sensors Article

Railway Tunnel Clearance Inspection Method Based on 3D Point Cloud from Mobile Laser Scanning Yuhui Zhou 1 , Shaohua Wang 2, *, Xi Mei 1 , Wangling Yin 3 , Chunfeng Lin 1 , Qingwu Hu 3,5, * and Qingzhou Mao 4 1 2 3 4 5

*

ID

China Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, China; [email protected] (Y.Z.); [email protected] (X.M.); [email protected] (C.L.) School of International Software, Wuhan University, No. 129, Luoyu Road, Wuhan 430072, China School of Remote Sensing and Information Engineering, Wuhan University, No. 129, Luoyu Road, Wuhan 430072, China; [email protected] State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (LIESMARS), Wuhan University, No. 129, Luoyu Road, Wuhan 430072, China; [email protected] Key Laboratory for National Geographic Census and Monitoring, National Administration of Surveying, Mapping and Geoinformation, Wuhan University, No. 129, Luoyu Road, Wuhan 430072, China Correspondence: [email protected] (S.W.); [email protected] (Q.H.); Tel.: +86-133-9715-8536 (S.W.); +86-189-710-70362 (Q.H.)

Received: 12 July 2017; Accepted: 2 September 2017; Published: 7 September 2017

Abstract: Railway tunnel clearance is directly related to the safe operation of trains and upgrading of freight capacity. As more and more railway are put into operation and the operation is continuously becoming faster, the railway tunnel clearance inspection should be more precise and efficient. In view of the problems existing in traditional tunnel clearance inspection methods, such as low density, slow speed and a lot of manual operations, this paper proposes a tunnel clearance inspection approach based on 3D point clouds obtained by a mobile laser scanning system (MLS). First, a dynamic coordinate system for railway tunnel clearance inspection has been proposed. A rail line extraction algorithm based on 3D linear fitting is implemented from the segmented point cloud to establish a dynamic clearance coordinate system. Second, a method to seamlessly connect all rail segments based on the railway clearance restrictions, and a seamless rail alignment is formed sequentially from the middle tunnel section to both ends. Finally, based on the rail alignment and the track clearance coordinate system, different types of clearance frames are introduced for intrusion operation with the tunnel section to realize the tunnel clearance inspection. By taking the Shuanghekou Tunnel of the Chengdu–Kunming Railway as an example, when the clearance inspection is carried out by the method mentioned herein, its precision can reach 0.03 m, and difference types of clearances can be effectively calculated. This method has a wide application prospects. Keywords: mobile laser scanning (MLS); point cloud; railway tunnel clearance; clearance coordinate system; tunnel cross section

1. Introduction The tunnel clearance is the space required for the safe operation of a locomotive along a fixed track, a spatial clearance free of any barrier within a certain width and height scope, to ensure the normal operation and safety of various types of traffic in the tunnel [1–5]. The most commonly used method for detecting railway clearance—the section detection method, can be divided into two categories, namely, contact type and non-contact type. In early days, contact measurement method was widely applied at home and abroad [6–9]. Through a framework where multiple extendable arms can be mounted on the flat car, when the flat car is running, all arms contact the tunnel walls, and the Sensors 2017, 17, 2055; doi:10.3390/s17092055

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sensors on the arms will convert the mobile signals to electrical signals to draw out the transverse and longitudinal sections for different positions. This equipment is relatively cheap compared with manual measurement and the measurement precision can be less than 30 mm, but the measuring speed is slow, only 10 km/h. Using this method to perform the section measurement will interfere with the train traffic on the busy main line, and cannot be applied to electrified sections [6,10,11]. In 1980, the Austrian company Plasser developed the GCM-10 clearance inspection car, with a maximum measuring speed of 18 km/h, where the laser radar ranging principle was applied. In 1983, a 3 km/h clearance inspection car has been developed in France, which used an argon laser light as the source, used a laser beam for scanning tunnel sections, and took photos for the laser belt at the preset laser height [11–17]. After the 1980s, to solve the detection problems on electrified sections, the non-contact detection method came into being. The Swiss company Amberg Technologies carried out studies for the project, connecting a laser tunnel section measurement instrument to a computer. The computer was used to control and achieve the functions of the section measurement instrument and display the measured section shape. This paved a new way for the future tunnel section measurement methods [11–14]. Many countries have developed tunnel clearance inspection cars. In 1986, a TV camera clearance inspection car was launched in the UK, which applied the double triangle relationship measurement principle to obtain any 5 m comprehensive profile with a speed up to 100 km/h [18–20]. In late 1990s, China developed the SJC-1 tunnel inspection car, which acquired a comprehensive section size at an interval of 5 m at 70 km/h [21–24]. In early 21st century, the BJSD-2 laser clearance inspection instrument has been developed, which can acquire the section in perpendicular to the tunnel middle line [25,26]. Hu et al., proposed a railway clearance inspection method based on visual perception. Japan has developed a clearance inspection car mounted with CCD sensors [4]. With the development of CCD sensor technology, video compression technology and image processing technology, computer video measurement technology has been increasingly applied to tunnel clearance inspection tasks, and the clearance inspection has been developing in a faster and more precise manner [27–33]. With the development of 3D laser technology, image processing technology and intelligent robot technology, the multi-sensor integrated 3D laser mobile scanning system runs at a speed of 120 km/h to obtain high density and high precision laser point clouds of tunnels for clearance inspection, which has become the current trend in railway clearance inspection. This method has to tackle with some issues such as what efforts should be made to quickly and automatically carry out the clearance intelligent analysis and calculation based on the 3D laser point cloud [3,34–37]. For the large volume of point cloud data from laser scanning systems, how to deal with the point cloud to calculate different clearance is still a big challenge. In view of the problems existing in the traditional tunnel clearance inspection methods, such as low density, slow speed and a lot of manual operations, this paper proposes a tunnel clearance inspection method based on a mobile laser scanning 3D point cloud. First, a dynamic coordinate system for railway tunnel clearance inspection has been proposed. A rail line extraction algorithm based on 3D linear fitting is implemented from the segmented point cloud to establish a dynamic clearance coordinate system. Second, a method to seamlessly connect all rail segments based on the railway clearance restrictions, and a seamless rail alignment is formed sequentially from the middle tunnel section to both ends. Finally, based on the rail alignment and the track clearance coordinate system, different types of clearance frames are introduced for intrusion operation with the tunnel section to realize the tunnel clearance inspection. By taking the Shuanghekou Tunnel of the Chengdu–Kunming Railway as an example, when the clearance inspection is carried out by the method mentioned herein, its precision can reach 0.03 m, and different types of clearances can be effectively calculated. This method has a wide application prospects.

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2. Methodology 2. Methodology A mobile 3D laser scanning system (MLS), which integrates a high performance laser scanner, highAprecision positioning and navigation system typically includes a Global Navigation Satellite mobile 3D laser scanning system (MLS), which integrates a high performance laser scanner, System (GNSS) receiver, CCD cameras, control board and industry computer on a vehicle, is used high precision positioning and navigation system typically includes a Global Navigation Satellite to obtain laser scanning data, cameras, positioning and navigation data and computer image data After System (GNSS) receiver, CCD control board and industry onsynchronously. a vehicle, is used to high positioning and navigation data fusion processing, it can provide accurate position and obtain laser scanning data, positioning and navigation data and image data synchronously. After high attitude data fornavigation the laser scanner to obtain high density and high precision 3D laser cloud of positioning and data fusion processing, it can provide accurate position andpoint attitude data thethe railway andtosurroundings [38–40].and Based onprecision the processing andpoint analysis of of 3Dthe laser point for laser track scanner obtain high density high 3D laser cloud railway cloud, the rail alignment and tunnel section, different types of clearance frames are introduced for track and surroundings [38–40]. Based on the processing and analysis of 3D laser point cloud, the 3D space operations to inspect the railway tunnel clearance. The overall technical process is shown rail alignment and tunnel section, different types of clearance frames are introduced for 3D space in Figure 1.to inspect the railway tunnel clearance. The overall technical process is shown in Figure 1. operations 1 Establishment of Tunnel Clearance Coordinate System

2 Profile Extraction

Segment of Point Cloud

Profile Interval Input

Rail point cloud extraction

Tunnel Cross Section Extraction

Standard Clearance Frame Model

Rail line fitting Point Cloud of Railway Tunnel

Clearance Frame Model Matching

Rail segments connection

Determination of clearance coordinate system

Clearance Inspection and Caculation 3

Result of Clearance Inspection

Clearance Calculation

Figure Figure 1. 1. Technical Technical flowchart flowchartof ofthe theproposed proposedtunnel tunnelclearance clearanceinspection inspectionmethod. method.

InFigure Figure1,1,the therailway railwaytunnel tunnel point cloud data obtained by using the MLS are pre-processed In point cloud data obtained by using the MLS are pre-processed into into segments along the line direction, to ensure that all rail segments are linear. Second, the straight segments along the line direction, to ensure that all rail segments are linear. Second, the straight rail rail segments are extracted section. The plane thecenterlines two centerlines the left railright and segments are extracted fromfrom each each section. The plane wherewhere the two of theof left rail and right rail are located, is used to determine the clearance measuring coordinate system. Then, the rail are located, is used to determine the clearance measuring coordinate system. Then, the tunnel tunnel cross section baseline is determined by relying on the clearance measuring coordinate system, cross section baseline is determined by relying on the clearance measuring coordinate system, and and cross sections are collected from the tunnel point cloud. based on the railway tunnel cross sections are collected from the tunnel point cloud. Finally,Finally, based on the railway tunnel testing testing rack model, the distance between the tunnel cross section and testing rack is calculated to rack model, the distance between the tunnel cross section and testing rack is calculated to realize the realize theinspection. clearance inspection. clearance 2.1. 2.1. Clearance Clearance Coordinate Coordinate System System and and Segments SegmentsofofTunnel TunnelPoint PointCloud Cloud The The tunnel tunnel clearance clearance is is aa limited limited cross cross section section profile profile perpendicular perpendicular to to the the centerline centerline of of the the alignment alignment [3,41–43]. [3,41–43]. The The centerline centerline of of the the alignment alignment should should be be obtained obtained first first in in the the tunnel tunnel clearance clearance inspection, inspection, and and then then aaclearance clearanceinspection inspectioncoordinate coordinatesystem systemshould shouldbe beestablished. established. The Theclearance clearance coordinate coordinate system system is is aa local local coordinate coordinate system, system, which which is is determined determined based based on on the the centerline centerline of of the the alignment asas shown in in Figure 2. The X axis is the centerline of the alignmentand andthe therail railsurface surface[1,3,41–43], [1,3,41–43], shown Figure 2. The X axis is the centerline of rail the surface, i.e., the central line of the Y axis is perpendicular to the X axis, is perpendicular rail surface, i.e., the central linerail. of the rail. Y axis is perpendicular toand the ZXaxis axis, and Z axis is perpendicular with the railupward. surface facing upward. to the rail with to thethe railrail surface facing Therefore, the the clearance clearance measuring measuring coordinate coordinate system system is is established established on on the the basis basis of of the the Therefore, determination of the rail tunnel structure is long andand narrow, andand the the rail determination rail straight straightline. line.The Therailway railway tunnel structure is long narrow, applied in the alignment is either linear ororcurved. will not not rail applied in the alignment is either linear curved.However, However,totoensure ensurethat that the the locomotive will turn over over due due to to the theexcessive excessive centripetal centripetal force force when when itit is is making making aa turn, turn, the the curvature curvature of of the thecurve curve turn rail is very small, and the rail in the small length range is almost linear, so this paper focuses on the

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rail is very small, and the rail in the small length range is almost linear, so this paper focuses on the pre-treatment of thetunnel tunnelpoint point cloud by segments the line, tothat ensure that eachof pre-treatment cloud datadata by segments along along the line, to ensure each segment pre-treatmentofofthe the tunnel point cloud data by segments along the line, to ensure that each segment oflinear, the rail isthat linear, and that eacha can establish a clearance measuring system local coordinate the rail is and each can establish clearance measuring local coordinate defined by segment of the rail is linear, and that each can establish a clearance measuring local coordinate system definedline, by atorail straight line, to carry out the tunnel clearance inspection. In this paper, theis asystem rail straight carry out the tunnel clearance inspection. In this paper, the tunnel point cloud defined by a rail straight line, to carry out the tunnel clearance inspection. In this paper, the tunnel point cloud is segmented interval of 5 m. segmented an interval of 5 m.atatan tunnel pointatcloud is segmented an interval of 5 m.

Figure 2. Definition of clearance coordinate system. Figure Figure 2. 2. Definition Definition of of clearance clearance coordinate coordinate system. system.

Figure 3 is the effect drawing of segments. From the top view of overall tunnel point cloud Figure 3 is is the the effect effect drawing of of segments. From the top view of overall overall tunnel tunnel point point cloud cloud shown in Figure 3a, this drawing alignment segments. is curved. After the segmented pretreatment along the Figure alignment is curved. After the segmented pretreatment along the shown ininFigure 3a,3a, thisthis alignment is curved. After the segmented alignment, the results of three representative segments are shown inpretreatment Figure 3b. along the alignment, alignment, the results of three representative segments shown the results of three representative segments are shown inare Figure 3b.in Figure 3b.

(a) (a)

(b) (b) Figure 3. Segmentation results of tunnel point cloud. (a) Top view of whole tunnel point cloud; (b) Figure 3. 3. Segmentation results cloud. (a) (a) TopTop view of whole tunnel point cloud; (b) Figure resultsofoftunnel tunnelpoint point cloud. view of whole tunnel point cloud; point cloud Segmentation of three segments. point cloud of three segments. (b) point cloud of three segments.

After the point cloud segmentation, the rail point cloud extraction and fitting can be made for After the point cloud segmentation, the rail point cloud extraction and fitting can be made for segments, so that each clearance measuring coordinate system can be defined in accordance with segments, so that each clearance measuring coordinate system can be defined in accordance with the clearance inspection points. Then, based on this coordinate system, the cross sections in parallel the clearance inspection points. Then, based on this coordinate system, the cross sections in parallel

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After the point cloud segmentation, the rail point cloud extraction and fitting can be made for segments, so that each clearance measuring coordinate system can be defined in accordance with the clearance inspection points. Then, based on this coordinate system, the cross sections in parallel with the YOZ plane are collected from the tunnel point cloud, and the tunnel clearance inspection Sensors 2017, x FOR PEERout REVIEW of 19 can be achieved by17,carrying the clearance distance computation combined with the5 tunnel testing rack model. 2.2. Rail

with the YOZ plane are collected from the tunnel point cloud, and the tunnel clearance inspection can be achieved by carrying out the clearance distance computation combined with the tunnel Linear Extraction and Establishment of Tunnel Clearance Coordinate System testing rack model.

The direct extraction of 3D rail based on point clouds requires the fine screening of tunnel point 2.2. Rail Linear Extraction and Establishment of Tunnel Clearance Coordinate System clouds. The rail point cloud is only reserved for fitting of the 3D rail point cloud, to obtain the 3D rail The direct extraction of 3D rail based on point clouds requires the fine screening of tunnel straight line and establish the tunnel clearance coordinate system. point clouds. The rail point cloud is only reserved for fitting of the 3D rail point cloud, to obtain the 3D rail straight line and establish the tunnel clearance coordinate system.

2.2.1. Rail Point Cloud Extraction

2.2.1. Rail Point Cloud Extraction

The rail is laid in the middle of the tunnel, and there is a large space between the rail and the The rail is laid in the middle of the tunnel, and there is a large space between the rail and the crown of the tunnel. The extraction of rail point cloud from a large amount of tunnel 3D laser point crown of the tunnel. The extraction of rail point cloud from a large amount of tunnel 3D laser point cloud includes two steps, coarse extraction extraction, as shown in Figure 4. cloud includes two steps, coarse extractionand and fine fine extraction, as shown in Figure 4.

Figure 4. Flowchart of rail point cloud extraction.

Figure 4. Flowchart of rail point cloud extraction. (1) Coarse Extraction

(1)

The coarse extraction is to separate point cloud of two rails from the whole tunnel point cloud Coarse Extraction

according the basic structure information of the tunnel. Firstly, the range of the point cloud can be

calculated to obtain the point coordinates of theof tunnel roughthe alignment The coarse extraction is center to separate point cloud two and railsthefrom wholedirection tunnel of point cloud rail. Secondly, the coarse rail lines can be reckoned with the center points and rough direction according the basic structure information of the tunnel. Firstly, the range of the point cloud can be considering the gauge information regarding a redundancy about 0.2 m around the two rail lines. calculatedThen, to obtain thecloud center of the tunnel thelines rough of rail. the point outpoint of the coordinates two rail lines and between theand two rail are alignment deleted. Thusdirection only Secondly, the thepoint coarse rail lines can be reckoned with the center points and rough direction considering cloud in the cube scope along the two rails is left. Thirdly, considering that the rails are at the bottom of the tunnel, the differential elevation of the points usedlines. to eliminate the gaugelocated information regarding a redundancy about 0.2 mvalue around the twoisrail Then, the point cloud out of the two rail lines and between the two rail lines are deleted. Thus only the point cloud in the cube scope along the two rails is left. Thirdly, considering that the rails are located at the bottom of the tunnel, the differential elevation value of the points is used to eliminate the tunnel top point cloud.

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Through the coarse extraction, point cloud of two tracks and adjacent points are separated from the the tunnel top point cloud. Through the coarse extraction, point cloud of two tracks and adjacent tunnel point cloud.

points are separated from the tunnel point cloud. Fine Extraction Fine(2) Extraction The rail cross section is I-shaped, composed of three parts, rail head, rail web, and rail bottom, The rail cross section is I-shaped, composed of three parts, railpoint head,cloud, rail web, and rail bottom, as shown in Figure 5. Among the coarse extraction results of rail the elevation values as shown in Figure 5. Among the coarse extraction results of rail point cloud, the elevation values on the on the rail head point (or rail face point) on the left and right tracks are the maximum. The fine rail head pointof(or rail point) the left and rightfrom tracks the extraction maximum.results The fine extraction extraction the railface track pointon cloud is the height theare coarse made by use of the rail track point cloudtoisachieve the height the coarseofextraction resultspoint madethrough by use of the rail surface, of the rail surface, the from fine extraction the rail surface screening the maximum point. to achieve the fine extraction of the rail surface point through screening the maximum point.

(2)

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the tunnel top point cloud. Through the coarse extraction, point cloud of two tracks and adjacent points are separated from the tunnel point cloud. (2) Fine Extraction The rail cross section is I-shaped, composed of three parts, rail head, rail web, and rail bottom, as shown in Figure 5. Among the coarse extraction results of rail point cloud, the elevation values on the rail head point (or rail face point) on the left and right tracks are the maximum. The fine extraction of the rail track point cloud is the height from the coarse extraction results made by use of the rail surface, to achieve the fine extraction of the rail surface point through screening the maximum point.

Figure5. 5. Rail Rail section. Figure section.

Considering the entire rail alignment extension, the overall alignment of rail includes three Considering the entire rail alignment extension, therising, overall ofrailway rail includes cases, rising, falling and retaining. In case of falling or thealignment elevation of sleeperthree in thecases, rising, falling and be retaining. In less casethan of falling or rising, elevation ofinrailway sleeper the first first half may greater or the elevation of the railway sleeper the second half.inThus, the half may entire be greater lessdivided than the elevation of railway sleeper second Thus, theofentire rail is rail isor then into several segments within 5 mintothe extract the half. surface point the rail then head divided several 5 mofto extract the surface point of the rail head one by one, one into by one, whichsegments can avoidwithin the effect rail irregularities.

which can avoid the effect of rail irregularities. As the rail surface is smooth enough to cause specular reflection, there are few laser points on the surface of rail head. Actually, the rail head only has laser points on both sides. There are edge points. Thus, the edge points of the both sides of the rail head are extracted to represent the rail. Then maximum elevation point in each segment is only the edge point on one side. To represent the Figure 5. Rail section. complete rail, the edge points on both sides are needed. Therefore, after the local maximum elevation alignment the overall alignment of rail point on Considering one side of the the entire rail is rail obtained, the extension, point corresponding to the other sideincludes can be three obtained cases, rising, falling and retaining. In case of falling or rising, the elevation of railway sleeper in the based plane distance and elevation difference constraint of the rail head. The points of the finally first half may be greater or less than(a)the elevation of railway sleeper in the second half. Thus, the (b) spliced segments are reflected by the edge points on both sides of the rail surface of the entire rail. entire rail is then divided into several segments within 5 m to extract the surface point of the rail Figure 6 shows the fine extraction result of railpoint point cloud. Figure 6. Fine extraction of rail cloud. (a) Front View; (b) Top View. head one by one, which can avoid the effect of rail irregularities.

As the rail surface is smooth enough to cause specular reflection, there are few laser points on the surface of rail head. Actually, the rail head only has laser points on both sides. There are edge points. Thus, the edge points of the both sides of the rail head are extracted to represent the rail. Then maximum elevation point in each segment is only the edge point on one side. To represent the complete rail, the edge points on both sides are needed. Therefore, after the local maximum elevation point on one side of the rail is obtained, the point corresponding to the other side can be obtained based plane distance and elevation difference constraint of the rail head. The points of the finally spliced segments are reflected by the edge points on both sides of the rail surface of the entire rail. Figure 6 shows the fine extraction result of rail point cloud. (b) (a) Figure 6. Fine extraction of rail point cloud. (a) Front View; (b) Top View.

Figure 6. Fine extraction of rail point cloud. (a) Front View; (b) Top View.

As the rail surface is smooth enough to cause specular reflection, there are few laser points on the surface of rail head. Actually, the rail head only has laser points on both sides. There are edge points. Thus, the edge points of the both sides of the rail head are extracted to represent the rail. Then maximum elevation point in each segment is only the edge point on one side. To represent the complete rail, the edge points on both sides are needed. Therefore, after the local maximum elevation point on one side of the rail is obtained, the point corresponding to the other side can be

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2.2.2. 3D Linear Fitting of Rail Line with Rail Point Cloud 2.2.2.The 3D Linear Fittingequation of Rail Line Railline Point space linear of with the rail is Cloud a continuous equation with six parameters, as Equation (1): The space linear equation of the rail line is a continuous equation with six parameters,

x − x0 y − y 0 z − z 0 (1) x − x0 = y − y0 = z − z0 m = n = p (1) m n p a point on the straight line, and is ,the direction vector of the where, ) aispoint n, pdirection ) is thevector where, ( x( 0x,0y, 0y, 0z,0z)0is on the straight line, and (m, n, p)( m of the straight line. straight line. In thisthe paper, and of fine the rail cloud, of two In this paper, after coarseafter and the finecoarse extraction theextraction rail point of cloud, twopoint edge points theedge rail points of obtained. the rail head The rail line can be 3D calculated by theof3D fitting of theusing two head are Theare railobtained. line can be calculated by the linear fitting thelinear two edge points edge points using the leastFigure square7 approach. is thefitting resultofofthe 3Drail linear of the railpoints lines the least square approach. is the resultFigure of 3D 7linear linesfitting with the edge with the edge points of the rail head. of the rail head. as Equation (1):

Figure 7. Rail Rail line line by by 3D linear fitting using least square approach.

In Figure 7,7,since sincethe thepoints points outer edge of rail the head rail head are more numerous than the In Figure onon thethe outer edge of the are more numerous than the points points on the inner edge due to the scanning angle of MLS, the rail line by 3D linear fitting will be on the inner edge due to the scanning angle of MLS, the rail line by 3D linear fitting will be closer to the closer to the outside of the rail. Both rails must be parallel to each other in practice. Therefore, the outside of the rail. Both rails must be parallel to each other in practice. Therefore, the two 3D rail lines two 3D rail linesshould 3D linear fitting to should be parallel to each other.ofHowever, because of noise in 3D linear fitting be parallel each other. However, because noise in laser scanning, point laser scanning, point cloud extraction and 3D linear fitting have small errors. Thus, the two rail cloud extraction and 3D linear fitting have small errors. Thus, the two rail lines will not be completely lines will not be completely parallel to each other, and there is a small angle between their direction parallel to each other, and there is a small angle between their direction vectors. To keep consistent vectors. To keep consistent with the actual rail structure and determine the clearance measuring with the actual rail structure and determine the clearance measuring coordinate system, the direction coordinate system, the direction vector of two rail lines should be slightly modified. Thus, the vector of two rail lines should be slightly modified. Thus, the average vector of the two rail lines are average vector of the two rail lines are used as the direction vector of each rail line, to ensure that used as the direction vector of each rail line, to ensure that the two rail lines are parallel to each other. the two rail lines are parallel to each other. Finally, the centerline of two rail lines is taken as the Finally, the centerline of two rail lines is taken as the centerline of the railway. centerline of the railway. 2.2.3. Connection of the Segmented Rail Lines 2.2.3. Connection of the Segmented Rail Lines The automatic extraction of rail in this paper is a process targeted at the rail in the segments The automatic extraction rail in this paperare is asequentially process targeted at theafter rail the in the segments which is approximately linear. of The linear sections connected extraction of which is approximately linear. The linear sections are sequentially connected after the extraction of the rail point cloud in the tunnel point cloud as well as the 3D linear fitting of rail lines, to obtain and the railthe point cloud infold the tunnel point cloudfor asall well the 3D linear fitting of rail lines, to so obtain reflect continuous line. It is difficult railas segments to be seamlessly connected, it is and reflecttothe line. Itrail is difficult forinto all arail segmentsfold to be seamlessly so necessary setcontinuous some rules fold to connect segments continuous line as long asconnected, the precision it is necessary to set some rules to connect rail segments into a continuous fold line as long as the is guaranteed. First, select a benchmark segment so that other segments move closer to it. To avoid the precision is guaranteed. First, select a benchmark segment so that other segments move closer to it.

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To avoid the excessive cumulative error, it is suggested that the segment in the middle of the tunnel be used as a benchmark, rather than those on both ends. In this way, other segments on both ends excessive cumulative error, it istosuggested that the in the middle of the tunnel used as a of the benchmark get closer it from afar, andsegment the error arising from hereof willbebe halved benchmark, rather than those on both ends. In this way, other segments on both ends of the benchmark compared with that from getting closer from one end. get closer to it frombetween afar, andthe the two errorfitting arisingrail from hereof lines will becan halved compared that from The distance straight be used as thewith restriction of getting closer from one end. checking the precision of the rail extraction and segmented rail connection. If the distance between distance between the two fitting rail straightfrom linesthe canstandard be used as the restriction of checking two The tracks in a given segment is largely deviating gauge, which is 1435 mm in the precision of the rail and rail connection. If the between cohesion, two tracksthe in China, it indicates thatextraction this section ofsegmented rail extraction is in error. In casedistance of rail segment asegment given segment is largely standard gauge,towhich is 1435 mm in China, it indicates with the distancedeviating betweenfrom two the track lines closest the standard gauge shall be selected that sectionsegments of rail extraction is in error.asInthe case of rail segment cohesion, the segment with two the fromthis multiple of tunnel center benchmark segment. The distance between distance track lines to the standard gauge shall segments parallel between lines is two equivalent to closest the distance from one point in be a selected straight from line multiple to the other. The of tunnel center as the segment. The between two parallel lines isthrough equivalent the direction vector of abenchmark straight line is ( m a straight line passes a to point , ndistance , p ) , and distance one point in a straight line to the other. The direction vector of a straight line is (m, n, p), ( x 0, y 0, zfrom 0 ) , then the distance d from the point outside the straight line P ( xp , yp , zp ) to the and a straight line passes through a point ( x0 , y0 , z0 ), then the distance d from the point outside the straight line can be calculated according to the Equation (2): straight line P( x p , y p , z p ) to the straight line can be calculated according to the Equation (2): 2

2

v yp − y 0 zp − z 0 u 2 u y − y z pn− z0 p 0 t p + dn = p

2

2 zp − z 0 xp − x 0 + x p2 − x 0 yp − y 0 + z −z x0 y p − y0 p p 0 xmp − x0 m x p − n (2) + m n p2 m2 2 pm +n + p d= (2) m2 + n2 + p2 In this paper, as the linear fitted rail line is the center line of the track, it is not inside the rail thisbetween paper, asthe the inner linear edge fittedand rail line the center the track, it is notthe inside rail edge, edge,Inbut the is outer edge. line The of distance between twothe center lines but between the inner edgeand andthe thewidth outer of edge. distance the two centerthe lines includes includes standard gauge railThe tread. Thus, between the distance between two tracks standard andEquation the width(2)of is rail tread.than Thus, thestandard distance gauge. between thedistance two tracks calculated by calculatedgauge by the larger the The empirical value the Equation (2) is larger than the standard gauge. The distance empirical value obtained through a obtained through a large number of testing data analysis is 1502 mm. The following is a simple large number testing of data analysis is 1502 mm. The following is a simple analysis of the validity of analysis of theofvalidity this empirical value. this empirical The type value. of rail is expressed as a mass kg per 1 m. The existing rail standards in China include type rail is60expressed mass kg 1 m. the Themass existing railrail standards in China include threeThe types, 75ofkg/m, kg/m andas50akg/m. Theper greater of the per meter, the greater the three types, kg/m, 60 improve kg/m and kg/m. The greater the line, massthe of the rail per are meter, the greater bearing load75will be. To the50carrying capacity of the main lines usually laid 75 the bearing be. rails. To improve the dimensions carrying capacity the rails line, the are usually laid kg/m or 60 load kg/mwill heavy The tread of the of three are main shownlines in Figure 8 [44–45]. 75 kg/m or 60data kg/m heavy rails.paper The tread dimensions of the rails are shown in Figure [44,45]. The rail type used in this is 60 kg/m, as shown inthree Figure 8, and the width of rail8 tread is The type data used in this paper is 60 kg/m, as shown inrail Figure 8, and theiswidth of rail is 73.0rail mm. Assuming that the rail straight line fitted by the point cloud located righttread in the 73.0 mm.ofAssuming thatdistance the rail straight by the is rail1508 point cloud located right in the middle middle the rail, the betweenline thefitted two tracks mm (theissum of the standard gauge of thetread rail, the distance between the two tracks is 1508 sum the standard and tread and width). Thus, the empirical distance of mm 1502(the mm is of more practical gauge and reasonably width). Thus, the empirical distance of 1502 mm is more practical and reasonably guidance. guidance.

(a)

(b)

(c)

Figure8.8.Dimensions Dimensionsofofthe therail railtread. tread.(a) (a)5050kg/m; kg/m;(b) (b)60 60kg/m; kg/m; (c) (c) 75 75 kg/m. kg/m. Figure

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order to toconnect connectall allthe thesegmented segmentedrail rail lines, a pair of segmented lines selected as In order lines, a pair of segmented railrail lines are are selected as the the connection benchmark from the center position of the tunnel center. The distance between the connection benchmark from the center position of the tunnel center. The distance between the benchmark railrail lines areare selected, all the benchmark rail lines lines should shouldbe beclosest closesttoto1502 1502mm. mm.After Afterthe the benchmark lines selected, all segmented rail rail lineslines can be fromfrom the benchmark lines to both direction of the tunnel the segmented canconnected be connected the benchmark lines to the both the direction of the startingstarting point and terminal point. First, endpoint of the first adjacent segmented rail linerail should tunnel point and terminal point.the First, the endpoint of the first adjacent segmented line coincidecoincide with thewith nearest of the benchmark rail line. rail Then, keep the keep length and direction should the endpoint nearest endpoint of the benchmark line. Then, the length and of first adjacent rail line and endpoint make suretothat thesure newthat rail line direction of firstsegmented adjacent segmented railmove line its andother move its othertoendpoint make the is parallel to the line original before this other sections are by analogy, new rail line is original parallel rail to the railprocessing. line beforeThe this processing. Thefollowed other sections are and the seamless connection of the previous segments achieved in sequence. The presented rail followed by analogy, and the seamless connection of theisprevious segments is achieved in sequence. connection method will not change the rail direction of all segments, the distance between the rails in The presented rail connection method will not change the rail direction of all segments, the distance all segments should be segments consistentshould to ensure the continuity of thethe whole rail. The result of between the rails in all be consistent to ensure continuity ofconnection the whole rail. The all segmentsresult are compared as shown in Figure 9.as shown in Figure 9. connection of all segments are compared

(a)

(b) Figure 9. The connection result of all segmented rail lines. (a) Before connection; (b) After Figure 9. The connection result of all segmented rail lines. (a) Before connection; (b) After connection. connection.

In Figure Figure 9, 9, the the two two outer outer segments segments are are segmented segmented rail rail segments, segments, and and the the middle middle line line is is the the In centerline of of the the rail. rail. In In Figure Figure 9a, 9a, the the adjacent adjacent segments segments are are represented represented in in different different colors colors so so that that aa centerline minor gap exists between their joint, as indicated in red circle in the figure. After the connection of the minor gap exists between their joint, as indicated in red circle in the figure. After the connection of segmented rail, all segments are seamlessly bonded, as shown in Figure 9b. the segmented rail, all segments are seamlessly bonded, as shown in Figure 9b. 2.2.4. Determination of Clearance Measuring Coordinate System 3.2.4. Determination of Clearance Measuring Coordinate System Tunnel clearance measuring coordinate system may be determined based on the following steps Tunnel clearance measuring coordinate system may be determined based on the following after two rail lines are obtained: steps after two rail lines are obtained: (1) Calculate rail centerline and determine axis X. (1) Calculate rail centerline and determine axis X. Two rail lines are parallel to each other and their direction vectors (m1 , n1 , p1 ) and (m2 , n2 , p2 ) Two rail lines are parallel to each other and their direction vectors ( m1, n1, p1) and meet the relationship in Equation (3): m1 (3): n p ( m 2, n 2, p 2) meet the relationship in Equation = 1 = 1 (3) m2 n2 p2

m1 n1 p1 = = m2 n2 p 2

(3)

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With known direction vectors L1 (m1 , n1 , p1 ) and L2 (m2 , n2 , p2 ) of two rail lines and points M1 ( x1 , y1 , z1 ) and M2 ( x2 , y2 , z2 ) respectively passing the two lines, direction vector L(m, n, p) obtained after the calculation of mean value of components of direction vectors L1 and L2 is the direction vector of center line of rail and point M( x, y, z) obtained after the calculation of mean value of coordinate components of points M1 ( x1 , y1 , z1 ) and M2 ( x2 , y2 , z2 ) is a point on the center line of rail. Equation (4) gives the relationship among three direction vectors and three points: p +p

m = m1 +2 m2 , n = n1 +2 n2 , p = 1 2 2 y +y x = x1 +2 x2 , y = 1 2 2 , z = z1 +2 z2

(4)

After direction vector L(m, n, p) and point M ( x, y, z) are obtained, the center line of railway may be determined according to Equation (1), i.e., the center line of track as well as axis X in the clearance measuring coordinate system. (2)

Determine axis Y.

The plane determined by two rail lines is the rail plane in tunnel clearance coordinate system, denoted as plane A. Axis Y in clearance coordinate system is perpendicular to axis X in plane A. The normal vector of plane B is the direction vector L(m, n, p) of the center rail line. The plane B is perpendicular to rail plane A. Two rail lines and plane B intersect at two points, the connecting line of which is axis Y and the center point of these two intersection points is the origin of coordinate system O for clearance calculation. The intersection points of rail line and plane B is calculated by linear parameter equation (as Equation (5)) and space plane equation (as Equation (6)):    x = x0 + mt y = y0 + nt   z = z + pt 0

(5)

where, ( x0 , y0 , z0 ) is a point on the line, (m, n, p) is direction vector of the line and t is a parameter: A( x − x p ) + B(y − y p ) + C (z − z p ) = 0

(6)

where, ( x p , y p , z p ) is a point on the plane and ( A, B, C ) is normal vector of the plane. The intersection points of rail line and plane B meets both linear parameter equation and space plane equation. Then, the parameter t of the intersection point can be obtained by combining Equations (5) and (6), as shown in Equation (7). Then, the coordinates ( x, y, z) of the intersection point can be obtained by parameter t based Equation (5): t= (3)

A ( x p − x0 ) + B ( y p − y0 ) + C ( z p − z0 ) Am + Bn + Cp

(7)

Determine axis Z.

The axis Z of the clearance measuring coordinate system meets the right-hand rule with axes X and Y in plane B, as shown in Figure 10. The green polyline in the figure is the cross section profile of tunnel at an interval of 1 m. 2.3. Profile Extraction Based on Clearance Coordinate System The most commonly used method of tunnel clearance inspection is the cross section inspection method [46]. The tunnel cross section at certain interval is obtained in the clearance measuring coordinate system. Tunnel clearance inspection is realized through contrastive analysis on actual cross section profiles and design profiles. To determine whether the tunnel space can guarantee the driving

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cross section profiles and design profiles. To determine whether the tunnel space can guarantee the driving safety of trains, it is judged by calculating the distance between locomotive model and rail safety of trains, it is judged by calculating the distance between locomotive model and rail tunnel cross tunnel cross section profile. section profile.

Figure 10. 10. Tunnel Tunnel clearance clearance coordinate coordinate system. system. Figure

In theclearance clearance measuring coordinate system 10,section if a perpendicular cross section In the measuring coordinate system shown shown in Figurein10,Figure if a cross perpendicular to the plane XOY is selected from the tunnel point cloud directly, the of to the plane XOY is selected from the tunnel point cloud directly, the number of pointsnumber on a cross points a cross section be too low tocross show the complete cross section profile due to the section on might be too low tomight show the complete section profile due to the limitation of point cloud limitation of point cloud density. A triangulated irregular network (TIN) is widely used in density. A triangulated irregular network (TIN) is widely used in representation of the physical surface. representation of the physical surface. A TIN comprises a triangular network of vertices, known as A TIN comprises a triangular network of vertices, known as mass points, with associated coordinates in mass points, with associated coordinates three dimensions connected by aedges to form a three dimensions connected by edges to form aintriangular tessellation[47,48]. Thus, TIN is introduced triangular tessellation[47–48]. Thus, a TIN is introduced to overcome the clearance to overcome the clearance inspection problem with the discrete point cloud, which can beinspection built with problem with thecloud, discrete point cloud,the which cancross be built with the tunnel cloud, or of presenting the tunnel point or presenting tunnel section via the point point of intersection TIN and the tunnel cross viasteps the point intersection of TIN and cross section. The specific steps are cross section. Thesection specific are as of below: as below: Step 1: establishment of TIN for the tunnel point cloud. This paper introduces TIN into the generation continuous tunnel model describes three-dimensional tunnel with TIN.TIN Dueinto to large Step 1:ofestablishment of TIN for and the tunnel point cloud. This paper introduces the data volume of tunnel point cloud, to reduce the amount of calculation in establishment of TIN, tunnel generation of continuous tunnel model and describes three-dimensional tunnel with TIN. Due to point data cloudvolume are firstof selected. clearance inspection only needs to along the cross section. large tunnel The point cloud, to reduce the amount of calculate calculation in establishment of In order to improve the robustness, we use points on a narrow stripe of the cross section. TIN, tunnel point cloud are first selected. The clearance inspection only needs to calculate These along can the also reduce theInamount of improve calculation tunnel TINwe building. Thus, points stripe on theof tunnel wall cross section. order to thefor robustness, use points ononly a narrow the cross and tunnel top within a certain scope along the cross section are reserved to generate the TIN of the section. These can also reduce the amount of calculation for tunnel TIN building. Thus, only points cross on thesection. tunnel wall and tunnel top within a certain scope along the cross section are reserved to Step 2: TIN obtainment of the tunnel cross section based on TIN. After the clearance measuring generate the of the cross section. coordinate system is determined, planecross B of the crossbased section is perpendicular to the rail line Step 2: obtainment of the tunnel section onwhich TIN. After the clearance measuring can be obtained. that ( xplane thecross datum pointwhich of cross on axis to X in p , y p , zBp ) coordinate systemAssuming is determined, ofisthe section is section perpendicular theclearance rail line measuring coordinate system, the plane B of cross section can be determined by the direction can be obtained. Assuming that ( xp , yp , zp ) is the datum point of cross section on axisvector X in ( A, B, C ) of axis X as Equation (8): clearance measuring coordinate system, the plane B of cross section can be determined by the direction vector ( A, B , C ) of axis X as Equation (8): A( x − x p ) + B(y − y p ) + C (z − z p ) = 0 (8)

A( x − xp ) + B ( y − yp ) + C ( z − zp ) = 0 (8) The point of intersection of each side of each triangle and cross section in TIN can be calculated The pointthe of intersection of each side each triangle and crossequation section in beintersection calculated by calculating point of intersection withofthe plane by parametric of TIN line. can Such by calculating the point of intersection with the plane by parametric equation of line. Such points are sorted by their coordinate z. The profile of tunnel cross section is obtained after ordered intersection points are sorted points are connected into lines.by their coordinate z. The profile of tunnel cross section is obtained after ordered points are connected into lines.

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2.4. Clearance Calculation 2.4. Clearance Calculation standard clearance test frame modelmodel (SCFM)(SCFM) of a rail of tunnel andtunnel its dimensions. Figure 11a 11ashows shows standard clearance test frame a rail and its Figure 11a shows standard clearance testmodel frame model (SCFM) ofdimensions. a rail tunnel and its Figure 11b shows simplified clearance testclearance frame and itsmodel dimensions. dimensions. Figure 11b shows simplified test frame and its dimensions. Figure 11b shows simplified clearance test frame model and its dimensions. Central axis Z of rail Central axis Z of rail

Surface of tracks Surface of tracks

(a) (a)

(b) (b)

Figure 11. Standard Figure 11. Standard Clearance Clearance test test frame frame Model Model of of Rail Rail Tunnel. Tunnel. (a) (a) Standard Standard clearance clearance frame frame model; model; Figure 11. Standard Clearance test frame Model of Rail Tunnel. (a) Standard clearance frame model; (b) Simplified model of SCFM. (b) Simplified model of SCFM. (b) Simplified model of SCFM.

Clearance calculation must be conducted through unification of standard clearance test frame Clearancecalculation calculationmust mustbe beconducted conductedthrough throughunification unificationof of standard clearance clearance test frame Clearance model of tunnel into clearance measuring coordinate system. Specificstandard steps are as below:test frame model of tunnel into clearance measuring coordinate system. Specific steps are as model measuringtest coordinate system. steps areplane asbelow: below: Stepof1:tunnel Place into the clearance standard clearance frame model in Specific ZOY horizontal and make the Step 1: Place the standard clearance test frame model in ZOY horizontal plane and make the mean the standard frame model in of ZOY planewith and axis make meanStep axis1:ofPlace the model overlapclearance with axistest Z and bottom axis thehorizontal model overlap Y,the as axis of the model overlapoverlap with axis Z and of the model axiswith Y, as axis shown in mean of the12. model with axisbottom Z and axis bottom axis of theoverlap modelwith overlap Y, as shownaxis in Figure Figure 12. shown in Figure 12.

Z Z

Y Y

O O

Figure 12. Unification of clearance test frame model and clearance coordinate system. Figure 12. 12. Unification Unification of of clearance clearance test test frame model and clearance coordinate system. Figure

Step 2: clearance inspection calculation. The railway tunnel clearance inspection is realized by Step clearance inspection The tunnel clearance by clearance inspection calculation. The railway railway tunnel profile clearance inspection is realized realizedtest calculating2:the distance between calculation. polyline of tunnel cross section andinspection standard is clearance calculating the distance between of crossinto section and standard calculating theThis distance between polyline of tunnel tunnel frame model. paper dividespolyline clearance test frame top, profile side and bevel typesclearance based ontest its frame model. This paper divides clearance test frame into top, side and bevel types based on its frame model. This paper divides clearance test frame into top, side and bevel types based on its structure. The significance of its clearance inspection is shown as below: structure. The significance of its clearance inspection is shown as below: structure. The significance of its clearance inspection is shown as below: (1) Clearance calculation between the cross section profile and the top of tunnel, the side of (1) tunnelClearance calculation between the cross section profile and the top of tunnel, the side of tunnel

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(1) Divide Clearance between the cross profilewall andwith the top of tunnel, theaccording side of tunnel the calculation cross section into tunnel topsection and tunnel certain height to the tunnel design calculate the distance between and the corresponding of Divide the material, cross section into tunnel top and tunnelcross wall section with certain height according part to the clearance test frame respectively (Figure 12). The distance represents the clearance between cross tunnel design material, calculate the distance between cross section and the corresponding part of section profile and respectively the top of tunnel, the12). sideThe of tunnel respectively. Thisclearance distance between can be used to clearance test frame (Figure distance represents the cross guideprofile tunneland widening trackthe alining. section the topor ofrail tunnel, side of tunnel respectively. This distance can be used to guide tunnel rail track alining. (2) widening Clearanceorcalculation between overhead contact line (OCL) and the top of clearance test frame (2) Clearance calculation between overhead contact line (OCL) and the top of clearance test frame

OCLisisgenerally generallynear nearthe thetop topofof centerline track (Figure is only possible to scrape the OCL centerline of of track (Figure 13).13). It isItonly possible to scrape the top top of clearance test frame. Therefore, it is only necessary to calculate its distance to the top of of clearance test frame. Therefore, it is only necessary to calculate its distance to the top of clearance test clearance test frame. may Suchbedistance be usedsag for analysis conducting sag analysis on OCL and guiding frame. Such distance used formay conducting on OCL and guiding the maintenance the maintenance of OCL to guarantee driving safety of train. of OCL to guarantee driving safety of train.

Figure Figure 13. 13. Point Point cloud cloud of of tunnel tunnel and and OCL. OCL.

Toimprove improvethe thereliability reliabilityof ofthe theclearance clearancecalculation, calculation, data data within within aa certain certain scope scope of of the the cross cross To section profile along the direction of axis X are generally selected to constitute the cross section section profile along the direction of axis X are generally selected to constitute the cross section zone zone for calculating the interval with the clearance test frame. Considering the density of thecloud, point for calculating the interval with the clearance test frame. Considering the density of the point cloud, thisdefines paper defines this asrespectively, 0.01 m, respectively, before after section the cross section profile this paper this scope asscope 0.01 m, before and after and the cross profile along the along theofdirection direction axis X. of axis X. 3. 3. Experimental Experimental Result Result and and Discussion Discussion 3.1. 3.1. Experiment Experiment Place Place and and Data Data Experiment Experiment data data in in this this paper paper are are point point clouds clouds of of the the Shuanghekou Shuanghekou Tunnel Tunnel of of the the Chengdu-Kunming Line from a mobile three-dimensional laser scanning system (as shown Chengdu-Kunming Line from a mobile three-dimensional laser scanning system (as shown in in Figure This system Figure 14). 14). This system is is composed composed of of aa three-dimensional three-dimensional laser laser scanning scanning sensor, sensor, GPS, GPS, inertial inertial measurement and control storage cellcell andand placed on aon track trolley for data measurementunit unit(IMU), (IMU),mileage mileagecoder coder and control storage placed a track trolley for acquisition with pushing. data acquisition with pushing. 2 and scanning precision The thethe tunnel pointpoint cloudcloud obtained is better 1 point/cm 2 and scanning Thedensity densityofof tunnel obtained is than better than 1 point/cm at 10 m is lower than 1 mm. The Shuanghekou Tunnel is located between Ganluo and Nanergang on precision at 10 m is lower than 1 mm. The Shuanghekou Tunnel is located between Ganluo and the Chengdu-Kunming Line with an overall ofoverall 1889.5 m. Figure 15 shows image and point Nanergang on the Chengdu-Kunming Line length with an length of 1889.5 m. the Figure 15 shows the cloud of the tunnel entrance and exit. image and point cloud of the tunnel entrance and exit.

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(b) (a) (b) (a) Figure 14. Mobile Laser Scanner (MLS) for railway tunnel point cloud collection. (a) Components of Figure 14. Mobile Laser Scanner (MLS) for railway tunnel point cloud collection. (a) Components of Figure 14.MLS Mobile Scanner for data railway tunnel point cloud collection. (a) Components of MLS; (b) on Laser platform trailer(MLS) for field collection. MLS; (b) MLS on platform trailer for field data collection. MLS; (b) MLS on platform trailer for field data collection.

(a) (a)

(b) (b)

(c) (c)

(d) (d)

Figure 15. Picture and point cloud of tunnel entrance and exit. (a) Picture of tunnel entrance; (b) Figure 15. Picture andentrance; point cloud of tunnel entrance exit. (a) Picture of tunnel Point cloud of tunnel (c) Picture of tunnel exit;and (d) Point cloud of tunnel exit. entrance; (b) Figure 15. Picture and point cloud of tunnel entrance and exit. (a) Picture of tunnel entrance; (b) Point Point cloud of tunnel entrance; (c) Picture of tunnel exit; (d) Point cloud of tunnel exit.

cloud of tunnel (c) Picture of sections tunnel exit; cloud tunnel exit.and analysis on tunnel This paper entrance; selects data of three of (d) the Point tunnel for of experiment This paper selects of entrance, three sections the tunnel for experiment analysis clearance inspection, i.e.,data tunnel tunnelof middle and tunnel exit. Table 1and describes the on datatunnel set. clearance inspection, tunnel entrance, tunnelof middle and tunnel Table 1 describes the dataon set.tunnel This paper selectsi.e., data of three sections the tunnel for exit. experiment and analysis Table 1. Experiment dataset. clearance inspection, i.e., tunnel entrance, tunnel middle and tunnel exit. Table 1 describes the data set. Table 1. Experiment dataset. Data set Position Radius of Curvature (m) Length (m) Section Number of Points Table 1. Experiment Tunnel entrance Radius 500 35 (m) Section 7 23,253,815 Data1set Position of Curvature (m) dataset. Length Number of Points Tunnelentrance middle Greater500 than 1000 35 27,367,654 12 Tunnel 35 77 23,253,815 Tunnel exit RadiusGreater Greater than1000 1000 35 (m) 7 30,127,334 Data set 23 Position of Curvature (m) Length Number of Points Tunnel middle than 35 7Section 27,367,654 3 Tunnel exit Greater than 1000 35 7 30,127,334 Tunnel

1

35system is established 7 23,253,815 For the entrance three data sets in Table 1,500 a clearance coordinate and clearance threemiddle data in Table 1, athan clearance coordinate is established clearance inspection analysis is sets conducted with the method mentioned in this precision of 2 For the Tunnel Greater 1000 35system 7paper. Theand 27,367,654 inspection analysis is conducted with than the 1000 method mentioned The 30,127,334 precision of 3 Tunnel exit Greater 35 in this paper. 7

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establishment of clearance may be expressed by theisfitting precision rail line. For the three data setscoordinate in Table 1,system a clearance coordinate system established andofclearance For clearance inspection, the value of clearance of different types is respectively calculated inspection analysis is conducted with the method mentioned in this paper. The precision of according to Section 2.4. coordinate system may be expressed by the fitting precision of rail line. establishment of clearance For clearance inspection, the value of clearance of different types is respectively calculated according 3.2. Experimental Result Analysis to Section 2.4.

3.2.1. Precision Result Clearance Coordinate System 3.2. Experimental Resultof Analysis Fitting precision of rail line in each section in data sets of three different positions is 3.2.1. Precision Result of Clearance Coordinate System respectively subject to statistics. This paper uses the mean value of distance between each rail point line precision in each section of three different positions is respectively and Fitting fitting precision rail line of as rail fitting indexinofdata railsets line, i.e., precision of clearance coordinate subject paper system,toasstatistics. shown inThis Table 2. uses the mean value of distance between each rail point and fitting rail line as fitting precision index of rail line, i.e., precision of clearance coordinate system, as shown in Table 2. Precision of clearance coordinate system (Unit: m). Table 2. Data Set 1 Data Set 2(Unit: m). Fitting Precision Table 2. Precision of clearance coordinate system Left Rail

Section No.

Fitting Precision

1 Section No.

2 1 3 2 4 3 5 4 5 6 6 7 7 MeanMean valuevalue

Right Rail

Left Rail

Data Set 1

Right Rail Data Set 2

0.025 0.030 0.020 Left Rail Right Rail Left Rail 0.012 0.011 0.020 0.025 0.008 0.013 0.030 0.0160.020 0.012 0.011 0.020 0.010 0.008 0.008 0.013 0.0130.016 0.019 0.010 0.021 0.008 0.0120.013 0.019 0.008 0.021 0.0090.012 0.009 0.009 0.008 0.008 0.0120.009 0.008 0.008 0.008 0.012 0.013 0.014 0.014 0.0140.014 0.013

0.024 Right Rail 0.013 0.024 0.011 0.013 0.016 0.011 0.008 0.016 0.008 0.008 0.008 0.021 0.021 0.014 0.014

Data Set 3 Left Rail

Right Rail

Data Set 3

0.021 0.029 0.021 0.018 0.029 0.016 0.018 0.015 0.016 0.015 0.018 0.018 0.019 0.019 0.019 0.019

Left Rail

0.011 0.029 0.011 0.017 0.029 0.015 0.017 0.020 0.015 0.020 0.007 0.007 0.018 0.018 0.017 0.017

Right Rail

According to Table 2, points of rail lines are extracted from the tunnel point cloud data. The According to Table 2, points of rail lines from the tunnel cloud data. The fitting fitting precision of three-dimensional for are railextracted line with point cloud point in different positions and precision of three-dimensional for rail line with point cloud in different positions and sections is better sections is better than 0.03 m, i.e., the precision of tunnel clearance coordinate system is better than than m, i.e.,meets the precision of tunnel clearance coordinate system bettersection than 0.03 m, which meets 0.03 0.03 m, which the requirement of clearance inspection. Theiscross profile is extracted the requirement inspection. Theoncross section profile is coordinate extracted from tunnel TIN at from tunnel TINof at clearance an interval of 1 m based clearance measuring system determined an interval of 1 m based on clearance measuring coordinate system determined via rail line, as shown via rail line, as shown in Figure 16: in Figure 16:

(a)

(b)

(c)

Figure 16. Tunnel cross section profile. (a) Top view; (b) Side view; (c) Phantom view. Figure 16. Tunnel cross section profile. (a) Top view; (b) Side view; (c) Phantom view.

3.2.2. Calculation of Clearance between Cross Section Profile and the Top of Clearance Test Frame and Side Figure 17 shows the result of clearance calculation between cross section profile in three different positions and the top of clearance test frame and side.

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17x shows theREVIEW result of clearance calculation between cross section profile in three different SensorsFigure 2017, 17, FOR PEER 16 of 19 positions and the top of clearance test frame and side.

Figure 17. Clearance inspection result of tunnel wall. Figure 17. Clearance inspection result of tunnel wall. Figure 17. Clearance inspection result of tunnel wall.

According to Figure 17, minimum clearance distance between tunnel cross section profile and According to Figure 17, minimum distance between tunnel cross section profile and and the top, the sideto ofFigure clearance frame, clearance is respectively 0.258 m, 0.598tunnel m andcross 0.401section m, indicating that According 17, test minimum clearance distance between profile the top,wall the side side of clearance clearance test the frame, is respectively respectively 0.258safe m, distances. 0.598 m m and and 0.401 0.401 m, m, indicating that tunnel and top do not cross border and are within the top, the of test frame, is 0.258 m, 0.598 indicating that tunnel wall and top do not cross the border and are within safe distances. tunnel wall and top do not cross the border and are within safe distances. 3.2.3. Clearance Calculation of OCL and the Top of Clearance Test Frame 3.2.3. Clearance Calculation of OCL and the Top of Clearance Test Frame 3.2.3.Figure Clearance Calculation of OCL the Top of Clearance Test Frame 18 presents the result of and clearance calculation between OCL and the top of clearance test Figure 18 presents the result of clearance calculation between OCL and the top of clearance test frame in three different positions. Figure 18 presents the result of clearance calculation between OCL and the top of clearance test frame in three different positions. frame in three different positions.

Figure 18. Clearance distance between OCL and the top of clearance test frame. Figure 18. Clearance distance between OCL and the top of clearance test frame.

Figure 18.sag Clearance distance between OCLThe and the top of clearance testis,frame. Figure Figure 18 18 reflects reflects sag degree degree of of OCL OCL indirectly. indirectly. The smaller smaller the the distance distance is, the the greater greater the the sag sag will be. Actual OCL sag is consistent with this clearance line chart. Minimum distance between OCL will Figure be. Actual OCL sag consistent with this clearance line chart. Minimum distance 18 reflects sag is degree of OCL indirectly. The smaller the distance is, the greaterbetween the sag and the top oftop clearance test frame is respectively 0.4350.435 m, 0.462 m and 0.390 m. This clearance can OCL and the of clearance test frame is respectively m, 0.462 m and 0.390 m. This clearance will be. Actual OCL sag is consistent with this clearance line chart. Minimum distance between guarantee safe safe passage of a train. As Figures 17 and have shown, the minimum distance are more can guarantee oftest a train. AsisFigures 1718 and 18 have shown, the 0.390 minimum distance are OCL and the top of passage clearance frame respectively 0.435 m, 0.462 m and m. This clearance than 10 times the precision of the clearance coordinate system in Table 2. This means the errors of the 3D more than 10 times the precision of the clearance coordinate system in Table 2. This means can guarantee safe passage of a train. As Figures 17 and 18 have shown, the minimum distance are linear fitting can be ignored and the clearance inspection result is reliable. errorsthan of 3D10 linear fitting can be ignored the clearance inspection result is reliable. more times the precision of theand clearance coordinate system in Table 2. This means the errors of 3D linear fitting can be ignored and the clearance inspection result is reliable. 3.3. Discussion

3.3. Discussion Though this paper realizes railway tunnel clearance inspection based on high-precision and high-density cloudrealizes obtainedrailway with mobile laserbased scanning, three-dimensional Though point this paper tunnelthree-dimensional clearance inspection on high-precision and

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3.3. Discussion Though this paper realizes railway tunnel clearance inspection based on high-precision and high-density point cloud obtained with mobile three-dimensional laser scanning, three-dimensional laser point clouds have a large data volume and such process as segmentation of tunnel point cloud, extraction of point cloud in each section of rail and establishment of TIN for cross section point cloud involve a lot of point cloud reading and writing throughput. It is necessary to further improve the efficiency of point cloud processing. For example, it is a feasible solution to index point clouds with hierarchy of segmentation and conduct parallel and accelerated processing based on GPU. In addition, the method in this paper does not apply to online clearance inspection. To establish online clearance coordinates in combination with real-time GPS/IMU integrated navigation, it is necessary to consider the configuration of the sensor in three-dimensional laser mobile scanning system. For example, it is a technical approach to resolve real-time clearance inspection by installing three-dimensional laser scanner parallels to clearance coordinate system, correcting it with real-time GPS/IMU integrated navigation and attitude and unifying it into the same clearance coordinate system [49]. Current clearance inspection is a kind of safety check before railway operation. The clearance inspection can be implemented after on-site data collection through post-processing and data analysis. The proposed clearance inspection approach is not sensitive to the time for the line extraction is based on the segmented point cloud. The clearance inspection calculation is implemented with the cross section profile with low computational complexity. However, the real time clearance inspection will increase the railway operation efficiency, and the next clearance inspection device and approach should take more consideration of the data processing. Moreover, this paper only defines one clearance test frame model. If multiple types of clearance test frame models are added and the distance between tunnel cross section profile and a certain clearance test frame model is calculated selectively, tunnel clearance inspection for different types of locomotives can be realized. 4. Conclusions Tunnel clearance inspection is vital for guaranteeing the safe operation of locomotives and improving the traffic capacity and cargo capacity. This paper introduces a three-dimensional laser mobile scanning system into the railway tunnel clearance calculation and inspection field, and puts forward a processing flow and technical frame for railway tunnel clearance inspection based on three-dimensional laser point clouds. According to the long and narrow structure of rail tunnel, three-dimensional laser point clouds of tunnels are subjected to segmented pretreatment along the direction of the railway line, to guarantee a straight line of rail in each section. Linear segments of rail are extracted from laser point clouds on this basis and a clearance measuring coordinate system is determined with the center line of two rails and the plane of the rails. TIN is established with the tunnel point cloud. Meantime, the point of intersection of TIN and the cross section will be calculated. Tunnel cross sections with equal intervals are thus produced. Finally, tunnel clearance inspection is realized by calculating the distance between the cross section profile and the tunnel clearance test frame with the tunnel cross section profile, combined with a tunnel testing-rack clearance calculation method. By taking the Shuanghekou Tunnel of the Chengdu-Kunming Railway as an example, when the clearance inspection is carried out by the method mentioned herein, its precision can reach 0.02 m, and difference types of clearances can be effectively calculated. This method thus has wide application prospects. Acknowledgments: This research was supported by the Fundamental Research Funds for the Central Universities (Grand No. 2042017KF0235), Key Technologies R&D Program of China (Grand No. 2015BAK03B04) and grand of the Key Laboratory for National Geographic Census and Monitoring, National Administration of Surveying, Mapping and Geoinformation(Grand No: 2015NGCM02).

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Author Contributions: Shaohua Wang and Yuhui Zhou conceived the study and wrote the paper; Wanling Yin, Qingwu Hu and Chunfeng Lin did the field data collection and data processing; Fang Mei and Qingzhou Mao implemented data analysis. Conflicts of Interest: The authors declare no conflict of interest.

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