance, to be discussed in further studies.
Acknowledgments: The authors are grateful to the National Basic Research Program of China (Grant No. 2015CB057400) for supporting this work. Author Contributions: This work has been done in collaboration between all authors. Xin Tang did the theoretical analyses and prepared the manuscript. Zhong-Sheng Chen designed the experiment and analyzed the experimental results. Yue Li and Zheng Hu did the simulation work and compared the results with those of the experiment. Yong-Min Yang revised the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations EMS ESA HSESCA PHM
Electrostatic monitoring system Electrostatic sensor array Hemisphere-shaped electrostatic sensors’ circular array Prognostics and health management
References 1. 2. 3. 4. 5. 6.
7. 8. 9. 10. 11.
Sun, J.Z.; Zuo, H.F.; Liu, P.P.; Wen, Z.H. Experimental study on engine gas-path component fault monitoring using exhaust gas electrostatic signal. Meas. Sci. Technol. 2013, 24, 125107. [CrossRef] Rahmat, M.F.; Thuku, I.T.; Tajdari, T.; Jusoff, K.; Ghazali, M.R. Sensing and filtering characteristics of electrostatic sensors for pneumatically conveyed particles. Int. J. Phys. Sci. 2011, 6, 5091–5103. Coombes, J.R.; Yan, Y. Experimental investigations into the flow characteristics of pneumatically conveyed biomass particles using an electrostatic sensor array. Fuel 2015, 151, 11–20. [CrossRef] Hu, H.L.; Dong, J.; Zhang, J.; Cheng, Y.J.; Xu, T.M. Identification of gas/solid two-phase flow regimes using electrostatic sensors and neural-network techniques. Flow Meas. Instrum. 2011, 22, 482–487. [CrossRef] Rahmat, M.F.; Isa, M.D.; Rahim, R.A.; Hussin, T.A. Electrodynamics sensor for the image reconstruction process in an electrical charge tomography system. Sensors 2009, 9, 10291–10308. [CrossRef] [PubMed] Addabbo, T.; Fort, A.; Garbin, R.; Mugnaini, M.; Rocchi, S.; Vignoli, V. Theoretical characterization of a gas path debris detection monitoring system based on electrostatic sensors and charge amplifiers. Measurement 2015, 64, 138–146. [CrossRef] Wen, Z.H.; Zuo, H.F.; Pecht, M.G. Electrostatic monitoring of gas path debris for aero-engines. IEEE Trans. Reliab. 2011, 60, 33–40. [CrossRef] Lin, J.; Chen, Z.S.; Hu, Z.; Yang, Y.M.; Tang, X. Analytical and numerical investigations into hemisphere-shaped electrostatic sensors. Sensors 2014, 14, 14021–14037. [CrossRef] [PubMed] Tang, X.; Chen, Z.; Li, Y.; Hu, Z.; Yang, Y. Theoretical analysis and fem simulations on dynamic sensitivity of hemisphere-shaped electrostatic sensors. Adv. Mech. Eng. 2016, 8. [CrossRef] Krabicka, J.; Yan, Y. Finite-element modeling of electrostatic sensors for the flow measurement of particles in pneumatic pipelines. IEEE Trans. Instrum. Meas. 2009, 58, 2730–2736. [CrossRef] Zhang, W.; Wang, C.; Yang, W.; Wang, C.-H. Application of electrical capacitance tomography in particulate process measurement—A review. Adv. Powder Technol. 2014, 25, 174–188. [CrossRef]
Sensors 2016, 16, 1403
12. 13.
14. 15. 16.
17. 18. 19. 20.
21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
31.
32.
22 of 23
Zhou, B.; Zhang, J.; Xu, C.; Wang, S. Image reconstruction in electrostatic tomography using a priori knowledge from ect. Nucl. Eng. Des. 2011, 241, 1952–1958. [CrossRef] Gao, H.; Xu, C.; Fu, F.; Wang, S. Effect of particle distribution on electrostatic tomography system. In Proceedings of the 7th International Symposium on Measurement Techniques for Multiphase Flows, Xi’an, China, 26–30 October 2012; pp. 269–276. Iliya, T.T.; Mohd, F.R. Development of a new method of sensitivity matrix for image reconstruction in electric charge tomography system using finite element method. J. Teknol. 2014, 70, 103–112. Li, Y.; Yang, W. Image reconstruction by nonlinear landweber iteration for complicated distributions. Meas. Sci. Technol. 2008, 19, 094014. [CrossRef] Martínez Olmos, A.; Botella, G.; Castillo, E.; Morales, D.P.; Banqueri, J.; García, A. A reconstruction method for electrical capacitance tomography based on image fusion techniques. Digit. Signal Process. 2012, 22, 885–893. [CrossRef] Tizhe Thuku, I.; Rahmat, M.F.A. Finite-element method modeling in 4 and 16 sensors electric-charge tomography systems for particles moving in pipeline. Flow Meas. Instrum. 2014, 38, 9–20. [CrossRef] Xu, C.; Li, J.; Gao, H.; Wang, S. Investigations into sensing characteristics of electrostatic sensor arrays through computational modelling and practical experimentation. J. Electrost. 2012, 70, 60–71. [CrossRef] Thuku, I.T.; Rahmat, M.F.; Wahab, N.A.; Tajdari, T.; Yusuf, A.A. 2-D finite-element modeling of electrostatic sensor for tomography system. Sens. Rev. 2013, 33, 104–113. [CrossRef] Ghazali, M.R.; Ibrahim, W.I.; Rahmat, M.F. Electrostatic sensor in circular and rectangular shape electrode for solid dry pneumatic conveyor system. In Proceedings of the 2011 International Conference on Circuits, System and Simulation, Bangkok, Thailand, 28–29 May 2011; IACSIT Press: Singapore, 2011; Volume 7, pp. 66–72. Xu, C.; Wang, S.; Tang, G.; Yang, D.; Zhou, B. Sensing characteristics of electrostatic inductive sensor for flow parameters measurement of pneumatically conveyed particles. J. Electrost. 2007, 65, 582–592. [CrossRef] Yang, W.Q.; Conway, W.F. Measurement of sensitivity distributions of capacitance tomography sensors. Rev. Sci. Instrum. 1997, 69, 233–236. [CrossRef] Guo, Z.; Shao, F.; Lv, D. Sensitivity matrix construction for electrical capacitance tomography based on the difference model. Flow Meas. Instrum. 2009, 20, 95–102. [CrossRef] Marashdeh, Q.; Teixeira, F.L. Sensitivity matrix calculation for fast 3-D electrical capacitance tomography (ECT) of flow systems. IEEE Trans. Magnet. 2010, 40, 1204–1207. [CrossRef] Wang, A.; Marashdeh, Q.M.; Teixeira, F.L.; Fan, L.S. Electrical capacitance volume tomography: A comparison between 12- and 24-channels sensor systems. Prog. Electromagn. Res. M 2015, 41, 73–84. [CrossRef] Zeeshan, Z.; Teixeira, F.L.; Marashdeh, Q. Sensitivity map computation in adaptive electrical capacitance volume tomography with multielectrode excitations. Electron. Lett. 2015, 51, 334–336. [CrossRef] Fisher, C.E. Gas path debris monitoring—A 21st century PHM tool. In Proceedings of the 2000 IEEE Aerospace Conference Proceedings, Big Sky, MT, USA, 25 March 2000; Volume 6, pp. 441–448. Powrie, H.; Novis, A. Gas path debris monitoring for F-35 joint strike fighter propulsion system PHM. In Proceedings of the 2006 IEEE Aerospace Conference, Big Sky, MT, USA, 4–11 March 2006; pp. 4012–4019. Wen, Z.; Ma, X.; Zuo, H. Characteristics analysis and experiment verification of electrostatic sensor for aero-engine exhaust gas monitoring. Measurement 2014, 47, 633–644. [CrossRef] Addabbo, T.; Fort, A.; Mugnaini, M.; Panzardi, E.; Vignoli, V. Multisensor electrostatic detection of moving charged particles. In Proceedings of the Sensors Applications Symposium (SAS 2016), Catania, Italy, 20–22 April 2016; pp. 445–450. Addabbo, T.; Fort, A.; Mugnaini, M.; Panzardi, E.; Vignoli, V. A smart measurement system with improved low-frequency response to detect moving charged debris. IEEE Trans. Instrum. Meas. 2016, 65, 1874–1883. [CrossRef] Xu, C.; Zhang, J.; Yang, D.; Zhou, B.; Tang, G.; Wang, S. Dense-phase pneumatically conveyed coal particle velocity measurement using electrostatic probes and cross correlation algorithm. J. Phys. 2009, 147, 012004. [CrossRef]
Sensors 2016, 16, 1403
33. 34.
23 of 23
Zhang, J.Q.; Yan, Y. On-line continuous measurement of particle size using electrostatic sensors. Powder Technol. 2003, 135–136, 164–168. [CrossRef] Zhou, B.; Yang, D.; Tang, G.; Xu, C.; Wang, S. Analysis on dynamic sensitivity of ring-shaped electrostatic sensor. Proc. CSEE 2008, 28, 44–49. © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
Analysis of the Dynamic Sensitivity of Hemisphere-Shaped Electrostatic Sensors’ Circular Array for Charged Particle Monitoring Xin Tang, Zhong-Sheng Chen *, Yue Li, Zheng Hu and Yong-Min Yang Science and Technology on Integrated Logistics Support Laboratory, National University of Defense Technology, Changsha 410073, China; [email protected] (X.T.); [email protected] (Y.L.); [email protected] (Z.H.); [email protected] (Y.-M.Y.) * Correspondence: [email protected]; Tel.: +86-139-7580-3247 Academic Editor: Vittorio M. N. Passaro Received: 1 July 2016; Accepted: 27 August 2016; Published: 31 August 2016
Abstract: Electrostatic sensor arrays (ESAs) are promising in industrial applications related to charged particle monitoring. Sensitivity is a fundamental and commonly-used sensing characteristic of an ESA. However, the usually used spatial sensitivity, which is called static sensitivity here, is not proper for moving particles or capable of reflecting array signal processing algorithms integrated in an ESA. Besides, reports on ESAs for intermittent particles are scarce yet, especially lacking suitable array signal processing algorithms. To solve the problems, the dynamic sensitivity of ESA is proposed, and a hemisphere-shaped electrostatic sensors’ circular array (HSESCA) along with its application in intermittent particle monitoring are taken as an example. In detail, a sensing model of the HSESCA is built. On this basis, its array signals are analyzed; the dynamic sensitivity is thereupon defined by analyzing the processing of the array signals. Besides, a component extraction-based array signal processing algorithm for intermittent particles is proposed, and the corresponding dynamic sensitivity is analyzed quantitatively. Moreover, simulated and experimental results are discussed, which validate the accuracy of the models and the effectiveness of the relevant approaches. The proposed dynamic sensitivity of ESA, as well as the array signal processing algorithm are expected to provide references in modeling, designing and using ESAs. Keywords: electrostatic sensor array; dynamic sensitivity; hemisphere-shaped electrostatic sensor; circular array; array signal processing algorithm
1. Introduction Electrostatic monitoring systems (EMSs) are featured with the advantages of robustness and low cost [1,2], making them very promising in parameter monitoring of gas-solid flows [3–5], exhaust debris monitoring-based PHM of gas turbines [1,6,7], etc. Electrostatic sensors are key components of EMSs. Among them, hemisphere-shaped electrostatic sensors were proposed by us as a trade-off between intrusive and non-intrusive electrostatic sensors. They combine the advantages of relatively high sensitivity, easy installation, flexible layout, accuracy in theoretical modeling and cause very little disturbance to flows [8,9]. The sensing principle of an electrostatic sensor is electrostatic induction. It determines that even if a particle carries a constant charge, the corresponding induced charge on an electrostatic sensor probe will reduce sharply when the distance between the particle and the probe gets larger. As a result, a near particle with quite weak charge can generate similar signals as a far particle with great charge. That is to say, the charge quantity of a particle can hardly be accurately monitored by a single electrostatic sensor if the position of the particle is not provided. In view of the sensitivity, this means that most
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electrostatic sensors have the drawback of inhomogeneous and quite localized sensitivity; thus, only particles near the probe can be effectively detected [8,10]. In a word, as for the applications that need the accurate particle charge (e.g., particle size monitoring or gas-solid flow density monitoring), an EMS that contains a single electrostatic sensor is usually of poor monitoring accuracy. Moreover, a total failure of the whole system will occur if only the sensor breaks down. Therefore, in order to obtain better monitoring accuracy and reliability, EMSs composed of multiple electrostatic sensors have become the trend [5,11,12]. They are usually called electrostatic sensor arrays (ESAs), and the electrostatic sensors are called the sensor unit. Two aspects are of high concern in relevant research: the first is the hardware design and related sensing characteristics analysis; the second is the application and related array signal processing algorithms. Circular ESA is a kind of representative hardware structure, which is made up by placing some identical electrostatic sensors uniformly around a circular pipeline in one cross-section [12–18]. Xu et al. used arc-sharped electrostatic sensors to construct circular ESAs and used the finite element method to study the sensing characteristics of the sensor units. Some geometric and material influence factors on the sensing characteristics were also analyzed [18]. Thuku et al. studied circular ESAs composed of rod-shaped electrostatic sensors [5,19]. A sensing model of the sensor units was built, and a comparison between four and 16 sensor systems was made [17]. In addition, differently-sized circularplate-shaped and rectangular plate-shaped electrostatic sensors were modeled and analyzed [20]; they are also suitable for circular ESAs. However, existing works on the sensing characteristics were generally focused on individual electrostatic sensors, thus lacking descriptions and models for the sensing characteristics of a whole ESA. In addition, as a fundamental and the most commonly-used sensing characteristic, sensitivity should reflect the monitoring accuracy of an EMS directly. As for an ESA, this means that a proper sensitivity definition should build a direct relationship between the monitored particles and the monitoring parameters of the whole ESA. However, the usually used spatial sensitivity only builds a basic relationship between static charged particles and corresponding induced charge on a sensor probe [10,18,21]; thus, it is called static sensitivity here. In practice, particles to be monitored are always moving. Furthermore, as a three-dimensionally-defined parameter, static sensitivity is difficult to accurately model when real boundary conditions are considered [9]. More importantly, follow-up processing of the induced charge is not considered in the definition, such as charge-voltage transformation and array signal processing algorithms. In a word, in order to build a direct relationship between the monitored particles and the monitoring parameters of a whole ESA, thus reflecting its monitoring accuracy directly, a more practical sensitivity definition needs to be defined in a systemic perspective. In the aspect of application, a circular ESA is usually used to detect the particle distribution over the cross-section of a pipeline and further infer gas-solid flow parameters, such as particle density and flow regime. In these cases, the particles to be monitored are continuous in the time domain. That is to say, there are always numerous particles passing a cross-section simultaneously, thus forming an obvious profile of the solid-phase, which can be imaged by tomography-based methods [5,11,14]. ESAs with arc-shaped sensor units usually adopt array signal processing algorithms based on electrical capacitance tomography [11,12,16,22,23]. They are suitable for dense gas-solid flows. There are also reports on volume tomography using multi-circular ESAs with arc-shaped sensor units [24–26]. ESAs with rod-shaped sensor units usually adopt algorithms based on electrostatic tomography [5,14,18]. They are suitable for both dense and dilute gas-solid flows. However, because of the limited number of sensor units, the tomography-based algorithms are faced with tough ill-conditioned problems, which lead to poor image resolution [11,16]. Improvements can be made by increasing the unit number [17] and adopting some iterative regularization methods, filtering methods, error minimization protocols, etc., which will increase the computation time [11,12,16]. As a result, the tomography-based algorithms only indicate approximate areas where particles concentrate, but they cannot accurately confirm where discrete particles are located. Moreover, the algorithms are more suitable for relatively stable flows, because the monitoring accuracy can be improved by making a compromise on the computation time.
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contrast, particles to be monitored could be quite intermittent in some applications. That is to say, there are only one or just a few particles passing a cross-section simultaneously. One representative application exhausttodebris monitoring-based PHM of gas turbines In this In contrast, is particles be monitored could be quite intermittent in some[7,17–29]. applications. Thatcase, is tothe say, occurrences of one fault-related particles arepassing accidental and instantaneous. In otherOne words, first, the there are only or just a few particles a cross-section simultaneously. representative particles to beis monitored are quite intermittent. Second, a fast signal processing algorithm is application exhaust debris monitoring-based PHM of gas array turbines [7,17–29]. In this case, the needed to avoid missing the fast-passing particles. Besides, the size and charge quantity of the occurrences of fault-related particles are accidental and instantaneous. In other words, first, the particles, rather than the distribution, are concerned. A ameasurement technique was algorithm studied byis particles to be monitored are quite intermittent. Second, fast array signal processing Addabbo et al. to estimate the trajectory position, charge and velocity of a moving needed to avoid missing the fast-passing particles. Besides, the size and charge quantity of the charged particles, particle. It was based on a small array whose electrostatic technique sensors have rather than the distribution, are concerned. A measurement wasimproved studied bylow-frequency Addabbo et al. response [30,31]. However, relevant studies scarce As for a circular ESA, arraybased signal to estimate the trajectory position, charge and are velocity of ayet. moving charged particle. It was on processing algorithms remain to be designed for the intermittent particle monitoring. a small array whose electrostatic sensors have improved low-frequency response [30,31]. However, To solve theare problems above, dynamic sensitivity of ESA is proposed to describe relevant studies scarce yet. As forthe a circular ESA, array signal processing algorithms remain tothe be sensitivity of ESAs in a systemic perspective. An ESA called the hemisphere-shaped electrostatic designed for the intermittent particle monitoring. sensors’ circular (HSESCA) along with its application in intermittent particle monitoring are To solve thearray problems above, the dynamic sensitivity of ESA is proposed to describe the sensitivity taken as an detail, a sensing model thehemisphere-shaped HSESCA, as well as that of thesensors’ sensor units is of ESAs in aexample. systemicIn perspective. An ESA calledofthe electrostatic circular built in Section 2. On this basis, array signals of the HSESCA are analyzed, and the dynamic array (HSESCA) along with its application in intermittent particle monitoring are taken as an example. sensitivity ESA is thereupon defined in Section 3. A extraction-based array signal In detail, a of sensing model of the HSESCA, as well as that of component the sensor units is built in Section 2. On this processing algorithm for discrete particle monitoring is designed in Section 4. Numerical basis, array signals of the HSESCA are analyzed, and the dynamic sensitivity of ESA is thereupon simulations and experiments are done for validations array in Section The main results are for concluded defined in Section 3. A component extraction-based signal5.processing algorithm discrete in Sectionmonitoring 6. particle is designed in Section 4. Numerical simulations and experiments are done for validations in Section 5. The main results are concluded in Section 6. 2. Sensing Model of an HSESCA 2. Sensing Model of an HSESCA This section builds a quantitative relationship between a charged particle and the induced chargeThis of an HSESCA, providesrelationship a theoreticalbetween foundation for thisparticle paper. and the induced charge section buildswhich a quantitative a charged of an HSESCA, which provides a theoretical foundation for this paper. 2.1. Basic Structure of an HSESCA 2.1. Basic Structure of an HSESCA An HSESCA with eight sensor units is installed on a grounded pipeline, as shown in Figure 1. An HSESCA with eight sensor units ishemispherical installed on a probes, grounded pipeline, as shown in Figure 1. It is It is mainly composed of eight identical a multi-channel signal conditioner mainly composed eight identical hemispherical probes, a multi-channel signal conditioner and an and an array signalof analyzer. Compared to a “flat head” probe leaning inward toward the pipeline, array signal analyzer. Compared to a “flat head” probe leaning inward toward the pipeline, it is it is much easier to build a theoretical sensing model for a hemispherical probe, because it much only easier to abuild a theoretical sensing model a hemispherical probe, because it onlybe contains a simple contains simple hemispheric surface. In for addition, a hemispherical probe should more durable hemispheric surface. In addition, a hemispherical probe should more durablesurface than a “flat head” than a “flat head” probe under severe working conditions, as be a hemispheric is free of probe under severe working conditions, as a hemispheric surface is free of damageable edges. damageable edges.
Figure Figure1.1.Schematic Schematicofofaagrounded groundedpipeline-installed pipeline-installedHSESCA. HSESCA.
The hemispherical probes are uniformly installed in a cross-section around the pipeline. It is The hemispherical probes are uniformly installed in a cross-section around the pipeline. It is called called the observation cross-section. Once the charged particles pass, the induced charge will be the observation cross-section. Once the charged particles pass, the induced charge will be generated generated on each probe and then converted into voltage array signals immediately by the on each probe and then converted into voltage array signals immediately by the multi-channel multi-channel signal conditioner for post-processing. Every channel of the conditioner is designed
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as an identical proportional two-stage amplifier as in Figure 2 [9]. The induced charge is proportionally intotwo-stage voltage inamplifier the first as stage and then amplified in theis as anconditioner identicaltransformed proportional in Figure 2 negatively [9]. The induced signal for post-processing. Every channel of the conditioner is designed as an charge identical second stage. Therefore, theinto total function each channel is isrepresented by transformed a negative proportionally transformed in2 the first stage and then negatively amplified in the proportional two-stage amplifier asvoltage in Figure [9].ofThe induced charge proportionally amplification coefficient K whose unit is V/C. A hemispherical probe and its signal conditioner second stage. Therefore, function of each channel is represented by a the negative into voltage in the first stagethe and total then negatively amplified in the second stage. Therefore, total channel compose an independent sensor unit Aofhemispherical the HSESCA.probe The and arrayits analyzer is amplification coefficient whose unit is aV/C. signalunit conditioner function of each channel isKrepresented by negative amplification coefficient K signal whose is V/C. composed of a signal acquisition card andunit a computer. Some specially-designed array signal channel compose an and independent sensor of the HSESCA. The array signal analyzer A hemispherical probe its signal conditioner channel compose an independent sensor unit ofis processing algorithms usually integrated in the to calculate the aarray monitoring composed of a signal acquisition card a computer. Someacquisition specially-designed signal the HSESCA. The array are signal analyzer isand composed of acomputer signal card and computer. parameters (denoted as M) of the whole HSESCA. processing algorithms are usually integrated in the computer calculate thecomputer monitoring Some specially-designed array signal processing algorithms are usually to integrated in the to parameters as M) of the whole HSESCA. calculate the (denoted monitoring parameters (denoted as M) of the whole HSESCA.
Figure 2. Schematic of a proportional two-stage signal conditioner channel. Figure2.2.Schematic Schematicof ofaaproportional proportionaltwo-stage two-stagesignal signalconditioner conditionerchannel. channel. Figure
As the sensitivity characteristics of an electrostatic sensor are quite localized [8–10] and the radiusAsofthe thesensitivity probes is much smaller than distances sensor between between characteristics of anthe electrostatic arethem, quiteinteractions localized [8–10] and the the As the sensitivity characteristics of an electrostatic sensor are quite localized [8–10] and the radius probes can be ignored. Thus, a sensor unit is firstly modeled to lay a foundation for the radius of the probes is much smaller than the distances between them, interactions between the of the probes is much smaller than the distances between them, interactions between the probes can be whole probesHSESCA. can be ignored. Thus, a sensor unit is firstly modeled to lay a foundation for the ignored. Thus, a sensor unit is firstly modeled to lay a foundation for the whole HSESCA. whole HSESCA. 2.2. Theoretical Modeling of a Hemisphere-Shaped Electrostatic Sensor Unit 2.2. Theoretical Modeling of a Hemisphere-Shaped Electrostatic Sensor Unit 2.2. Theoretical Hemisphere-Shaped Electrostatic Sensorcoordinate Unit As shown Modeling in Figureof3,aone sensor unit is kept. A Descartes system is built with the As shown in Figure 3, one sensor unit is kept. A Descartes coordinate system is built with the centerAs of shown the probe’s bottom face set as the origin. The axial direction of the pipeline that of the in Figure 3, one unitorigin. is kept. A axial Descartes coordinate system isand built with the center of the probe’s bottom facesensor set as the The direction of the pipeline and that of the probe are setprobe’s as the bottom x-axis and the as z-axis, respectively. Then, the y-axis is determined byofthe center of the face set the origin. The axial direction of the pipeline and that the probe are set as the x-axis and the z-axis, respectively. Then, the y-axis is determined by the right-hand right-hand rule automatically. Accordingly, a point in the pipeline isthe denoted as P(x, y, z). probe are set as the x-axis and the z-axis, respectively. Then, y-axis is determined by the rule automatically. Accordingly, a point in the pipeline is denoted as P(x, y, z). right-hand rule automatically. Accordingly, a point in the pipeline is denoted as P(x, y, z).
Figure 3. 3. Schematic Schematic of of aa grounded grounded pipeline-installed pipeline-installed sensor Figure sensor unit unit of of the the HSESCA. HSESCA.
Figure 3. Schematic of a grounded pipeline-installed sensor unit of the HSESCA.
19 s), states are are reached reached instantaneously instantaneously (10 (10−−19 Because electrostatic equilibrium states s), the interaction −19 the in by between probe and charged particles the pipeline can be described a Because electrostatic equilibrium states are reached instantaneously (10 pure s), theelectrostatic interaction is determined by Poisson equation and boundary conditions as: field [18,21]. Itprobe is uniquely uniquely determined bythe thein Poisson equation and Dirichlet boundary conditions as: between theIt and charged particles the pipeline can beDirichlet described by a pure electrostatic field [18,21]. It is uniquely determined by the Poisson equation and Dirichlet boundary conditions as: 2 ∈ Γ t Pϕt ( P0,) P=0,ΓP 2 ρt (Pt )P 2 P 0, P Γ 2 ϕ P = const t , P 2 ( ) ( ) ∇ ϕt( P) = (1) P−= ε , s.t. , s. t. ttt P const t , P Γ∈1 Γ1 (1) t P lim ϕt ( P) = 0 t 2 , s.t. lim t PP → t P = (1) P∞const 0 t , P Γ1 P t limΓ2t isPthe 0inner wall of the pipeline. ρt (P) is the where Γ1 is the hemispherical surface of the probe P and where Γ 1 is the hemispherical surface of the probe and Γ2 is the inner wall of the pipeline. ρt(P) is the volume charge density in the pipeline at time t, and ϕt (P) is the corresponding potential distribution. volume in the pipeline at time t, andand φt(P) potential distribution. where Γcharge 1 is thedensity hemispherical surface of the probe Γ2 isis the the corresponding inner wall of the pipeline. ρt(P) is the volume charge density in the pipeline at time t, and φt(P) is the corresponding potential distribution.
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Sensors 2016, 16, 1403 of 23 Besides, const(t) is a constant function of t, describing the equipotential surface of the probe. ε is5the 2 permittivity of free space, and is the Laplace operator. On account of the pipeline being much bigger than the probe, the electrostatic field on the Besides, const(t) is a constant function of t, describing the equipotential surface of the probe. ε is the inner wall is simplified as that on2 one infinite plane [2,6,17]. In this case, when a charged particle is permittivity of free space, and ∇ is the Laplace operator. simplified as a point charge q [8,10], φt(P) is firstly solved using the Green function and the method On account of the pipeline being much bigger than the probe, the electrostatic field on the inner of image charges. Then, the sensing model at P(x, y, z) is obtained according to the relationship wall is simplified as that on one infinite plane [2,6,17]. In this case, when a charged particle is simplified between the induced charge and the potential distribution on a conductor surface [8,9]. That is: as a point charge q [8,10], ϕt (P) is firstly solved using the Green function and the method of image 3 2π y, z) a is obtained according to therelationship between the qa at qzP(x, charges. Then, the sensing model Q x, y , z = d r 2 b2 2 xy cos 2 yr sin 2 rdr 0 on a conductor surface [8,9]. That is: induced charge and the potential 2 0 b distribution 3 4 2 (2) 3 qa z 2πR a R2 a 2a xr cos yr sin 2 3 −2 + qa 3 qz d2π r a+ 2 rdr 2 Q ( x, y, z) = − 2bb− 2π − 2yrsinθ rdr 0 b2 0 0dθ 0h r + b − 2xycosθ i− 32 (2) R R 3 4 2 a qa z 2π a −2a ( xrcosθ +yrsinθ ) rdr + 2πb dθ 0 r2 + 3 0 b2 where Q is the total induced charge on the probe, a is the radius of the probe and b = x 2 y 2 z 2 p iswhere the distance the point charge and the origin. Q is thebetween total induced charge on the probe, a is the radius of the probe and b = x2 + y2 + z2 is the distance between the point charge and the origin. 2.3. Theoretical Modeling of an HSESCA 2.3. Theoretical Modeling of an HSESCA In order to build a sensing model for all of the sensor units in the same coordinate system, order to build sensing model all ofEquation the sensor(2) units in the sameinto: coordinate system, firstly, firstly,Inaccording to theasymmetry of thefor probe, is transformed according to the symmetry of the probe, Equation (2) is transformed into: 3 a qa qb cos 2 Q x, y , z = d r 2 b 2 2br sin sin 2 rdr − 23 bqa qbcosβ 2 R 02π R0 a 2 3 2 Q ( x, y, z) = − rdr (3) 2 b − 2brsinβsinθ 2 b − 0a dθ a04 r 2 + 2 qa 3 cos 2π a r sin sin 2 3 −rdr (3) R R 3 2 + d r + 4 2 2π a qa2 cosβ 0 dθ0 rb22 + a2 − 2ab rsinβsinθ rdr + 2 b2πb 2 b 0 0 b
= arccos( z /) bis) the is included the included between the linethe from the pointtocharge to the where where ββ = arccos(z/b angleangle between the line from point charge the origin and origin and of the probe. Then, a new coordinate Descartes coordinate system is built by translating the axis ofthe theaxis probe. Then, a new Descartes system is built by translating the originalthe one original one 2) (see 2) to of the cross-section. observation cross-section. Meanwhile, theare sensor units (see Figure to Figure the center ofthe thecenter observation Meanwhile, the sensor units numbered are numbered anticlockwise, withof coordinates of the i-th probe as (0, yi, zof i) and those of the anticlockwise, with coordinates the i-th probe denoted as (0,denoted yi , zi ) and those the point charge point charge denoted asthe P(x,new y, z)coordinate in the newsystem; coordinate system; shown denoted as P(x, y, z) in as shown in as Figure 4. in Figure 4.
Figure βi in the new Descartes coordinate system. Figure4.4.Schematic Schematicofofbiband i and βi in the new Descartes coordinate system.
Thereupon, the sensing model of the i-th sensor unit is derived from Equation (3) as: Thereupon, the sensing model of the i-th sensor unit is derived from Equation (3) as: − 3 Ra 2 dθ 0 r2 + bi 2 − 2bi rsinβ i sinθ rdr i 3 −2 R 2π R a 2 a4 3 2a2 i rsinβ i sinθ i + qa cosβ rdr 2 b 0 dθ 0 r + 2 − qa
Qi ( x, y, z) = − b −
qbi cosβ i R 2π 2π 0
2πbi
bi
i
(4)
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where bi is the distance from the charged particle to the i-th probe and βi is the included angle between the point charge and the axis of the i-th probe. They are determined by geometrical relationships: q
bi =
x 2 + ( y − y i )2 + ( z − z i )2
(5)
h i β i = arccos (yi 2 + zi 2 − yyi − zzi )/lbi
(6)
p
where l = yi 2 + zi 2 is the distance between the origin O and the bottom face of a probe. Further, the sensing model of the HSESCA is obtained by making a superposition of sensing models of all of the sensor units. That is: Q A ( x, y, z) = ∑ Qi ( x, y, z) = −∑ i
i
+ ∑ qa i
3 cosβ
2πbi
2
qa bi i
−∑ i
R 2π 0
dθ
qbi cosβ i R 2π 2π 0
Ra 0
r2 +
dθ
a4 bi 2
Ra
−
0
r2 + bi 2 − 2bi rsinβ i sinθ
2a2 i rsinβ i sinθ bi
− 23
− 3
2
rdr (7)
rdr
In addition, an FEM-based calibration method was proposed as a supplement to consider the actual boundary conditions [9]. It is used to improve the accuracy of the sensing models when a charged particle is in the observation cross-section. The main steps are as follows: First, an FEM model of a grounded pipeline-installed probe is built. The model provides simulated induced charge with high fidelity. Then, the relative error between the simulated and the theoretical induced charge is analyzed. On this basis, a calibration item calculated by using fitting methods is added to eliminate the relative error. When the inner radius of the pipeline is 200 mm and the button face of a probe is 2 mm apart away from the inner wall, Equation (4) is calibrated as: ( 0 Qi,x =0 ( y, z )
=
Qi,x=0 (y, z) ( p1 bi p2 + p3 ) Qi,x=0 (y, z)
, if bi ≥ D , if bi < D
(8)
where D = −0.0188 βi + 0.0444 is the calibration boundary that is determined according to the variation trend of the relative error [10]. In the area of bi < D, the relative error is negligible; thus, the sensing model is only calibrated where bi ≥ D. The calibration parameters are obtained using fitting methods; they are: 2 2 p1 = −5.7311 × 10−8 e8.7639βi − 6.103e0.5724βi 2 2 (9) p2 = −43.9996e0.1261βi + 45.9113e0.113βi − 2 2 7.0643×10 β i 4.4059β2i − 4 p3 = 1.0479e + 1.2218 × 10 e 0 It is obvious that Equation (7) is calibrated as Q0A,x=0 (y, z) = ∑ Qi,x =0 ( y, z ). i
3. Definition of the Dynamic Sensitivity of ESA 3.1. Definition of the Static Sensitivity of ESA In order to make a comparison with the dynamic sensitivity of ESA, the static sensitivity of ESA is defined here. The static sensitivity of an electrostatic sensor is defined as the absolute induced charge on the probe generated by a unit charge [7,8,21]. Analogously, the static sensitivity of ESA is defined as the absolute induced charge on all of the probes of an ESA generated by a unit charge. That is: S A ( x, y, z) = −
Q A ( x, y, z) q
(10)
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The minus indicates that the induced charge and the point charge q are of opposite signs. As for an HSESCA, its static sensitivity model is derived from Equations (9) and (10): SA ( x, y, z) = ∑ i
a bi
i + ∑ bi cosβ 2π
R 2π
i
R 2π 3 − ∑ a cosβ2 i 0 2πb i i
dθ
0
dθ
Ra 0
Ra
r2
0
+
r2 + bi 2 − 2bi rsinβ i sinθ
a4 bi 2
−
2a2 i rsinβ i sinθ bi
− 32
− 3
2
rdr (11)
rdr
When actual boundary conditions are considered, the model in the observation cross-section can also be calibrated in a similar way as Equation (8), that is S0A,x=0 (y, z) = − Q0A,x=0 (y, z) /q. 3.2. Theoretical Array Signals of an HSESCA Array signal processing algorithms are included in the definition of the dynamic sensitivity of ESA. In order to find effective array signal processing algorithms for an HSESCA, the characteristics of its array signal shave to be analyzed. It is assumed that a charged particle moves along the pipeline’s axial direction at a constant velocity [10,32]. In this case, the x-coordinates of the particle are denoted with velocity v and time t, while the y-coordinates and z-coordinates are regarded as constants. In this way, induced charge on the i-th probe is expressed by Qi (x0 + vt, y, z), where x0 is the initial x-coordinate. After that, the induced charge is transformed and amplified into voltage according to the amplification coefficient K of the signal conditioner (see Figure 4), thus obtaining the out-put signal of the i-th sensor unit. That is: ui (t) = KQi ( x0 + vt, y, z)
(12)
Then, by combining Equations (4) and (12), one can get: ui ( t ) = −
− 3 Ra 2 rdr dθ 0 r2 + bi 2 − 2bi rsinβ i sinθ 3 − R R 3 2 2 2π a 2a i rsinβ i sinθ a4 2 i + qKa cosβ rdr 2 b 0 dθ 0 r + 2 −
qKa bi
−
qKbi cosβ i R 2π 2π 0
2πbi
q
bi
(13)
i
where bi = ( x0 + vt)2 + (y − yi )2 + (z − zi )2 . In order to provide a visualized view of the array signals, here, we set K = −1, q = 1C, and the time when the particle reaches the observation cross-section is set as the zero time (i.e., x0 = 0). The radius of the hemispherical probes is set to 12 mm, and the motion path is set to y = 100 mm and z = 70 mm (see Figure 3). Besides, the velocities of the charged particle are set to 1 m/s, 2 m/s and 3 m/s, respectively. Then, the array signals of the HSESCA are calculated by using Equation (13), as shown in Figure 5. This shows that all of the signal peaks umax,i appear when the charged particle reaches the observation cross-section; when q is set as a constant, the i-th peak is just determined by the relative position between the motion path and the i-th sensor unit, but has nothing to do with the particle’s velocity. Moreover, it is obvious that the peaks will change if the position of the charged particle changes. In a word, different combinations of peaks of the array signals indicate different position information of the charged particle in the observation cross-section. In order to build a quantitative and direct relationship between a charged particle and the out-put signal peaks of a single electrostatic sensor, the dynamic sensitivity of the electrostatic sensor was proposed by us. It is defined as the absolute value of the out-put signal peak of an electrostatic sensor when a unit point charge passes [9]. As for the i-th sensor unit, the relationship is built by its dynamic sensitivity model as: 0 KQi,x umax,i =0 ( y, z ) SD,i (y, z) = = (14) q q 0 where Qi,x =0 ( y, z ) is shown as Equation (8).
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It is worth noting that in many applications, the monitoring parameters are reflected by the charge quantity of the monitored particles directly or indirectly, such as the particle size, concentration, flow rate, etc. [4,33]. Therefore, it is significant to ensure that the charge quantity of any particle can be accurately monitored no matter where it crosses the observation cross-section. Accordingly, a reasonable way of processing the array signals is as follows: first, obtaining the position information of the monitored particles from the array signals; then, weighting the signal components induced by particles in the less sensitive area according to the position information. In this way, the charge quantity of 16, any particle can be effectively reflected. Sensors 2016, 1403 8 of 22
Figure5.5.(a–h) (a–h)Theoretical Theoreticalarray arraysignals signalsof ofthe theHSESCA HSESCAfrom fromNo. No.1–No. 1–No.88sensor sensorunits. units. Figure
In orderand to build a quantitative and direct relationship 3.3. Definition Interpretation of the Dynamic Sensitivity of ESA between a charged particle and the out-put signal peaks of a single electrostatic sensor, the dynamic sensitivity of the electrostatic Thewas aimproposed of proposing theItdynamic sensitivity of ESA isvalue to build a direct relationship between sensor by us. is defined as the absolute of the out-put signal peak of an moving charged particles thepoint monitoring parameters offor an the ESA, thus reflecting its monitoring electrostatic sensor when and a unit charge passes [9]. As i-th sensor unit, the relationship accuracy “Dynamic” heremodel has two is built bydirectly. its dynamic sensitivity as:implications: the first is making a distinction from static sensitivity, that is dynamic sensitivity is proposed for moving charged particles; the second is that the uESA KQi, x 0 ( y , z ) according to different array signal ,i is changeable specific expression of the dynamic sensitivity SD ,i y , z =of max (14) q q processing algorithms. More detailed interpretations are provided by taking intermittent particle monitoring, for example, as follows. where Qi, x 0 ( y , z ) is shown as Equation (8). In some applications, the particles to be monitored are intermittent. One representative application It is worth noting that in many applications, the monitoring parameters are reflected by the is exhaust debris monitoring-based PHM of gas turbines. When faults (e.g., fatigue or carbon charge quantity of the monitored particles directly or indirectly, such as the particle size, deposition) occur on gas path components of gas turbines, some fault-related particles will be concentration, flow rate, etc. [4,33]. Therefore, it is significant to ensure that the charge quantity of produced and charged. Thus, the condition information of the gas path components can be obtained any particle can be accurately monitored no matter where it crosses the observation cross-section. by monitoring the particles [1,6,7,28]. In general, the fault-related particles are intermittent. Moreover, Accordingly, a reasonable way of processing the array signals is as follows: first, obtaining the it is considered that larger particles carry greater charge, which indicates more serious faults [1,7]. position information of the monitored particles from the array signals; then, weighting the signal Therefore, the charge quantity of any fault-related particle should be accurately monitored. components induced by particles in the less sensitive area according to the position information. In As for a single electrostatic sensor, for example the i-th sensor unit of the HSESCA, its dynamic this way, the charge quantity of any particle can be effectively reflected. sensitivity model builds a relationship between moving charged particles and its out-put voltage signals, as Equation (14). This is expressed by Figure 6. 3.3. Definition and Interpretation of the Dynamic Sensitivity of ESA The aim of proposing the dynamic sensitivity of ESA is to build a direct relationship between moving charged particles and the monitoring parameters of an ESA, thus reflecting its monitoring accuracy directly. “Dynamic” here has two implications: the first is making a distinction from static sensitivity, that is dynamic sensitivity is proposed for moving charged particles; the second is that the specific expression of the dynamic sensitivity of ESA is changeable according to different array signal processing algorithms. More detailed interpretations are provided by taking intermittent particle monitoring, for example, as follows. In some applications, the particles to be monitored are intermittent. One representative
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faults [1,7]. Therefore, the charge quantity of any fault-related particle should be accurately faults [1,7]. Therefore, the charge quantity of any fault-related particle should be accurately monitored. monitored. As for a single electrostatic sensor, for example the i-th sensor unit of the HSESCA, its dynamic As formodel a singlebuilds electrostatic sensor, for example the i-th sensor particles unit of the HSESCA, its dynamic sensitivity a relationship between moving charged and its out-put voltage Sensors 2016, 16, 1403 9 of 23 sensitivity model builds a relationship between moving charged particles and its out-put voltage signals, as Equation (14). This is expressed by Figure 6. signals, as Equation (14). This is expressed by Figure 6.
qS D,i ( y, z ) qS D,i ( y, z )
Figure Figure 6. 6. Signal Signal flow flow diagram diagram of of the the i-th i-th sensor sensor unit unit of of the the HSESCA. HSESCA. Figure 6. Signal flow diagram of the i-th sensor unit of the HSESCA.
This means that a charged particle contains two kinds of information, charge quantity q and This means that a charged contains two kinds of information, charge quantity q and charged particle information, to the unit’s dynamic sensitivity position (y, z). They codetermine the signal peak umax,i according position (y, z). They codetermine the signal peak u according to the unit’s dynamic sensitivity max,i according to (y,(y,z).z), thatcodetermine signal peak umax,i is umax,i = qSthe D,i(y, z). However, the relationship is irreversible in practical model SD,i model SSD,i (y, z), that is = qSD,i (y, z). z). However, However, the the relationship relationship is irreversible irreversible in practical D,i(y, is uumax,i max,i = practical D,i(y, applications. This is because the position information is difficult to is obtain by using a single applications. This is is because the the position information is difficult to obtaintobyobtain using aby single electrostatic applications. This because position information is difficult using a single q electrostatic sensor; thus, the value of SD,i(y, z) is not determined. As a result, the charge quantity sensor; thus, the value of S (y, z) is not determined. As a result, the charge quantity q cannot beq D,i(y, z) is not determined. As a result, the charge quantity electrostatic sensor; thus, the value of S D,i cannot be calculated backward for the lack of position information. This is the basic reason for the calculated for the lack of This is the basic reason for the low monitoring cannot be backward calculated backward forposition the lackinformation. of position low monitoring accuracy of a single electrostatic sensor. information. This is the basic reason for the accuracy of a single electrostatic sensor. low monitoring accuracy of a single electrostatic sensor. It has been mentioned that the array signals of an HSESCA contain the position information of It has been mentioned that the array signals of an contain the position information of an HSESCA HSESCA positionaccuracy a monitored particle (see Section 3.2), which can be used to improve the monitoring of the a monitored particle (see Section 3.2), which can be used to improve the monitoring accuracy of the HSESCA. This is expressed by Figure 7. HSESCA. This is expressed expressed by by Figure Figure 7. 7.
qS D,1 ( y, z ) qS D,1 ( y, z )
qS D,2 ( y, z ) qS D,2 ( y, z )
qS D,3 ( y, z ) qS D,3 ( y, z )
qS D,4 ( y, z ) qS D,4 ( y, z )
qS D,5 ( y, z ) qS D,5 ( y, z )
qS D,6 ( y, z ) qS D,6 ( y, z )
qS DA ( y, z ) qS DA ( y, z )
( y, z ) ( y, z )
Figure 7. Signal flow diagram of the HSESCA. Figure 7. 7. Signal Signal flow flow diagram diagram of of the the HSESCA. HSESCA. Figure
This means that a charged particle contains two kinds of information, charge quantity q and This means that a charged particle contains two kinds of information, charge quantity q and max,i of each sensor unit according to its dynamic position z). They the signal peak utwo This(y, means thatcodetermine a charged particle contains kinds of information, charge quantity q and max,i of each sensor unit according to its dynamic position (y, z). They codetermine the signal peak u (y, z). Then,the the peaks areu processed by a certain array signal processing sensitivity SD,i position (y, model z). They codetermine signal peak max,i of each sensor unit according to its dynamic D,i(y, z). Then, the peaks are processed by a certain array signal processing sensitivity model S algorithm to calculate monitoring M.byIn this process, the processing estimatedalgorithm position sensitivity model SD,i (y, z).the Then, the peaks parameter are processed a certain array signal algorithm to(y’,calculate the monitoring parameter M.and In used. this Therefore, process, the estimated position D,i(y, z) are information z’) of the particle is usually obtained valves of S to calculate the monitoring parameter M. In this process, the estimated position information (y’, z’) of D,i(y, z) are information (y’, z’) of the particle is usually obtained and used. Therefore, valves of S determined the position making valves it possible the charge quantity q the particle isby usually obtainedinformation, and used. Therefore, of S to (y, calculate z) are determined by the position determined by the position information, making it possibleD,ito calculate the charge quantity q information, making it possible to calculate the charge quantity q backward. In fact, the monitoring parameters of many applications are just the charge quantity or some derivative values of it. As a
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result, by using an HSESCA and corresponding array signal processing algorithms, the monitoring accuracy can be improved. In order to provide a unified and convenient expression for different array signal processing algorithms, dynamic operator FD is proposed to denote the array signal processing algorithms. It builds the relationship between the array signals and monitoring parameters of an ESA (see Figure 7). Further, the dynamic sensitivity of ESA is defined in the observation cross-section as the absolute value of a monitoring parameter when a unit charge passes. As for intermittent particle monitoring, the dynamic sensitivity model of an HSESCA is expressed as: M FD [Umax (y, z)] FD [qSD (y, z)] = | FD [SD (y, z)]| SDA (y, z) = = = q q q
(15)
where U max (y, z) is the vector of the signal peaks and SD (y, z) is the vector of dynamic sensitivity values of the sensor units. The q is reducible because FD has to be designed as a linear operator of q. It is seen from Equation (15) that the essence of the dynamic sensitivity of ESA is a recombination of the dynamic sensitivity of the sensor units according to a dynamic operator, which builds a direct relationship between moving charged particles and the system monitor values of an ESA. In other words, the dynamic sensitivity of ESA reflects the monitoring accuracy of an ESA directly by taking array signal processing algorithms into consideration. The concept of dynamic sensitivity has been used by Zhou et al. [34], but the physical meaning is quite different. 4. A Component Extraction-Based Array Signal Processing Algorithm for Intermittent Particles A proper array signal processing algorithm is significant to ensuring the monitoring accuracy of an ESA. As for intermittent particle monitoring (e.g., exhaust debris monitoring-based PHM of gas turbines), it has been mentioned that the accurate charge quantity of any monitored particle is desired; thus, the position information of the particle should be used. In addition, the demand for real-time monitoring should be met to avoid missing momentary faults; thus, the corresponding array signal processing algorithms have to be fast enough. To meet the conditions above, a component extraction-based array signal processing algorithm is designed. It is based on a simple idea that a monitored particle is located near the sensor units that produce larger signal peaks. According to this idea, a set of common components is extracted from the peaks of the array signals. The components are considered to be generated by a set of imaginary point charges. They have fixed positions, but their imaginary charge quantities vary with the position of the monitored particle. In this way, the position information of the monitored particle can be used according to different charge quantities of the imaginary point charges. It is worth noting that the accurate position of a particle is not needed in the algorithm, but it is made use of by introducing a component extraction-based method. As a result, the algorithm only contains some simple steps, which are convenient for computer processing. More details are provided as follows. As shown in Figure 8, three main steps and one pre-step are contained in the component extraction-based array signal processing algorithm. The condition in Figure 4 is taken as an example below, that is to say, the HSESCA contains eight sensor units, and a charged particle moves along a motion path of y = 100 mm and z = 70 mm. The first step is re-sorting. When a charged particle passes the observation cross-section, the corresponding signal peaks of the eight sensor units are recorded as a vector U max . Then, U max is re-sorted into U r incrementally according to the absolute values of the signal peaks. That is to say, the i-th absolute smallest peak is denoted as uri ; thus, the new vector is U r {ur1 , ur2 , ur3 , ur4 , ur5 , ur6 , ur7 , ur8 }. For example, the No. 2 probe is the nearest one to the point charge, while the No. 6 probe is the farthest one to the point charge (see Figure 3); thus, according to the fact that nearer probes produce larger signal peaks, one will have ur1 = umax,6 , ur8 = umax,2 .
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W C
Figure 8. Flow diagram of of the component arraysignal signal processing algorithm. Figure 8. Flow diagram the componentextraction-based extraction-based array processing algorithm.
The The second stepstep is component clear that thataamonitored monitored particle is located second is componentextraction. extraction. It It is is clear particle is located nearnear the the sensor units thatthat produce larger if aasignal signalcomponent component is only contained in one sensor units produce largersignal signalpeaks. peaks. Thus, Thus, if is only contained in one signal peak, its value implies how close the particle is to the corresponding sensor probe. Analogously, signal peak, its value implies how close the particle is to the corresponding sensor probe. if a signal component contained in is every signal peak, its value implies howits close the particle to theclose Analogously, if a signaliscomponent contained in every signal peak, value impliesishow central point. Accordingly, a set of common signal components is extracted from U by using Equation r the particle is to the central point. Accordingly, a set of common signal components is extracted (16). In detail, the absolute smallest signal peak u is firstly denoted as c ; it is a common signal as c1; r1 1 from Ur by using Equation (16). In detail, the absolute smallest signal peak ur1 is firstly denoted component contained in every signal peak. Then, the second absolute smallest peak ur2 is denoted as it is a common signal component contained in every signal peak. Then, the second absolute smallest the sum of c1 and c2 . It is obvious that c2 is a common signal component contained in every signal peak ur2 is denoted as the sum of c1 and c2. It is obvious that c2 is a common signal component peak, except ur1 , and so on; a vector of eight common signal components is extracted from U r , that is contained except ur1, and so on; a vector of eight common signal components C{c1 ,c2 ,inc3 every , c4 , c5 , signal c6 , c7 , c8peak, }. is extracted from Ur, that is C{c 1,c2, c3, c4, c5, c6, c7, c8}.
ur1 = c1 ur 1 c1 u u c c r2 = c1 + c2 1 u2 = c + c2 + c3 r2 c 2 r3 c 3 1 ur 3 c1 ur4c = cc1 + cc42 + c3 + c4 ur 4 c 1 2 3 u cur5= c3c+ c4 + c5 c 2 c1 + c 3 c2 c+4 1 5 r5 u = c + c + c +cc54 +cc6 5 + c6 u c c c r6 2 3 1 r6 1 2 3 4 uur 7r7=c 1c c4c+ c5c + c6c 7+ c7 c 2 c2 + c 3 c3 c+4 1+ 5 6 u c c c c c c c 8c8 u r8r 8= c11+ c22 + 33 + c44 + c55 + c6 6 +c 7c7+
(16)
(16)
The The third stepstep is weighting ofall, all,the theextracted extracted signal components third is weightingand andsummation. summation. First First of signal components are are considered to generated be generated setofofimaginary imaginary point based on on the the symmetry of of considered to be byby a aset pointcharges. charges.InIndetail, detail, based symmetry the circular array and the idea that a charged particle is located near the sensor units that produce the circular array and the idea that a charged particle is located near the sensor units that produce larger signal peaks, imaginarypoint pointcharge charge qq11 located located in point is firstly assumed to to inthe thecentral central point is firstly assumed larger signal peaks, an an imaginary generate c1 . Then, because c2 is contained in every signal peak, except that of the No. 6 sensor unit, an generate c1. Then, because c2 is contained in every signal peak, except that of the No. 6 sensor unit, imaginary point charge q is located in the connection line between the origin, and the No. 2 probe an imaginary point charge 2q2 is located in the connection line between the origin, and the No. 2 is assumed to generate c2 . Analogously, as c3 is produced by every sensor unit except the No. 5 probe is assumed to generate c2. Analogously, as c3 is produced by every sensor unit except the No. 5 and No. 6 sensor units, q3 located in the bisector of the No. 1 and the No. 2 probes is assumed to 3 located in the bisector of the No. 1 and the No. 2 probes is assumed to and generate No. 6 sensor c3 , andunits, so on;qeight imaginary point charges are decomposed from the charged particle q, as so 9. on;Among eight them, imaginary point charges are decomposed from the2charged particle q, generate c3,inand shown Figure the point charge q8 should be quite close to the No. probe, because quite of close to the No.point 2 probe, as shown in Figure Among them, point charge q8 should its relevant signal9.component is onlythe produced by that probe. The be positions the imaginary because its are relevant signal component produced that probe. Thetheir positions of the charges considered to be fixed due toistheonly symmetry of theby HSESCA. However, imaginary imaginary point charges are considered to be fixed due to the symmetry of the HSESCA. However, their imaginary charge quantities, which are determined by the values of the extracted components, vary with the position of the monitored particle. In other words, the charge quantities of the imaginary point charges imply the position information of the monitored particle.
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charge quantities, which are determined by the values of the extracted components, vary with the position of the monitored particle. In other words, the charge quantities of the imaginary point charges Sensors 2016,the 16, position 1403 12 of 22 imply information of the monitored particle.
Figure 9. 9. The original particleqqand anditsitsimaginary imaginary point charges. Figure The originalcharged charged particle point charges.
Next, thethecharge quantitiesof of imaginary point charges are calculated, can be Next, charge quantities thethe imaginary point charges are calculated, which can bewhich regarded regarded as a process of weighting the components extracted components the position information. as a process of weighting the extracted according to according the positiontoinformation. According According to the dynamic sensitivity model of the sensor units as Equation (14), the i-th imaginary to the dynamic sensitivity model of the sensor units as Equation (14), the i-th imaginary point charge /sithe , where si issensitivity the dynamic of unit the at No. sensor of unit at point charge is as expressed qi = sci iis is expressed qi = ci /si , as where dynamic of thesensitivity No. 2 sensor the2position qi . By recording: the position of qi. By recording: wi = 1/si
wi = 1/si
(17)
one will have qi = wi ci , where wi is just the weight coefficient of ci . = wmonitoring ici, where w i is just the coefficient of ci.up the imaginary point charges: one will Finally, have qithe parameter M weight is obtained by summing
(17)
Finally, the monitoring parameter M is obtained by summing up the imaginary point charges: M=
∑ qi = W · C
i q W C M i i
(18)
(18)
where W is the vector of the weight coefficients and C is the vector of the extracted signal components. where W q is the vector of thelines weight andcomponents C is the could vectorbeof thebut extracted When is in some symmetric of thecoefficients HSESCA, some zero, it does notsignal affect the computing components. When q isprocess. in some symmetric lines of the HSESCA, some components could be zero, W is determined the pre-stepprocess. (see Figure 8). Firstly, according to the estimated positions of the but it does not affect theincomputing imaginary point charges, an initial value each weight coefficient is set using (17). Then, of W is determined in the pre-step (seeofFigure 8). Firstly, according to theEquation estimated positions the initial values are optimized by numerical simulations to make M and q as close as possible in the (17). the imaginary point charges, an initial value of each weight coefficient is set using Equation whole observation cross-section. In this study, W was finally determined as {238, 232, 208, 122, 119, Then, the initial values are optimized by numerical simulations to make M and q as close as 98, 31, 0.9} when K = −1. As for a certain HSESCA, the pre-step needs to be done only once, then the possible in the whole observation cross-section. In this study, W was finally determined as {238, 232, weight coefficients are regarded as a priori values in calculating M. 208, 122,According 119, 98, 31, 0.9} when K = −1. As for a certain HSESCA, the pre-step needs to be done only to the definition of the dynamic sensitivity of ESA, the dynamic sensitivity in once, then the weight are regarded asarray a priori values in calculating accordance with thecoefficients component extraction-based signal processing algorithmM. is modeled as:
According to the definition of the dynamic of ESA, the dynamic sensitivity in sensitivity M W · C accordance with the component extraction-based = signal processing algorithm is modeled SDA (y, z) = array (19) as: q q M W C S DA of y , the z HSESCA at different positions in the observation (19) This reflects the monitoring accuracy q q cross-section after adopting the algorithm.
This reflects the monitoring accuracy of the HSESCA at different positions in the observation cross-section after adopting the algorithm. It is seen from the steps that the accurate position of the monitored particle was not obtained. However, the position information was made use of by using the component extraction-based method. In addition, even accurate positions of the imaginary point charges were not necessary. As a result, the proposed array signal processing algorithm only contains some simple steps, making it
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It is seen from the steps that the accurate position of the monitored particle was not obtained. SensorsHowever, 2016, 16, 1403 13 of 22 the position information was made use of by using the component extraction-based method.
In addition, even accurate positions of the imaginary point charges were not necessary. As a result, the
5. Numerical Experiment proposedSimulation array signal and processing algorithm only contains some simple steps, making it promising in applications that need fast processing of the array signals.
5.1. Simulated Results and Discussion
5. Numerical Simulation and Experiment
5.1.1. Simulated Dynamic Sensitivity of the Sensor Units 5.1. Simulated Results and Discussion
As mentioned above, an HSESCA with eight sensor units is installed on a grounded pipeline. 5.1.1. Simulated Dynamic Sensitivity of the Sensor Units The pipeline has an inner radius of 200 mm; the hemispherical probes have a radius of 12 mm with As mentioned above, an HSESCA withwall eightof sensor is installed onsake a grounded pipeline.the their button faces 2 mm far from the inner the units pipeline. For the of simplicity, The pipeline has an inner radius of 200 mm; the hemispherical probes have a radius of 12 mm with their the amplification coefficient of the signal conditioner is set to K = −1. Under these conditions, button faces 2 mm the units inner is wall of the pipeline. For the sake of (14) simplicity, amplification dynamic sensitivity of far thefrom sensor calculated by using Equation at the the grid points shown coefficient of the signal conditioner is set to K = − 1. Under these conditions, the dynamic sensitivity of in Figure 10. It is seen that the grid points are representative, as they cover almost the whole the sensor units is calculated by using Equation (14) at the grid points shown in Figure 10. It is seen observation cross-section. that the grid points are representative, as they cover almost the whole observation cross-section.
Figure Grid points theobservation observation cross-section. Figure 10. 10. Grid points ininthe cross-section.
The simulated results shown thesurface surfacediagrams diagrams in Figure that thethe sensor The simulated results are are shown byby the Figure11. 11.ItItisisseen seen that sensor the same dynamic sensitivity becausethey they are are identical identical in except thatthat the the units units have have the same dynamic sensitivity because ingeometry, geometry, except ◦ in turn, according to the positions of the units. In addition, as for any sensor unit, diagrams rotate 45 diagrams rotate 45° in turn, according to the positions of the units. In addition, as for any sensor its dynamic reaches the maximum value value near the probe it decreases unit, its dynamicsensitivity sensitivity reaches the maximum near thesurface, probe and surface, and it sharply decreases as the distance to the probe increases. To make a quantitative view, the contour diagram of the No. 7 sharply as the distance to the probe increases. To make a quantitative view, the contour diagram of sensor unit is provided as Figure 12. It shows that the dynamic sensitivity is greater than 0.9 near the No. 7 sensor unit is provided as Figure 12. It shows that the dynamic sensitivity is greater than the probe surface. However, it decreases to below 0.1 just about 30 mm away and decreases to below 0.9 near theabout probe surface. However, it decreases to below 0.1 just about 30units mm is away and decreases 0.001 150 mm away. In a word, the dynamic sensitivity of the sensor inhomogeneous to below 0.001localized, about 150 mm away. a word, thesensor dynamic sensitivity of thedetect sensor units is and quite which means thatIn a hemispherical unit can only effectively charged inhomogeneous and quite localized, which means that a hemispherical sensor unit can only particles near its probe. Therefore, it is of practical value to overcome this drawback by using ESAs, effectively detect charged particlesaccuracy. near its probe. Therefore, it is of practical value to overcome this thus improving the monitoring drawback by using ESAs, thus improving the monitoring accuracy.
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Figure 11.(a–h) (a–h) Surface diagrams ofofdynamic dynamic sensitivityof ofthe the sensor units from No. 1–No. 8. Figure 11. (a–h) Surface diagrams dynamicsensitivity sensitivity sensor units from No.No. 1–No. 8. 8. Figure 11. Surface diagrams of of the sensor units from 1–No.
Figure Contourdiagram diagramof of dynamic dynamic sensitivity thethe No. 7 sensor unit.unit. Figure 12.12. Contour sensitivityofof No. 7 sensor
Figure 12. Contour diagram of dynamic sensitivity of the No. 7 sensor unit.
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5.1.2. Simulated Static Sensitivity of the HSESCA 5.1.2. Simulated Static Sensitivity of the HSESCA The static sensitivity of the HSESCA in the observation cross-section is calculated by using The static sensitivity of the HSESCA in the observation cross-section is calculated by using Equation (11) and the calibration method. The results are shown in Figure 13. Equation (11) and the calibration method. The results are shown in Figure 13.
Figure 13. 13. (a) (a) Surface Surface and and (b) (b) contour contour diagrams diagrams of of the the static static sensitivity sensitivity of of the the HSESCA. HSESCA. Figure
It is is seen seenfrom fromFigure Figure 13 that, in observation the observation cross-section, thesensitivity static sensitivity of the 13 that, in the cross-section, the static of the HSESCA HSESCA symmetrically in accordance with the distribution of the probes. In addition, distributesdistributes symmetrically in accordance with the distribution of the probes. In addition, just like the just like the dynamicofsensitivity of a certain sensor the static sensitivity ofreaches the HSESCA reaches dynamic sensitivity a certain sensor unit, the staticunit, sensitivity of the HSESCA the maximum the maximum value than 0.9 near probes, and it decreases sharply distance to the value greater than 0.9greater near the probes, and the it decreases sharply as distance to theasprobes increases. probes increases. In most of the central area, the values of static sensitivity are below 0.05. That is to In most of the central area, values of static sensitivity are below 0.05. That is to say, the static say, the static sensitivity HSESCA is inhomogeneous and which quite localized, which means that sensitivity of the HSESCAofisthe inhomogeneous and quite localized, means that an HSESCA will an will onlycharged effectively detect particles near the summation probes if just using the onlyHSESCA effectively detect particles nearcharged the probes if just using of the induced summation of the induced charges to reflect the charge quantity of a monitored particle. Definitely, charges to reflect the charge quantity of a monitored particle. Definitely, the static sensitivity in the the static sensitivity in the center region can improved by increasing size and of center region can be improved by increasing thebesize and number of probes. the However, thisnumber will cause probes. However, this will problems in installation increase the disturbance to to theensure flow. problems in installation andcause increase the disturbance to theand flow. Therefore, it is advisable Therefore, it isaccuracy advisable to center ensureregion the monitoring accuracyarray in the center region algorithms. by using the monitoring in the by using appropriate signal processing appropriate array signal processing algorithms. 5.1.3. Simulated Dynamic Sensitivity of the HSESCA 5.1.3.For Simulated Sensitivity of the the sakeDynamic of simplicity, here, we setHSESCA the amplification coefficient K = −1. Then, by placing a pointFor charge q = 1 of C in turn at each grid shown in Figure coefficient 10, the corresponding signal peaks of the sake simplicity, here, wepoint set the amplification K = −1. Then, by placing a point charge q = 1 C in turn at each grid point shown in Figure 10, the corresponding signal peaks of
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ofsensor the sensor units are calculated using Equation (14). they Next, are processed by the all ofallthe units are calculated using Equation (14). Next, arethey processed by the component component extraction-based array signal processing algorithm (see Section 4) to get the monitoring extraction-based array signal processing algorithm (see Section 4) to get the monitoring parameter parameter value corresponding to each grid point. In this way, the values of dynamic sensitivity at value corresponding to each grid point. In this way, the values of dynamic sensitivity at all of the grid all of the grid points are obtained. The results are shown in Figure 14. points are obtained. The results are shown in Figure 14.
Figure 14. 14. (a)(a) Surface and (b) dynamicsensitivity sensitivityofof the HSESCA. Figure Surface and (b)contour contourdiagrams diagrams of the dynamic the HSESCA.
is seen from Figure that dynamic sensitivityofofthe theHSESCA HSESCAdistributes distributes symmetrically symmetrically in It isItseen from Figure 14 14 that thethe dynamic sensitivity in accordance with the distribution of the probes. In addition, it is obvious that the dynamic accordance with the distribution of the probes. In addition, it is obvious that the dynamic sensitivity sensitivity has relatively high values, not only near the probes, but also in most of the area of the has relatively high values, not only near the probes, but also in most of the area of the observation observation cross-section. By making a comparison between Figures 13 and 14, it is shown that the cross-section. By making a comparison between Figures 13 and 14, it is shown that the dynamic dynamic sensitivity and the static sensitivity have close values near the probes and the inner wall of sensitivity and the static sensitivity close near the probes and the inner wall theof pipeline. the pipeline. However, the meanhave value of values the static sensitivity is only about 0.04 in of most the However, mean value sensitivity is only about 0.04 0.95. in most the central area, while central the area, while thatof ofthe thestatic dynamic sensitivity reaches about Theofsensitivity represents thatcharge of the measurement dynamic sensitivity reaches sensitivity accuracy, that isabout to say0.95. the The closer to one therepresents sensitivitycharge is, the measurement higher the accuracy, that is to say the closer to one the sensitivity is, the higher the accuracy is. Therefore, in the accuracy is. Therefore, in the case of intermittent particle monitoring, the monitoring ability gets caseenhanced of intermittent particle monitoring, the monitoring ability getsthe enhanced by 23 times in most of by 23 times in most of the central area because of using component extraction-based array signal processing algorithm, which implies significantarray improvements in sensitivity the central area because of using the component extraction-based signal processing algorithm, homogeneity and monitoring accuracyinof the HSESCA. Furthermore, it shows that there still which implies significant improvements sensitivity homogeneity and monitoring accuracy of the distribute relatively low values near the inner wall of the pipeline, except where the probes are HSESCA. Furthermore, it shows that there still distribute relatively low values near the inner wall of located. This is unavoidably caused the influence of the pipeline on the field. the pipeline, except where the probes arebylocated. This is unavoidably caused byelectrostatic the influence of the However, using a strategy to optimize the number of sensor units combined with optimizations pipeline on the electrostatic field. However, using a strategy to optimize the number of sensor on units the proposed algorithm is likely to alleviate this drawback, which deserves further studies.
combined with optimizations on the proposed algorithm is likely to alleviate this drawback, which deserves further studies.
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5.2.Experimental ExperimentalResults Resultsand andDiscussion Discussion 5.2. 5.2. Experimental Results 5.2.1.Experiment ExperimentApparatus Apparatus 5.2.1. 5.2.1. Experiment Apparatus Experimentalresults resultswere wereobtained obtainedby byusing usingan aneight-channel eight-channelHSESCA HSESCA experiment apparatus. Experimental obtained by using eight-channel HSESCAexperiment experiment apparatus. Experimental results apparatus. As showninin inFigure Figure15, 15,the theexperiment experimentapparatus apparatusis mainlycomposed composedof ofan anelectrostatic electrostaticgenerator, generator, a As shown generator, As shown Figure 15, the experiment apparatus isismainly mainly composed electrostatic particle release device, pipeline, an HSESCA, HSESCA, Faraday cylinder and aa computer. computer. The particle release device, a pipeline, an HSESCA, a Faraday cylinder cylinder and a computer. The electrostatic aa particle release device, aa pipeline, an aa Faraday and The electrostatic generator produces ionized air in the particle release device by high voltage, which generator produces ionized air inionized the particle devicerelease by highdevice voltage, makes released electrostatic generator produces air inrelease the particle by which high voltage, which makes released released particles particles charged. An HSESCA that has has eight sensor sensor units isis installed installed in the the particles charged. An HSESCA that has eight sensor that units is installed in the midsection of the grounded makes charged. An HSESCA eight units in midsection of the the grounded grounded pipeline. produces array signals when a charged charged particle falls midsection of pipeline. produces array signals when particle falls pipeline. It produces array signals when aItIt charged particle falls through the apipeline. Then, the signals through the pipeline. Then, the signals are processed by using specially-designed software through the by pipeline. Then, the signalssoftware are processed by inusing specially-designed software are processed using specially-designed integrated the computer. The Faraday cylinder integratedwith in the the computer. The Faradaybelow cylinder connected with charge meter placed below below integrated in computer. The cylinder with aa charge meter isis placed connected a charge meter is Faraday placed theconnected pipeline. A charged particle will finally fall into the pipeline. A charged particle will finally fall into the Faraday cylinder; thus, the charge quantity the pipeline. A charged particle will finally fall into the Faraday cylinder; thus, the charge quantity the Faraday cylinder; thus, the charge quantity of the particle is read from the charge meter with a ofthe theparticle particleisisread readfrom fromthe thecharge chargemeter meter withaameasurement measurement resolutionof of11pC. pC.Steel Steelballs ballswith with of measurement resolution of 1 pC. Steel ballswith with a diameter of 2resolution mm are used as the experimental a diameter of 2 mm are used as the experimental particles. To create a consistent condition with the a diameter 2 mmaare used as the experimental particles. To create a consistent condition the particles. Toofcreate consistent condition with the numerical simulation, the pipeline haswith an inner numerical simulation, the pipeline has an inner radius of 200 mm; the hemispherical probes have a numerical simulation, the pipeline has an inner of 200 mm; hemispherical radius of 200 mm; the hemispherical probes haveradius a radius of 12 mmthe with their buttonprobes faces 2have mm afar radiusof of12 12mm mmwith withtheir theirbutton button faces 2 mm far from the inner wall of the pipeline. radius from the inner wall of the pipeline.faces 2 mm far from the inner wall of the pipeline.
Figure Structure of the HSESCA experiment apparatus. apparatus. Figure15. 15.Structure Structureof ofthe theHSESCA HSESCAexperiment experiment Figure 15. apparatus.
Inthe theexperiment, experiment,the the particles were released different test points, as shown shown in Figure Figure 16. In particles were released atatat different test points, asas shown in in Figure 16.16. The In the experiment, the particles were released different test points, The points were set along two typical lines in the observation cross-section. Line 1 is the axis of the points were were set along two typical lines lines in theinobservation cross-section. LineLine 1 is the of the The points set along two typical the observation cross-section. 1 is axis the axis of No. the 1 No. 11unit, sensor unit, and Line the bisector ofand thethe No. and the No. No. sensor units. Each12 line No. sensor 22 isis the the No. 11 and the 88 sensor units. Each line sensor andunit, Lineand 2 is Line the bisector of bisector the No. 1of No. 8 sensor units. Each line contains test contains 12test test points, which areuniformly uniformly spaced by15 15to mm. Inorder order toreduce reduce theposition position error contains 12 which are spaced by mm. In to the error points, which arepoints, uniformly spaced by 15 mm. In order reduce the position error of each release ofeach each releaseand andthe the measurement error ofthe thecharge charge quantity, 10tests tests were doneThen, ateach each point. of release measurement error of quantity, 10 were done at point. and the measurement error of the charge quantity, 10 tests were done at each point. the mean Then, the mean valves of the measured signal peaks and those of the charge quantities were further Then, of thethe mean valves of the measured those of the charge were valves measured signal peaks andsignal those peaks of the and charge quantities were quantities further used to further calculate usedto tocalculate calculatethe thestatic staticsensitivity andthe thedynamic dynamicsensitivity sensitivityof ofthe theHSESCA. HSESCA. used the static sensitivity and thesensitivity dynamic and sensitivity of the HSESCA.
Figure 16.Test Test pointsset set inthe the experiment. Figure Figure 16. 16. Test points points setin in theexperiment. experiment.
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5.2.2. Array Array Signals Signals of of the the HSESCA HSESCA 5.2.2. Five sets sets of of typical typical array array signals signals with Five with aa sample sample frequency frequency of of 4096 4096 Hz Hz are are shown shown in in Figure Figure 17. 17. P44 and They were were acquired acquiredwhen whenparticles particleswere werereleased releasedatatPP11,,PP22,, PP33,, P They and P P55,,respectively respectively (see (see Figure Figure 16). 16). Among them, them,PP1 1isisthe theorigin; origin; 2 and 4 are away the origin; P3 Pand P5 are 120 mm Among P2Pand P4 Pare 60 60 mmmm away fromfrom the origin; P3 and 5 are 120 mm away away from the origin. Besides, the charge quantities of the particles were measured be − −32 from the origin. Besides, the charge quantities of the particles were measured to be −32topC, 20 pC, pC, -20 and −29respectively. pC, respectively. − 46pC, pC,−46 −25pC, pC−25 andpC −29 pC,
17. Array signals signals of of the the HSESCA. HSESCA. (a) (a) Released Released at atPP11 with with − −32 released at at PP22 Figure 17. 32 pC charge; (b) released with − -20 −46 at PP44 with with − −25 with 20 pC pC charge; charge; (c) (c) released at P33 with − 46 pC pC charge; charge; (d) released at 25 pC charge; −29 (e) released released at at PP55 with − (e) 29pC pCcharge. charge.
Figure 17 17 shows shows that that the the measured measured signals signals are are similar similar in in shape shape as as those those obtained obtained by by numerical numerical Figure simulations (see Figure 5), except the sign symbol. The measured ones are minus because of the simulations (see Figure 5), except the sign symbol. The measured ones are minus because of the minus minus charge quantities of the particles. Besides, a signal variation trend versus the positions in charge quantities of the particles. Besides, a signal variation trend versus the positions in Line 1 can be Line 1 can be observed from Figure 17a–c. In detail, the signals of all of the sensor units are almost observed from Figure 17a–c. In detail, the signals of all of the sensor units are almost coincident at P1 , coincident at P1, which is explained by the same distance from P1 to every probe. However, with the which is explained by the same distance from P1 to every probe. However, with the release position release position moving from P1 to P3, the signal peak of the No. 1 sensor unit gets larger and larger. moving from P1 to P3 , the signal peak of the No. 1 sensor unit gets larger and larger. Conversely, other Conversely, other signal peaks decrease with respect to that of the No. 1 sensor unit; among them, signal peaks decrease with respect to that of the No. 1 sensor unit; among them, that of the No. 5 that of the No. 5 sensor unit decreases the most. In addition, two symmetric sensor units about sensor unit decreases the most. In addition, two symmetric sensor units about Line 1 have the same Line 1 have the same decrease scale in their signal peaks. A similar trend can also be observed when decrease scale in their signal peaks. A similar trend can also be observed when the release position the release position moves from P1 to P5 along Line 2. This is because a charged particle induces moves from P1 to P5 along Line 2. This is because a charged particle induces greater charge on closer greater charge on closer probes, and vice versa. In a word, the measured array signals have probes, and vice versa. In a word, the measured array signals have validated the theoretical ones in validated the theoretical ones in form. Moreover, it is validated that different combinations of peaks form. Moreover, it is validated that different combinations of peaks of the array signals imply different of the array signals imply different position information of the particles. This agrees with the position information of the particles. This agrees with the theoretical analysis and is the precondition theoretical analysis and is the precondition of the proposed array signal processing algorithm. of the proposed array signal processing algorithm. Ten tests were done at the release positions of P1, P2, P3, P4 and P5, respectively. The absolute charge quantities of the particles and the absolute signal peaks of the No. 1 sensor unit were measured. Their relationships are shown in Figure 18.
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Ten tests were done at the release positions of P1 , P2 , P3 , P4 and P5 , respectively. The absolute charge quantities of the particles and the absolute signal peaks of the No. 1 sensor unit were measured. Sensors 2016, 16, 1403 19 of 22 Their relationships are shown in Figure 18.
Figure 18. Relationships between the absolute charge quantities and the absolute peak voltages of the No. 1 sensor unit. Figure 18. Relationships between the absolute charge quantities and the absolute peak voltages of the Figure 18. Relationships between the absolute charge quantities and the absolute peak voltages of 1 sensor ThisNo. shows anunit. obvious proportional relationship between the absolute charge quantities the No. 1 sensor unit.
and the absolute peak voltages at each position. The different slopes indicate different values of shows obvious proportional relationship between thethe absolute charge quantities and and the This showsan an obvious proportional relationship between absolute charge quantities dynamicThis sensitivity with respect to different positions, and greater slopes represent greater values absolute peak voltages at each position. The different slopes indicate different values of dynamic the absolute peak voltages at each position. The different slopes indicate different values of dynamic sensitivity. The errors are acceptable and can be explained by the position error ofofeach sensitivity with respect to different and greaterand slopes represent greater values of dynamic dynamic with respecterror topositions, different greater slopes greater values release and sensitivity the measurement of thepositions, charge quantity. As a represent result, the proportional sensitivity. errors are acceptable can be explained byexplained the position error of eacherror release and of dynamicThe sensitivity. The errors areand acceptable and can be by the position of each characteristic of the signal conditioner is validated. the measurement of the charge quantity. As charge a result, quantity. the proportional of the signal release and the error measurement error of the As a characteristic result, the proportional conditioner is of validated. characteristic the signal conditioner is validated.
5.2.3. Static Sensitivity Test of the HSESCA
5.2.3. Static Test of 5.2.3. StaticaSensitivity Sensitivity Testbetween ofthe theHSESCA HSESCA To make comparison the theoretical and experimental results of the static sensitivity
of the HSESCA, the theoretical values in Line and 1 and and Line 2 were firstly calculated by of using To between the experimental results of of thethe static sensitivity Tomake makeaacomparison comparison between thetheoretical theoretical experimental results static sensitivity the HSESCA, the theoretical values in Line 1 and Line 2 were firstly calculated by using Equation (11) Equation and the when −1. Then, to the definition of static of the (11) HSESCA, thecalibration theoreticalmethod values in LineK1= and Line 2according were firstly calculated by using and the as calibration method when K = −1. when Then, to the definition of static sensitivity as the sensitivity Equation (10), the experimental value each test point was by dividing Equation (11) and the calibration method Kaccording =at−1. Then, according to obtained the definition of static Equation (10), the experimental value at each test point was obtained by dividing the summation of sensitivity (10), the experimental valuequantity at each test point was obtained by dividing the summation ofas allEquation of the signal peaks by the charge of the corresponding particle, followed all of the signal peaks by the charge quantity of the corresponding particle, followed by a scaling to the all of the peaks by theare charge quantity of the19, corresponding particle,represent followed by asummation scaling to of suppose K signal = −1. The results shown in Figure where the curves suppose K=− The results shown in Figure 19, where the curves represent theoretical values by a scaling to1.and suppose K = are −1. represent The results areexperimental shown in Figure 19, where thethe curves represent the theoretical values the points the values. and the points represent the experimental theoretical values and the points representvalues. the experimental values.
Figure 19. Experimental and theoretical values of static sensitivity (a) in Line 1 and (b) in Line 2.
Figure Experimental and theoreticalvalues values of of static static sensitivity 1 and (b)(b) in Line 2. 2. Figure 19. 19. Experimental and theoretical sensitivity(a) (a)ininLine Line 1 and in Line
It can be seen that the experimental values show fine consistencies with the theoretical ones. It can be seen that the experimental values show fine consistencies with the theoretical ones. Further analysis shows that the mean absolute value of relative error from all of the test points in Further analysis shows that the mean absolute value of relative error from all of the test points in Line 1 is 2.2544%, and that in Line 2 is 1.3516%. The errors are acceptable and can be explained by Line 1 is 2.2544%, and that in Line 2 is 1.3516%. The errors are acceptable and can be explained by the errors in controlling the particles’ falling positions and measuring their charge quantities. the Therefore, errors in the controlling the particles’ falling measuring their charge quantities. sensing model of the HSESCA, as positions well as thatand of the sensor units are validated.
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It can be seen that the experimental values show fine consistencies with the theoretical ones. Further analysis shows that the mean absolute value of relative error from all of the test points in Line 1 is 2.2544%, and that in Line 2 is 1.3516%. The errors are acceptable and can be explained by the Sensors 16, 1403 20 of 22 errors 2016, in controlling the particles’ falling positions and measuring their charge quantities. Therefore, the sensing model of the HSESCA, as well as that of the sensor units are validated. 5.2.4. Dynamic Sensitivity Test of the HSESCA 5.2.4.Theoretical Dynamic Sensitivity Test of theresults HSESCA and experimental of the dynamic sensitivity of the HSESCA were also
compared. Whenand the amplification to K = −1, the theoretical in Line and Theoretical experimental coefficient results of was the set dynamic sensitivity of the values HSESCA were1 also Line 2 were firstly calculated (see Section 5.1.3). After that, the measured signal peaks were compared. When the amplification coefficient was set to K = −1, the theoretical values in Line 1 and processed the calculated component extraction-based array signal processing algorithm to obtain the Line 2 wereby firstly (see Section 5.1.3). After that, the measured signal peaks were processed experimental values. In detail, the peaks decomposed, summated to obtain the by the component extraction-based arraywere signal processing weighted algorithmand to obtain the experimental values of monitoring Then, the corresponding values of are values. In the detail, the peaksparameter. were decomposed, weighted and summated to dynamic obtain thesensitivity values of the calculated using Equation (19), followed by avalues scaling supposesensitivity K = −1. The are shown in monitoringby parameter. Then, the corresponding ofto dynamic areresults calculated by using Figure where the by curves represent the Ktheoretical valuesare and the in points Equation20, (19), followed a scaling to suppose = −1. The results shown Figurerepresent 20, where the experimental values. curves represent the theoretical values and the points represent the experimental values.
Figure (a) in in Line Line 11 and and (b) (b) in in Line Line 2. 2. Figure 20. 20. Experimental Experimental and and theoretical theoretical values values of of dynamic dynamic sensitivity sensitivity (a)
It is observed that the experimental values match well with the theoretical ones. Further It is observed that the experimental values match well with the theoretical ones. Further analysis analysis shows that the mean absolute value of relative error from all of the test points in Line 1 is shows that the mean absolute value of relative error from all of the test points in Line 1 is 3.3233%, and 3.3233%, and that in Line 2 is 0.5936%. Just as the results in the static sensitivity test, the errors here that in Line 2 is 0.5936%. Just as the results in the static sensitivity test, the errors here are acceptable and are acceptable and can be explained by the errors in controlling the particles’ falling positions and can be explained by the errors in controlling the particles’ falling positions and measuring their charge measuring their charge quantities. In addition, by making a comparison between Figures 19 and 20, quantities. In addition, by making a comparison between Figures 19 and 20, it is seen that the values it is seen that the values of dynamic sensitivity are larger than 0.8 in most of the section of Line 1 of dynamic sensitivity are larger than 0.8 in most of the section of Line 1 and Line 2, but those of the and Line 2, but those of the static sensitivity are almost below 0.1. This demonstrates that the static sensitivity are almost below 0.1. This demonstrates that the monitoring accuracy of the HSESCA monitoring accuracy of the HSESCA for intermittent particles has been improved significantly by for intermittent particles has been improved significantly by using the component extraction-based using the component extraction-based signal processing algorithm, which agrees with the signal processing algorithm, which agrees with the theoretical analysis above. Therefore, the proposed theoretical analysis above. Therefore, the proposed algorithm is proven to be effective in actual algorithm is proven to be effective in actual measurements. More details can be found in Sections 5.1.2 measurements. More details can be found in Sections 5.1.2 and 5.1.3. and 5.1.3. 6. 6. Conclusions Conclusions
By the array array signals signals into consideration, the By taking taking the the processing processing of of the into consideration, the dynamic dynamic sensitivity sensitivity of of ESA ESA has beendefined definedtotodescribe describe sensitivity characteristics of ESAs in a systemic perspective. It has been thethe sensitivity characteristics of ESAs in a systemic perspective. It builds builds a direct relationship between the monitored particles and the monitoring parameters of a a direct relationship between the monitored particles and the monitoring parameters of a whole whole ESA, thus reflecting the monitoring accuracy directly. An HSESCA along with its application ESA, thus reflecting the monitoring accuracy directly. An HSESCA along with its application in in intermittent particle monitoring has taken been as taken as an example. Its sensitivity dynamic in sensitivity in intermittent particle monitoring has been an example. Its dynamic accordance accordance with a proposed component extraction-based array signal processing algorithm has with a proposed component extraction-based array signal processing algorithm has been analyzed been analyzed Relevant quantitatively. Relevant numerical been made, and experimental quantitatively. numerical simulations havesimulations been made,have and experimental validations have validations have been carried out on an eight-channel HSESCA experiment apparatus. Detailed been carried out on an eight-channel HSESCA experiment apparatus. Detailed results have been results have been provided, compared andare discussed, whichasare summarized as follows: provided, compared and discussed, which summarized follows: 1. 2.
The experimental results match well with the theoretical ones, which has validated the accuracy of the theoretical models and effectiveness of the corresponding methods. Compared with static sensitivity, the dynamic sensitivity of the HSESCA has much greater values in most of the observation cross-section. This demonstrates that the component extraction-based array signal processing algorithm is effective at overcoming the defect of
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3.
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The experimental results match well with the theoretical ones, which has validated the accuracy of the theoretical models and effectiveness of the corresponding methods. Compared with static sensitivity, the dynamic sensitivity of the HSESCA has much greater values in most of the observation cross-section. This demonstrates that the component extraction-based array signal processing algorithm is effective at overcoming the defect of inhomogeneous and localized static sensitivity, thus making a significant improvement on the monitoring accuracy for intermittent particles. There still exist relatively less sensitive zones near the inner wall of the pipeline after adopting the proposed algorithm. This is caused by the influence of the pipeline on the electrostatic field. A strategy to optimize the number of sensor units combined with optimizations on the proposed algorithm is likely to alleviate the drawback, which deserves further studies. Ill-conditioning and noise may impact the results of the proposed array signal processing algorithm. This is of great significance, to be discussed in further studies.
Acknowledgments: The authors are grateful to the National Basic Research Program of China (Grant No. 2015CB057400) for supporting this work. Author Contributions: This work has been done in collaboration between all authors. Xin Tang did the theoretical analyses and prepared the manuscript. Zhong-Sheng Chen designed the experiment and analyzed the experimental results. Yue Li and Zheng Hu did the simulation work and compared the results with those of the experiment. Yong-Min Yang revised the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations EMS ESA HSESCA PHM
Electrostatic monitoring system Electrostatic sensor array Hemisphere-shaped electrostatic sensors’ circular array Prognostics and health management
References 1. 2. 3. 4. 5. 6.
7. 8. 9. 10. 11.
Sun, J.Z.; Zuo, H.F.; Liu, P.P.; Wen, Z.H. Experimental study on engine gas-path component fault monitoring using exhaust gas electrostatic signal. Meas. Sci. Technol. 2013, 24, 125107. [CrossRef] Rahmat, M.F.; Thuku, I.T.; Tajdari, T.; Jusoff, K.; Ghazali, M.R. Sensing and filtering characteristics of electrostatic sensors for pneumatically conveyed particles. Int. J. Phys. Sci. 2011, 6, 5091–5103. Coombes, J.R.; Yan, Y. Experimental investigations into the flow characteristics of pneumatically conveyed biomass particles using an electrostatic sensor array. Fuel 2015, 151, 11–20. [CrossRef] Hu, H.L.; Dong, J.; Zhang, J.; Cheng, Y.J.; Xu, T.M. Identification of gas/solid two-phase flow regimes using electrostatic sensors and neural-network techniques. Flow Meas. Instrum. 2011, 22, 482–487. [CrossRef] Rahmat, M.F.; Isa, M.D.; Rahim, R.A.; Hussin, T.A. Electrodynamics sensor for the image reconstruction process in an electrical charge tomography system. Sensors 2009, 9, 10291–10308. [CrossRef] [PubMed] Addabbo, T.; Fort, A.; Garbin, R.; Mugnaini, M.; Rocchi, S.; Vignoli, V. Theoretical characterization of a gas path debris detection monitoring system based on electrostatic sensors and charge amplifiers. Measurement 2015, 64, 138–146. [CrossRef] Wen, Z.H.; Zuo, H.F.; Pecht, M.G. Electrostatic monitoring of gas path debris for aero-engines. IEEE Trans. Reliab. 2011, 60, 33–40. [CrossRef] Lin, J.; Chen, Z.S.; Hu, Z.; Yang, Y.M.; Tang, X. Analytical and numerical investigations into hemisphere-shaped electrostatic sensors. Sensors 2014, 14, 14021–14037. [CrossRef] [PubMed] Tang, X.; Chen, Z.; Li, Y.; Hu, Z.; Yang, Y. Theoretical analysis and fem simulations on dynamic sensitivity of hemisphere-shaped electrostatic sensors. Adv. Mech. Eng. 2016, 8. [CrossRef] Krabicka, J.; Yan, Y. Finite-element modeling of electrostatic sensors for the flow measurement of particles in pneumatic pipelines. IEEE Trans. Instrum. Meas. 2009, 58, 2730–2736. [CrossRef] Zhang, W.; Wang, C.; Yang, W.; Wang, C.-H. Application of electrical capacitance tomography in particulate process measurement—A review. Adv. Powder Technol. 2014, 25, 174–188. [CrossRef]
Sensors 2016, 16, 1403
12. 13.
14. 15. 16.
17. 18. 19. 20.
21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
31.
32.
22 of 23
Zhou, B.; Zhang, J.; Xu, C.; Wang, S. Image reconstruction in electrostatic tomography using a priori knowledge from ect. Nucl. Eng. Des. 2011, 241, 1952–1958. [CrossRef] Gao, H.; Xu, C.; Fu, F.; Wang, S. Effect of particle distribution on electrostatic tomography system. In Proceedings of the 7th International Symposium on Measurement Techniques for Multiphase Flows, Xi’an, China, 26–30 October 2012; pp. 269–276. Iliya, T.T.; Mohd, F.R. Development of a new method of sensitivity matrix for image reconstruction in electric charge tomography system using finite element method. J. Teknol. 2014, 70, 103–112. Li, Y.; Yang, W. Image reconstruction by nonlinear landweber iteration for complicated distributions. Meas. Sci. Technol. 2008, 19, 094014. [CrossRef] Martínez Olmos, A.; Botella, G.; Castillo, E.; Morales, D.P.; Banqueri, J.; García, A. A reconstruction method for electrical capacitance tomography based on image fusion techniques. Digit. Signal Process. 2012, 22, 885–893. [CrossRef] Tizhe Thuku, I.; Rahmat, M.F.A. Finite-element method modeling in 4 and 16 sensors electric-charge tomography systems for particles moving in pipeline. Flow Meas. Instrum. 2014, 38, 9–20. [CrossRef] Xu, C.; Li, J.; Gao, H.; Wang, S. Investigations into sensing characteristics of electrostatic sensor arrays through computational modelling and practical experimentation. J. Electrost. 2012, 70, 60–71. [CrossRef] Thuku, I.T.; Rahmat, M.F.; Wahab, N.A.; Tajdari, T.; Yusuf, A.A. 2-D finite-element modeling of electrostatic sensor for tomography system. Sens. Rev. 2013, 33, 104–113. [CrossRef] Ghazali, M.R.; Ibrahim, W.I.; Rahmat, M.F. Electrostatic sensor in circular and rectangular shape electrode for solid dry pneumatic conveyor system. In Proceedings of the 2011 International Conference on Circuits, System and Simulation, Bangkok, Thailand, 28–29 May 2011; IACSIT Press: Singapore, 2011; Volume 7, pp. 66–72. Xu, C.; Wang, S.; Tang, G.; Yang, D.; Zhou, B. Sensing characteristics of electrostatic inductive sensor for flow parameters measurement of pneumatically conveyed particles. J. Electrost. 2007, 65, 582–592. [CrossRef] Yang, W.Q.; Conway, W.F. Measurement of sensitivity distributions of capacitance tomography sensors. Rev. Sci. Instrum. 1997, 69, 233–236. [CrossRef] Guo, Z.; Shao, F.; Lv, D. Sensitivity matrix construction for electrical capacitance tomography based on the difference model. Flow Meas. Instrum. 2009, 20, 95–102. [CrossRef] Marashdeh, Q.; Teixeira, F.L. Sensitivity matrix calculation for fast 3-D electrical capacitance tomography (ECT) of flow systems. IEEE Trans. Magnet. 2010, 40, 1204–1207. [CrossRef] Wang, A.; Marashdeh, Q.M.; Teixeira, F.L.; Fan, L.S. Electrical capacitance volume tomography: A comparison between 12- and 24-channels sensor systems. Prog. Electromagn. Res. M 2015, 41, 73–84. [CrossRef] Zeeshan, Z.; Teixeira, F.L.; Marashdeh, Q. Sensitivity map computation in adaptive electrical capacitance volume tomography with multielectrode excitations. Electron. Lett. 2015, 51, 334–336. [CrossRef] Fisher, C.E. Gas path debris monitoring—A 21st century PHM tool. In Proceedings of the 2000 IEEE Aerospace Conference Proceedings, Big Sky, MT, USA, 25 March 2000; Volume 6, pp. 441–448. Powrie, H.; Novis, A. Gas path debris monitoring for F-35 joint strike fighter propulsion system PHM. In Proceedings of the 2006 IEEE Aerospace Conference, Big Sky, MT, USA, 4–11 March 2006; pp. 4012–4019. Wen, Z.; Ma, X.; Zuo, H. Characteristics analysis and experiment verification of electrostatic sensor for aero-engine exhaust gas monitoring. Measurement 2014, 47, 633–644. [CrossRef] Addabbo, T.; Fort, A.; Mugnaini, M.; Panzardi, E.; Vignoli, V. Multisensor electrostatic detection of moving charged particles. In Proceedings of the Sensors Applications Symposium (SAS 2016), Catania, Italy, 20–22 April 2016; pp. 445–450. Addabbo, T.; Fort, A.; Mugnaini, M.; Panzardi, E.; Vignoli, V. A smart measurement system with improved low-frequency response to detect moving charged debris. IEEE Trans. Instrum. Meas. 2016, 65, 1874–1883. [CrossRef] Xu, C.; Zhang, J.; Yang, D.; Zhou, B.; Tang, G.; Wang, S. Dense-phase pneumatically conveyed coal particle velocity measurement using electrostatic probes and cross correlation algorithm. J. Phys. 2009, 147, 012004. [CrossRef]
Sensors 2016, 16, 1403
33. 34.
23 of 23
Zhang, J.Q.; Yan, Y. On-line continuous measurement of particle size using electrostatic sensors. Powder Technol. 2003, 135–136, 164–168. [CrossRef] Zhou, B.; Yang, D.; Tang, G.; Xu, C.; Wang, S. Analysis on dynamic sensitivity of ring-shaped electrostatic sensor. Proc. CSEE 2008, 28, 44–49. © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
