IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 17, NO. 6, NOVEMBER 2013
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Fuzzy Reasoning of Accident Provenance in Pervasive Healthcare Monitoring Systems Yongli Wang, Member, IEEE, and Xiaohua Hu, Member, IEEE
Abstract—In pervasive healthcare monitoring environments, data provenance, as one metadata, can help people analyze the reasons for medical accidents that are generated by complex events. This reasoning processing often encounters inaccurate time and irreversible reasoning problems. How to solve the uncertain process and fuzzy transformation time presents many challenges to the study of data provenance. In this paper, we propose a backward derivation model with the provenance semantic, backward fuzzy time reasoning net (BFTRN), to solve these two problems. We design a backward reasoning algorithm motivated by time automation theory based on this model. With regard to given life-critical alarms and some constraints, it cannot only derive all evolution paths and the possibility distribution of paths from historical information, but also efficiently compute the value of fuzzy time function for each transition of lift-critical complex alarms in the healthcare monitoring system. We also analyze the properties of BFTRN model in this paper. Experiments on real dataset show that the proposed model is efficient. Index Terms—Fuzzy time automation, life-critical alarm, provenance, reasoning uncertainty.
I. INTRODUCTION HE development of portable computing devices and miniature sensing devices presents many new opportunities for personal healthcare [1]. Digital messages from medical devices, like alarms or clinical data streams, are partitioned into small packets and are sent through the device’s antenna to a shared wireless network access point. For patient data, like anesthesia awareness or heart monitors, each device may be constantly sending a stream of packets that can be assembled in the correct sequence at a central station or computer system. In practical scenarios, medical error may be generated by multiple alarm (event) paths. A complex alarm is to be triggered, only some
T
Manuscript received August 12, 2012; revised February 24, 2013; accepted July 17, 2013. Date of publication July 24, 2013; date of current version November 12, 2013. This work was supported in part by the National Natural Science Foundation of China under Grant 61170035, in part by Jiangsu 973 Project BK2011022, in part by National Natural Science Foundation of Jiangsu under Grant BK2011702, in part by the special project of Nanjing Scientific Committee Foundation 020142010, and in part by the Fundamental Research Funds for the Central Universities 30920130112006. Y. Wang is with the Nanjing University of Science and Technology, Nanjing 210094, China. He is also visiting the College of Information Science and Technology, Drexel University, Philadelphia, PA 19104 USA (e-mail: [email protected]). X. Hu is with the College of Information Science and Technology, Drexel University, Philadelphia, PA 19104 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JBHI.2013.2274518
alarms occurred in accordance with the specific order, and within a specified time interval. Random waiting strategies of collision detection (CD) protocol will likely cause uncertain order of some alarms, and the uncertain delay of alarm. If there is a medical accident, it is difficult to figure out what caused the accident and how to generate the accident. Medical professionals need to investigate the trustworthiness of some recognized alarm. When the system detected an abnormal alarm, the caregiver should want to trace the audit trail of data [2]. Provenance systems may be constructed to support a lot of applications, such as data quality, audit trail, replication recipes, and attribution. Consequently, the study of provenance has been increasingly popular recently. The provenance of data products generated by complex transformations such as workflows is of considerable value to scientists [3]. We use the term data product or dataset to refer to data in any form, such as files, tables, and collections. The two prominent features of the provenance of a data product are the ancestral data product(s) from which this data product evolved, and the process of transformation of these ancestral data product(s), possibly through workflows, that helped derive this data product. Petri nets are a terrific tool for modeling systems with interacting concurrent components. Authors in [4] used their timed extensions in performance modeling. However, the existing alarm recognition methods cannot provide the ability to trace the provenance of alarm, this work presents a solution. We create a life-critical alarm firing network, which is similar to a fuzzy time Petri net, for a healthcare monitoring scenario. The abstraction of this net includes “state-like” objects P and “event-like” objects T and dependencies between these objects A. Section III describes the detailed definition in this paper. An alarm reasoned from the alarm firing network may be produced by probabilistic classification methods, and the trigger time of every node may be uncertain. We focus on the uncertain provenance during state transition of alarm and the time of the transition process. In order to resolve aforementioned problems, this paper designs a backward fuzzy time reasoning net (BFTRN) model, which can provide effective audit reasoning for a state transition in multiple alarms firing processes. Based on this model, the state information of complex alarm and provenance can be better understood, the contributions of this paper showed as follows: 1) we propose a formal description of the state information and retrospective operation in the evolution of complex alarms, which describes the association between various states clearly by using fuzzy timestamp;
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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 17, NO. 6, NOVEMBER 2013
2) we implement a fuzzy reasoning algorithm to backward reason the evolution of complex alarm process efficiently, which can compute the possibility distribution function of each path. We have organized this paper as the following. Section II is the related work. Section III describes BFTRN models and related definitions of itself. Section IV introduces the concrete implementation of algorithms. Section V validates BFTRN model and fuzzy reasoning algorithm. Finally, the conclusion and future work can be found in Section VI. II. RELATED WORK Provenance can be used to trace the audit trail of data [5], and detect errors in data generation [6]. Pedigree can establish the copyright and ownership of data, enable its citation [7], and determine liability in case of erroneous data. Provenance (Lineage) can be not only associated with data products, but also with the processing that enabled the creation of the data. The general provenance semantic model is 7-W model [8]. The issue of data provenance support is a weighty one for healthcare monitoring systems, as the medical domain often makes it mandatory to support functions such as “dependency analysis” or “data replay” needed to satisfy auditing and other regulatory requirements. [9] proposed a simple, but useful, hybrid provenance model called time-value centric (TVC) provenance. Authors in [10] proposed an innovative provenance approach in agent-mediated healthcare systems. Authors in [11] proposed a tool to navigate through and analyze such provenance information, based on the use of a portal framework that allows different views of provenance information to coexist. Image integrity is closely related to its authenticity. The fidelity of information in a medical record is essential; this natural demand means to identify the provenance and authorship of the information. [12] presented a new method using cryptographic means to improve the trustworthiness of medical images, providing a stronger link between the image and information on its integrity and authenticity, without compromising image quality to the end user. However, the existing works mostly focus on document level provenance for web-based healthcare service, without considering the smaller provenance granularity. To the best of our knowledge, no work about tracing provenance of complex lifecritical alarms generated by medical sensors or device existed so far. There are no time concepts in the traditional basic Petri net. In order to model and analyze various real-time systems, researchers have proposed many types of time Petri net to deal with uncertainty of time in real-time system. Murata has proposed fuzzy-timing high-level Petri nets (FTHNs) [13], which has taken fuzzy set theory for describing the uncertainty or subjectivity. In FTHNs model, the fuzzy time is expressed by four fuzzy time functions or possibility distributions, which includes fuzzy timestamp, fuzzy enabling time, fuzzy firing time, and
fuzzy time delay. Every fuzzy time delay corresponds that a transition t is transferred to a place p. However, the FTHNs model lacks an effective description of time constraints and quantitative analysis of uncertainty of the conflict. Authors in [14] proposed extended fuzzy time Petri net (EFTN), which has added an effective temporal constraint description. However, EFTN model lacks support of backward reasoning method and new applications for lineage tracing work. Authors in [4] described a method to use Petri nets to simulate and validate a multivendor central patient monitoring system that connects to multiple portable patient monitors. However, the Petri nets-based simulation cannot provide backward analyzing function of life-critical errors. The existing models cannot resolve to infer the uncertain provenance of giving target place. In this paper, we propose a BFTRN model, which includes the determination of fuzzy temporal constraint of transition and possibility distribution of the evolution path of complex alarms, to analyze the howprovenance and when-provenance of lift-critical error alarm in the pervasive healthcare monitoring system.
III. MODEL AND DEFINITION In the pervasive health monitoring environment, an alarm is a response of sensors when they satisfy certain conditions. We call triple tuples ai an alarm, where i is an alarm ID, which is a combination of an encoded number of physical locations of sensor and the category of alarm: ai = (I; T ; D)
(1)
where I is a sensor ID that can represent the location of the sensor or an individual action, T is a time stamp when the sensor is activated, and D is duration which is the time difference after one sensor is activated by the next sensor. A basic alarm is an alarm that does not contain the other alarms triggered by some sensors. Basic alarms include low pulse alarm, low consciousness alarm, etc. In practice, people are interested in multiple numbers of alarms instead of an individual alarm. A complex alarm is a series of alarms that comprise some basic alarms arranged in order of time of occurrence. On the other hand, a complex alarm is probably a fusion of some basic alarms or other complex alarms. The how-provenance and when-provenance are more valuable than the other provenance for healthcare monitoring application because they contain the life cycle of various alarms. In this work, how-provenance not only includes information about involving basic alarms, but also includes the temporal information about involving basic alarms. It records information about origin sensor data items and the process of their derivations. When-provenance mainly focuses on fuzzy occurrence time and delay of alarms. We image a scenario, if a monitoring system detected that a patient at the critical stage had stop breathing in a life-critical healthcare monitoring room, say intensive care unit (ICU),
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ual decisions. The context DB store several context parameters, such as sensor location, temperature conditions, humidity conditions, lighting and conditions, which also influence the overall computation process. Reasoning provenance based on BFTRN is the other fundamental function in “alarm fusion and provenance reasoning” layer. Once a medical accident occurs, the administrator or the investigator need analyze the cause of some interested accident alarms. In the following, we model this analysis net and describe the computation of how-provenance and when-provenance using this model.
Fig. 1.
Framework of provenance-aware life-critical monitoring system.
medicals or administers want to know what alarm, at what time, and how results in the accident. They need to construct an analysis network to trace the audit trail of alarm. The provenance knowledge can help to diagnose and alert in advance. Because some alarms occur in parallel with other alarms such as “monitoring heartbeat” and “detecting the depth of anesthesia”, and that sensor data are uncertain, the analysis network to attribute alarm must consider fuzzy reasoning. We design a provenance-aware lift-critical monitoring system to detect the complex alarm and the reason the provenance of interested alarms.
A. Provenance-Aware Life-Critical Monitoring System The framework of provenance-aware life-critical monitoring system is shown in Fig. 1. Unlike most existing life monitoring system, the proposed system provides a provenance analyzing function for an interest alarm. The first column of Fig. 1 is a pervasive life-critical monitoring environment. It consists of various sensors, such as heart monitoring, bispectral index and pulse oximetry, which detect various life-critical alarms. As shown in Fig. 1, these alarms include HMAlarm, BISAlarm, POAlarm, and LoBatAlarm, which monitor heartbeat, the depth of anesthesia, and the pulse of a patient and battery status of the device. In early fusion stage entitled “sensor data processor” in the second column of Fig. 1, the features extracted from the sensor streams are first combined and then sent to an analysis unit (usually a classifier) that provides the decision about the task. On the other hand, in a late fusion approach, which is entitled “alarm fusion and provenance reasoning” in the third column of Fig. 1, the different analysis units first provide the local decisions (in probability score) based on individual sensor data features and then combine these local decisions to make a global decision about an event. In the “multisensor decision aggregation”, the scores from the individual event detectors are fused to obtain a final score about the occurrence of that event, due to the uncertainty in individ-
B. BFTRN Model In this paper, we construct a provenance analysis network for patient’s alarm, BFTRN, based on EFTN [14]. We add an effective temporal constraint and some related sets into each token and each transition. The basic idea of BFTRN is “any” phenomena or system can be described in terms of “cause and effect”. The state-like objects become the cause for the event-like objects to occur. The effect of this event-like object is another state-like object. Definition 1: BFTRN is a 9-tuple (P, T, A, I, O, FT, CT, D, M0 ), where 1) P is a finite set of states or places, P = {p1 , p2 , . . . , pn }, it represents state-like objects in the pervasive healthcare monitoring system. E.g., the level of the pulse is ok; 2) T is a finite set of alarms or transitions, T = {t1 , t2 , . . . , tn }, which meets P ∪ T = Φ and P ∩ T = Φ; 3) A is a finite subset of (P × T ) ∪ (T × P ) called the flow relation or the dependency relation; 4) I is an input function, which defines a map from P to T . I (t) consists of a set of places; 5) O is an output function, which defines a map from T to P . O(t) consists of set of places; 6) FT is a set of all fuzzy timestamps, which relates to tokens. An unrestricted timestamp is [0,0,0,0]; 7) CT is a mapping function from transition set T to the firing temporal constraint of transitions, CT: T → h[a, b, c, d], 0 ≤ a ≤ b ≤ c ≤ d, 0 ≤ h ≤ 1. h[a, b, c, d] is effective temporal interval of tokens, where a, b, c, d are all timestamps, and the possibility of the available tokens in [b, c] is h, the possibility of the available tokens in [a, b] and [c, d] is less than h, the tokens lying outside [a, d] are not available; 8) D is a set of fuzzy delay time that is related to outgoing arcs of transitions; 9) M0 is an initially marking function, M0 : P → FT. A marking of the system corresponds to a vector about places. To handle uncertain, temporal information, we define four fuzzy time functions, which is similar to fuzzy time Petri-net model [13]. They showed as following: fuzzy timestamp πi (τ ) of place pi , fuzzy enabling time et (τ ), fuzzy firing time ot (τ ) and fuzzy delay time dt (τ ) of transition t.
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C. Concepts Supporting Provenance Reasoning in BFTRN We introduce backward reasoning function in fuzzy time Petri net to support provenance operation, so a backward reasoning algorithm, based on BFTRN, can describe the complex evolution of concurrent alarms more intuitively. In order to facilitate the description of the algorithm, the following concepts are essential: Definition 2: Previous relation places set (PRPS) is the set of place pi , which meets pi = I(ti ) (ti is transition), denoted by PRPS(ti ). Accordingly, next relation places set (NRPS) is the set of place pi , which meets pi = O(ti ), denoted by NRPS(ti ). |PRPS(ti )|, and |NRPS(ti )| represents the number of their elements, respectively. Definition 3: Input transition set (ITS) ITS(pi ) is the set of transition ti , which meets pi ∈ NRPS(ti ). Accordingly, output transition set (OTS) OTS(pi ) is the set of transition ti , which meets pi ∈ PRPS(ti ), |ITS(pi )| and |OTS(pi )| represent the number of their elements, respectively. Definition 4: ni (pi , πpi (τ ), ITS(pi ), OTS(pi ))) is a node of place pi that has 4 tuples, where πpi (τ ) represents the fuzzy timestamp of pi . NPNS denotes pending nodes set—the set of ni whose πpi is unknown. Accordingly, processed nodes set (HPNS) denotes the set of ni whose all πpi is known. Initialized nodes set (INS) denote the set of new whose πpi is known at the initial stage. Definition 5: Transition paths set (TPS) consists of triple tuples TPSi . TPSi = {(tj , hj , • tj )}, i, j = 1, 2, . . . , n, where hj represents the number of layers and • tj represents the set of transition, which includes all directly previous transitions of tj ; evolution paths set (EPS) of Ptarget is the set of sequence Epathi that can be constructed based on TPSi . Epathi = {{pstart }(ts , hs , $) {Ps }, . . . ,(tj , hj , • tj ) {Pj }, . . . , (tn , hn , • tn ){Ptarget }}, i = 1, 2, . . . n, and{Pj } ∈ NRPS(tj ), i.e. {Pj } is the next relation place set of the current transition tj . How-provenance in BFTRN mainly reflects the relationship between places, transitions; thus, given a goal place, BFTRN should generate its EPS and describe all intermediate information. Given a couple of conditions, BFTRN should provide the formal description and effectively reasoning of fuzzy timestamp of token. It should provide the fuzzy time function of transition, which exactly reflected when-provenance. IV. BFTRN-BASED BACKWARD REASONING ALGORITHM A. Description of Backward Reasoning Algorithm The main idea of backward reasoning algorithm is: first, from the target places, we introduce a traversing algorithm (which is similar to depth first search) to get every evolution path (EP), which consists of procedure DFS_Visit_P and DFS_Visit_T that visits the places and transitions, respectively. The procedure HandlingPath is to generate the sub path. Secondly, we transform EPS to TPS. Finally, procedure ProcessingEPS computes every fuzzy time function value of each place and transition and the value of possibility distribution of each EP. We omitted the description of these four procedures due to page limit.
B. Properties of Algorithm Proposition 1: BFTRN-based backward reasoning algorithm is completeness. Proof: Based on aforementioned BFTRN definition, we run backward reasoning algorithm from the target places Ptarget , every related place and transition can be attributed and computed repeatedly. Finally, we achieve EPS of Ptarget . Similar to white-path theorem in breadth-first search, the processing of depth-first search color places or transitions during the searching period to mark their state. Each vertex (place or transition) is marked white initially, and will be marked GRAY when it has been discovered, and will be marked BLACK when the searching has finished. Each vertex v (place or transition) has two timestamps: the first timestamp d[v] will be recorded when v is gray, and the second timestamp f [v] will be recorded when v is black; therefore, every vertex can be visited only one time. Thus, all elements in EPS will be constructed, which can prove the completeness of BFTRN. Lemma 1: In a depth-first tree of a BFTRN graph (where the place or transition can be represented by vertex), vertex v is a descendant of vertex u if and only if when u is visited at
WANG AND HU: FUZZY REASONING OF ACCIDENT PROVENANCE IN PERVASIVE HEALTHCARE MONITORING SYSTEMS
the timestamp d[u], there is a path from u to v which entirely consists of white vertices. Proof: =>: Now suppose vertex v is a descendant of vertex u and w is a vertex in the path from u to v, we have d[u] < d[w] because w is not visited at time d[u]; thus, w will be marked white.
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Fuzzy Reasoning of Accident Provenance in Pervasive Healthcare Monitoring Systems Yongli Wang, Member, IEEE, and Xiaohua Hu, Member, IEEE
Abstract—In pervasive healthcare monitoring environments, data provenance, as one metadata, can help people analyze the reasons for medical accidents that are generated by complex events. This reasoning processing often encounters inaccurate time and irreversible reasoning problems. How to solve the uncertain process and fuzzy transformation time presents many challenges to the study of data provenance. In this paper, we propose a backward derivation model with the provenance semantic, backward fuzzy time reasoning net (BFTRN), to solve these two problems. We design a backward reasoning algorithm motivated by time automation theory based on this model. With regard to given life-critical alarms and some constraints, it cannot only derive all evolution paths and the possibility distribution of paths from historical information, but also efficiently compute the value of fuzzy time function for each transition of lift-critical complex alarms in the healthcare monitoring system. We also analyze the properties of BFTRN model in this paper. Experiments on real dataset show that the proposed model is efficient. Index Terms—Fuzzy time automation, life-critical alarm, provenance, reasoning uncertainty.
I. INTRODUCTION HE development of portable computing devices and miniature sensing devices presents many new opportunities for personal healthcare [1]. Digital messages from medical devices, like alarms or clinical data streams, are partitioned into small packets and are sent through the device’s antenna to a shared wireless network access point. For patient data, like anesthesia awareness or heart monitors, each device may be constantly sending a stream of packets that can be assembled in the correct sequence at a central station or computer system. In practical scenarios, medical error may be generated by multiple alarm (event) paths. A complex alarm is to be triggered, only some
T
Manuscript received August 12, 2012; revised February 24, 2013; accepted July 17, 2013. Date of publication July 24, 2013; date of current version November 12, 2013. This work was supported in part by the National Natural Science Foundation of China under Grant 61170035, in part by Jiangsu 973 Project BK2011022, in part by National Natural Science Foundation of Jiangsu under Grant BK2011702, in part by the special project of Nanjing Scientific Committee Foundation 020142010, and in part by the Fundamental Research Funds for the Central Universities 30920130112006. Y. Wang is with the Nanjing University of Science and Technology, Nanjing 210094, China. He is also visiting the College of Information Science and Technology, Drexel University, Philadelphia, PA 19104 USA (e-mail: [email protected]). X. Hu is with the College of Information Science and Technology, Drexel University, Philadelphia, PA 19104 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JBHI.2013.2274518
alarms occurred in accordance with the specific order, and within a specified time interval. Random waiting strategies of collision detection (CD) protocol will likely cause uncertain order of some alarms, and the uncertain delay of alarm. If there is a medical accident, it is difficult to figure out what caused the accident and how to generate the accident. Medical professionals need to investigate the trustworthiness of some recognized alarm. When the system detected an abnormal alarm, the caregiver should want to trace the audit trail of data [2]. Provenance systems may be constructed to support a lot of applications, such as data quality, audit trail, replication recipes, and attribution. Consequently, the study of provenance has been increasingly popular recently. The provenance of data products generated by complex transformations such as workflows is of considerable value to scientists [3]. We use the term data product or dataset to refer to data in any form, such as files, tables, and collections. The two prominent features of the provenance of a data product are the ancestral data product(s) from which this data product evolved, and the process of transformation of these ancestral data product(s), possibly through workflows, that helped derive this data product. Petri nets are a terrific tool for modeling systems with interacting concurrent components. Authors in [4] used their timed extensions in performance modeling. However, the existing alarm recognition methods cannot provide the ability to trace the provenance of alarm, this work presents a solution. We create a life-critical alarm firing network, which is similar to a fuzzy time Petri net, for a healthcare monitoring scenario. The abstraction of this net includes “state-like” objects P and “event-like” objects T and dependencies between these objects A. Section III describes the detailed definition in this paper. An alarm reasoned from the alarm firing network may be produced by probabilistic classification methods, and the trigger time of every node may be uncertain. We focus on the uncertain provenance during state transition of alarm and the time of the transition process. In order to resolve aforementioned problems, this paper designs a backward fuzzy time reasoning net (BFTRN) model, which can provide effective audit reasoning for a state transition in multiple alarms firing processes. Based on this model, the state information of complex alarm and provenance can be better understood, the contributions of this paper showed as follows: 1) we propose a formal description of the state information and retrospective operation in the evolution of complex alarms, which describes the association between various states clearly by using fuzzy timestamp;
2168-2194 © 2013 IEEE
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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 17, NO. 6, NOVEMBER 2013
2) we implement a fuzzy reasoning algorithm to backward reason the evolution of complex alarm process efficiently, which can compute the possibility distribution function of each path. We have organized this paper as the following. Section II is the related work. Section III describes BFTRN models and related definitions of itself. Section IV introduces the concrete implementation of algorithms. Section V validates BFTRN model and fuzzy reasoning algorithm. Finally, the conclusion and future work can be found in Section VI. II. RELATED WORK Provenance can be used to trace the audit trail of data [5], and detect errors in data generation [6]. Pedigree can establish the copyright and ownership of data, enable its citation [7], and determine liability in case of erroneous data. Provenance (Lineage) can be not only associated with data products, but also with the processing that enabled the creation of the data. The general provenance semantic model is 7-W model [8]. The issue of data provenance support is a weighty one for healthcare monitoring systems, as the medical domain often makes it mandatory to support functions such as “dependency analysis” or “data replay” needed to satisfy auditing and other regulatory requirements. [9] proposed a simple, but useful, hybrid provenance model called time-value centric (TVC) provenance. Authors in [10] proposed an innovative provenance approach in agent-mediated healthcare systems. Authors in [11] proposed a tool to navigate through and analyze such provenance information, based on the use of a portal framework that allows different views of provenance information to coexist. Image integrity is closely related to its authenticity. The fidelity of information in a medical record is essential; this natural demand means to identify the provenance and authorship of the information. [12] presented a new method using cryptographic means to improve the trustworthiness of medical images, providing a stronger link between the image and information on its integrity and authenticity, without compromising image quality to the end user. However, the existing works mostly focus on document level provenance for web-based healthcare service, without considering the smaller provenance granularity. To the best of our knowledge, no work about tracing provenance of complex lifecritical alarms generated by medical sensors or device existed so far. There are no time concepts in the traditional basic Petri net. In order to model and analyze various real-time systems, researchers have proposed many types of time Petri net to deal with uncertainty of time in real-time system. Murata has proposed fuzzy-timing high-level Petri nets (FTHNs) [13], which has taken fuzzy set theory for describing the uncertainty or subjectivity. In FTHNs model, the fuzzy time is expressed by four fuzzy time functions or possibility distributions, which includes fuzzy timestamp, fuzzy enabling time, fuzzy firing time, and
fuzzy time delay. Every fuzzy time delay corresponds that a transition t is transferred to a place p. However, the FTHNs model lacks an effective description of time constraints and quantitative analysis of uncertainty of the conflict. Authors in [14] proposed extended fuzzy time Petri net (EFTN), which has added an effective temporal constraint description. However, EFTN model lacks support of backward reasoning method and new applications for lineage tracing work. Authors in [4] described a method to use Petri nets to simulate and validate a multivendor central patient monitoring system that connects to multiple portable patient monitors. However, the Petri nets-based simulation cannot provide backward analyzing function of life-critical errors. The existing models cannot resolve to infer the uncertain provenance of giving target place. In this paper, we propose a BFTRN model, which includes the determination of fuzzy temporal constraint of transition and possibility distribution of the evolution path of complex alarms, to analyze the howprovenance and when-provenance of lift-critical error alarm in the pervasive healthcare monitoring system.
III. MODEL AND DEFINITION In the pervasive health monitoring environment, an alarm is a response of sensors when they satisfy certain conditions. We call triple tuples ai an alarm, where i is an alarm ID, which is a combination of an encoded number of physical locations of sensor and the category of alarm: ai = (I; T ; D)
(1)
where I is a sensor ID that can represent the location of the sensor or an individual action, T is a time stamp when the sensor is activated, and D is duration which is the time difference after one sensor is activated by the next sensor. A basic alarm is an alarm that does not contain the other alarms triggered by some sensors. Basic alarms include low pulse alarm, low consciousness alarm, etc. In practice, people are interested in multiple numbers of alarms instead of an individual alarm. A complex alarm is a series of alarms that comprise some basic alarms arranged in order of time of occurrence. On the other hand, a complex alarm is probably a fusion of some basic alarms or other complex alarms. The how-provenance and when-provenance are more valuable than the other provenance for healthcare monitoring application because they contain the life cycle of various alarms. In this work, how-provenance not only includes information about involving basic alarms, but also includes the temporal information about involving basic alarms. It records information about origin sensor data items and the process of their derivations. When-provenance mainly focuses on fuzzy occurrence time and delay of alarms. We image a scenario, if a monitoring system detected that a patient at the critical stage had stop breathing in a life-critical healthcare monitoring room, say intensive care unit (ICU),
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ual decisions. The context DB store several context parameters, such as sensor location, temperature conditions, humidity conditions, lighting and conditions, which also influence the overall computation process. Reasoning provenance based on BFTRN is the other fundamental function in “alarm fusion and provenance reasoning” layer. Once a medical accident occurs, the administrator or the investigator need analyze the cause of some interested accident alarms. In the following, we model this analysis net and describe the computation of how-provenance and when-provenance using this model.
Fig. 1.
Framework of provenance-aware life-critical monitoring system.
medicals or administers want to know what alarm, at what time, and how results in the accident. They need to construct an analysis network to trace the audit trail of alarm. The provenance knowledge can help to diagnose and alert in advance. Because some alarms occur in parallel with other alarms such as “monitoring heartbeat” and “detecting the depth of anesthesia”, and that sensor data are uncertain, the analysis network to attribute alarm must consider fuzzy reasoning. We design a provenance-aware lift-critical monitoring system to detect the complex alarm and the reason the provenance of interested alarms.
A. Provenance-Aware Life-Critical Monitoring System The framework of provenance-aware life-critical monitoring system is shown in Fig. 1. Unlike most existing life monitoring system, the proposed system provides a provenance analyzing function for an interest alarm. The first column of Fig. 1 is a pervasive life-critical monitoring environment. It consists of various sensors, such as heart monitoring, bispectral index and pulse oximetry, which detect various life-critical alarms. As shown in Fig. 1, these alarms include HMAlarm, BISAlarm, POAlarm, and LoBatAlarm, which monitor heartbeat, the depth of anesthesia, and the pulse of a patient and battery status of the device. In early fusion stage entitled “sensor data processor” in the second column of Fig. 1, the features extracted from the sensor streams are first combined and then sent to an analysis unit (usually a classifier) that provides the decision about the task. On the other hand, in a late fusion approach, which is entitled “alarm fusion and provenance reasoning” in the third column of Fig. 1, the different analysis units first provide the local decisions (in probability score) based on individual sensor data features and then combine these local decisions to make a global decision about an event. In the “multisensor decision aggregation”, the scores from the individual event detectors are fused to obtain a final score about the occurrence of that event, due to the uncertainty in individ-
B. BFTRN Model In this paper, we construct a provenance analysis network for patient’s alarm, BFTRN, based on EFTN [14]. We add an effective temporal constraint and some related sets into each token and each transition. The basic idea of BFTRN is “any” phenomena or system can be described in terms of “cause and effect”. The state-like objects become the cause for the event-like objects to occur. The effect of this event-like object is another state-like object. Definition 1: BFTRN is a 9-tuple (P, T, A, I, O, FT, CT, D, M0 ), where 1) P is a finite set of states or places, P = {p1 , p2 , . . . , pn }, it represents state-like objects in the pervasive healthcare monitoring system. E.g., the level of the pulse is ok; 2) T is a finite set of alarms or transitions, T = {t1 , t2 , . . . , tn }, which meets P ∪ T = Φ and P ∩ T = Φ; 3) A is a finite subset of (P × T ) ∪ (T × P ) called the flow relation or the dependency relation; 4) I is an input function, which defines a map from P to T . I (t) consists of a set of places; 5) O is an output function, which defines a map from T to P . O(t) consists of set of places; 6) FT is a set of all fuzzy timestamps, which relates to tokens. An unrestricted timestamp is [0,0,0,0]; 7) CT is a mapping function from transition set T to the firing temporal constraint of transitions, CT: T → h[a, b, c, d], 0 ≤ a ≤ b ≤ c ≤ d, 0 ≤ h ≤ 1. h[a, b, c, d] is effective temporal interval of tokens, where a, b, c, d are all timestamps, and the possibility of the available tokens in [b, c] is h, the possibility of the available tokens in [a, b] and [c, d] is less than h, the tokens lying outside [a, d] are not available; 8) D is a set of fuzzy delay time that is related to outgoing arcs of transitions; 9) M0 is an initially marking function, M0 : P → FT. A marking of the system corresponds to a vector about places. To handle uncertain, temporal information, we define four fuzzy time functions, which is similar to fuzzy time Petri-net model [13]. They showed as following: fuzzy timestamp πi (τ ) of place pi , fuzzy enabling time et (τ ), fuzzy firing time ot (τ ) and fuzzy delay time dt (τ ) of transition t.
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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 17, NO. 6, NOVEMBER 2013
C. Concepts Supporting Provenance Reasoning in BFTRN We introduce backward reasoning function in fuzzy time Petri net to support provenance operation, so a backward reasoning algorithm, based on BFTRN, can describe the complex evolution of concurrent alarms more intuitively. In order to facilitate the description of the algorithm, the following concepts are essential: Definition 2: Previous relation places set (PRPS) is the set of place pi , which meets pi = I(ti ) (ti is transition), denoted by PRPS(ti ). Accordingly, next relation places set (NRPS) is the set of place pi , which meets pi = O(ti ), denoted by NRPS(ti ). |PRPS(ti )|, and |NRPS(ti )| represents the number of their elements, respectively. Definition 3: Input transition set (ITS) ITS(pi ) is the set of transition ti , which meets pi ∈ NRPS(ti ). Accordingly, output transition set (OTS) OTS(pi ) is the set of transition ti , which meets pi ∈ PRPS(ti ), |ITS(pi )| and |OTS(pi )| represent the number of their elements, respectively. Definition 4: ni (pi , πpi (τ ), ITS(pi ), OTS(pi ))) is a node of place pi that has 4 tuples, where πpi (τ ) represents the fuzzy timestamp of pi . NPNS denotes pending nodes set—the set of ni whose πpi is unknown. Accordingly, processed nodes set (HPNS) denotes the set of ni whose all πpi is known. Initialized nodes set (INS) denote the set of new whose πpi is known at the initial stage. Definition 5: Transition paths set (TPS) consists of triple tuples TPSi . TPSi = {(tj , hj , • tj )}, i, j = 1, 2, . . . , n, where hj represents the number of layers and • tj represents the set of transition, which includes all directly previous transitions of tj ; evolution paths set (EPS) of Ptarget is the set of sequence Epathi that can be constructed based on TPSi . Epathi = {{pstart }(ts , hs , $) {Ps }, . . . ,(tj , hj , • tj ) {Pj }, . . . , (tn , hn , • tn ){Ptarget }}, i = 1, 2, . . . n, and{Pj } ∈ NRPS(tj ), i.e. {Pj } is the next relation place set of the current transition tj . How-provenance in BFTRN mainly reflects the relationship between places, transitions; thus, given a goal place, BFTRN should generate its EPS and describe all intermediate information. Given a couple of conditions, BFTRN should provide the formal description and effectively reasoning of fuzzy timestamp of token. It should provide the fuzzy time function of transition, which exactly reflected when-provenance. IV. BFTRN-BASED BACKWARD REASONING ALGORITHM A. Description of Backward Reasoning Algorithm The main idea of backward reasoning algorithm is: first, from the target places, we introduce a traversing algorithm (which is similar to depth first search) to get every evolution path (EP), which consists of procedure DFS_Visit_P and DFS_Visit_T that visits the places and transitions, respectively. The procedure HandlingPath is to generate the sub path. Secondly, we transform EPS to TPS. Finally, procedure ProcessingEPS computes every fuzzy time function value of each place and transition and the value of possibility distribution of each EP. We omitted the description of these four procedures due to page limit.
B. Properties of Algorithm Proposition 1: BFTRN-based backward reasoning algorithm is completeness. Proof: Based on aforementioned BFTRN definition, we run backward reasoning algorithm from the target places Ptarget , every related place and transition can be attributed and computed repeatedly. Finally, we achieve EPS of Ptarget . Similar to white-path theorem in breadth-first search, the processing of depth-first search color places or transitions during the searching period to mark their state. Each vertex (place or transition) is marked white initially, and will be marked GRAY when it has been discovered, and will be marked BLACK when the searching has finished. Each vertex v (place or transition) has two timestamps: the first timestamp d[v] will be recorded when v is gray, and the second timestamp f [v] will be recorded when v is black; therefore, every vertex can be visited only one time. Thus, all elements in EPS will be constructed, which can prove the completeness of BFTRN. Lemma 1: In a depth-first tree of a BFTRN graph (where the place or transition can be represented by vertex), vertex v is a descendant of vertex u if and only if when u is visited at
WANG AND HU: FUZZY REASONING OF ACCIDENT PROVENANCE IN PERVASIVE HEALTHCARE MONITORING SYSTEMS
the timestamp d[u], there is a path from u to v which entirely consists of white vertices. Proof: =>: Now suppose vertex v is a descendant of vertex u and w is a vertex in the path from u to v, we have d[u] < d[w] because w is not visited at time d[u]; thus, w will be marked white.
