Fault Diagnosis Models for Electric Locomotive Systems Based on Fuzzy Reasoning Spiking Neural P Systems

Fault Diagnosis Models for Electric Locomotive Systems Based on Fuzzy Reasoning Spiking Neural P Systems Tao Wang1, Gexiang Zhang1,andMarioJ.P´erez-Jim´enez2(B) 1School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China [email protected], [email protected] 2Department of Computer Science and Artificial Intelligence, Research Group on Natural Computing, University of Sevilla, 41012 Sevilla, Spain [email protected] Abstract. This paper discusses the application of fuzzy reasoning spiking neural P systems with real numbers (rFRSN P systems) to fault diagnosis of electric locomotive systems. Relationships among breakdown signals and faulty sections in subsystems of electric locomotive systems are described in the form of fuzzy production rules firstly and then fault diagnosis models based on rFRSN P systems for these subsystems are built according to these rules. Fuzzy production rules for diagnosing electric locomotive systems are abstracted from the fault diagnosis analysis of the subsystems and the causality among faulty sections, faulty subsystems and electric locomotive systems. Finally, a diagnosis model based on rFRSN P systems for electric locomotive systems is proposed. Keywords: Fuzzy reasoning spiking neural P system ·Fault diagnosis ·Electric locomotive system ·Real number ·SS4 electric locomotive systems 1 Introduction Spiking neural P systems (SN P systems), introduced in [2] in the framework of membrane computing, is a new class of computing devices which are inspired by the neurophysiological behavior of neurons sending electrical impulses (spikes) along axons to other neurons. Since then, SN P systems have become a hot topic in membrane computing [3]-[21], including investigations focusing on the use of SN P systems and their variants to solve engineering problems in power systems [18]-[21]. In [18], fuzzy reasoning spiking neural P systems with real numbers (rFRSN P systems) were introduced in order to capture the diagnosis knowledge representation and reasoning. The merits of rFRSN P systems lie in visually describing fuzzy production rules in a fuzzy diagnosis knowledge systems, where they effectively model the relationships among breakdown signals and faulty sections and represent and handle fuzzy knowledge/information. This paper discusses the c Springer International Publishing Switzerland 2014 M. Gheorghe et al. (Eds.): CMC 2014, LNCS 8961, pp. 385–395, 2014. DOI: 10.1007/978-3-319-14370-5 24 386 T. Wang et al. application of rFRSN P systems to the fault diagnosis of the Shaoshan4 (SS4) electric locomotive systems (always indicate SS4 electric locomotive systems). Electric locomotive systems are composed of several subsystems with different functions; meanwhile, these subsystems consist of numerous sections. Thus, a locomotive system can be viewed as a hierarchical tree structure of sections and subsystems [22,23]. To build fault diagnosis models based on rFRSN P systems for different subsystems, relationships among breakdown signals and faulty sections in subsystems are abstracted and described in the form of fuzzy production rules firstly. Then, fault diagnosis models for these subsystems are built based on these rules. Fuzzy production rules for diagnosing electric locomotive systems are derived in accordance with causality rules among faulty sections, faulty subsystems and SS4 electric locomotive systems. It is worth pointing out that rFRSN P systems used in this paper contain three types of rule neurons, i.e., GENERAL, AND and OR, while the ones in [18] only contain two types: AND and OR. This paper is structured as follows. Section 2introduces preliminary definitions and concepts utilsed in this work. The fault diagnosis models for key subsystems and electric locomotive systems are presented in Section 3. Conclusions are drawn in Section 4. 2 Preliminaries In this section, we briefly review the basic concepts of rFRSN P systems [18]. Here, only the necessary prerequisites are introduced. Definition 1: An rFRSN P system of degree m≥1 is a tuple Π=(O,σ1,..., σm,syn, in,out), where: (1) O={a}is a singleton alphabet (ais called spike); (2) σ1,...,σ mare neurons, of the form σi=(θi,ci,ri),1≤i≤m, where: (a) θiis a real number in [0, 1] representing the potential value of spikes (i.e. value of electrical impulses) contained in neuron σi; (b) ciis a real number in [0, 1] representing the fuzzy truth value corresponding to neuron σi; (c) rirepresents a firing (spiking) rule contained in neuron σiwith the form E/aθ→aβ, where Eis the firing condition and its form will be specified below, θand βare real numbers in [0, 1]; (3) syn ⊆{1,2,...,m}×{1,2,...,m}with i=jfor all (i, j)∈syn, 1≤i, j ≤ m, is a directed graph of synapses between the linked neurons; (4) in, out ⊆{1,2,...,m}indicate the input neuron set and the output neuron set of Π, respectively. In rFRSN P systems, each neuron associates with either a fuzzy proposition or a fuzzy production rule, and ci∈[0, 1] is used to express a truth value of this fuzzy proposition or confidence factor (CF) of this fuzzy production rule. Each neuron σicontains only one firing (spiking) rule, of the form E/aθ→aβ, where E=anand nis the number of input synapses from other neurons to the neuron. It can be applied if and only if σicontains at least nspikes, otherwise, the rule cannot be enabled until nspikes are received. For neuron σi, if its firing Fault Diagnosis Models for Electric Locomotive Systems 387 rule is applied, then its pulse value θiis consumed and a new spike with value β is produced in σi. Once the spike with value βis emitted from σi, each neuron σjwith (i, j)∈syn immediately receives this spike. In rFRSN P systems, the neurons are extended to four types (proposition neurons and three kinds of rule neurons: GENERAL,AND and OR) and the pulse value contained in each neuron is no longer the number of spikes represented by a real value, but a real number in [0, 1] representing the potential value of spikes contained in neuron σi. For neuron σi,ifθi>0, then the neuron contains a spike with pulse value θi; otherwise, it contains no spike and its pulse is 0. For different types of neurons, their definitions and the operations for pulse values are different. We only introduce the definition of GENERAL rule neurons. Details about the other three types of neurons can be found in [18]. Definition 2:AGENERAL rule neuron is associated with a fuzzy production rule which has only one proposition in the antecedent part of the rule. Such a neuron is represented by a rectangle, as shown is Fig. 1. AGENERAL rule neuron has only one presynaptic proposition neuron and one or more postsynaptic proposition neurons. If a GENERAL rule neuron receives a spike from its presynaptic proposition neuron and its firing condition is satisfied, then the neuron fires and produces a new spike with the potential value β=θ∗c, where β,θand care real numbers in [0, 1]. F 5 T ET DD o T D F E T  E D D E E xxx xxx *(1(5$/ F 5 *(1(5$/ Fig. 1. AGENERAL rule neuron (a) and its simplified form (b) 3 Fault Diagnosis Models for Electric Locomotive Systems Based on rFRSN P Systems In this section, fault diagnosis models based on rFRSN P systems for SS4 electric locomotive systems and their main subsystems, i.e., main circuit systems, power supply systems, traction and breaking systems, are proposed. Since an SS4 electric locomotive system can be viewed as a hierarchial tree structure of subsystems and sections shown in Fig. 2, we can build the diagnosis models from leaves to the top (that is, the root) of the tree. Thus, we firstly build the models for subsystems and then analyze these models and relationships among an electric locomotive system, its subsystems and faulty sections in these subsystems. Finally, a fault diagnosis model for SS4 electric locomotive systems is proposed. 3.1 A Fault Diagnosis Model for the Main Circuit Systems Fuzzy production rules (Rules 1 to 16), describing the relationships between breakdown signals detected and candidate faulty sections, for main circuit 388 T. Wang et al. (OHFWULFORFRPRWLYH V\VWHPVKDVIDXOWV 0DLQFLUFXLWV\VWHP KDVIDXOWV 3RZHUVXSSO\V\VWHP KDVIDXOWV 7UDFWLRQDQGEUDNLQJ V\VWHPKDVIDXOWV 1RFXUUHQWLQ SDQWRJUDSK xxx &RQWDFWRU EUHDNGRZQ '&9LQSXW EUHDNGRZQ xxx '&9 EUHDNGRZQ 0DLQWUDFWLRQ LQYHUWRUEUHDNGRZQ xxx 3KDVHFXUUHQW VHQVRULQRSHUDWLRQ Fig. 2. A hierarchial tree structure of components in an SS4 electric locomotive system systems of electric locomotives are described as follows, where CF represents the certainty (confidence) factor of a rule, P1,...,P 18 are propositions whose meanings are shown in Table 1. According to these fuzzy production rules, a fault diagnosis model based on rFRSN P systems for main circuit systems Π1=(O,σ1,...,σ 34,syn,in,out) is built, as shown in Fig. 3, where: (1) O={a}is the singleton alphabet (ais called spike); (2) σ1,...,σ 18 are proposition neurons associated with propositions P1,...,P 18, respectively; (3) σ19,...,σ 28,σ 30,...,σ 34 are GENERAL rule neurons associated with fuzzy production rules R1,...,R 10,R 12,...,R 16, respectively; σ29 is an OR rule neuron associated with fuzzy production rule R11; (4) syn ={(1,19),(2,20),(3,21),(4,22),(5,23),(6,24),(7,25),(8,26),(9,27), (10,28),(11,29),(12,29),(13,30),(14,31),(15,32),(16,33),(17,34),(19,13), (20,13),(21,13),(22,14),(23,14),(24,14),(25,15),(26,15),(27,16),(28,16), (29,17),(30,18),(30,15),(31,18),(31,15),(32,18),(33,15),(34,18)}; (5) in ={σ1,...,σ 12},out ={σ18}. Rule 1: IF P1THEN P13 (CF=0.95); Rule 9: IF P9THEN P16 (CF=0.95) Rule 2: IF P2THEN P13 (CF=0.85); Rule 10: IF P10 THEN P16 (CF=0.9) Rule 3: IF P3THEN P13 (CF=0.9); Rule 11: IF P11 OR P12 THEN P17 (CF=0.9) Rule 4: IF P4THEN P14 (CF=0.8); Rule 12: IF P13 THEN P15 AND P18(CF=1.0) Rule 5: IF P5THEN P14 (CF=0.85); Rule 13: IF P14 THEN P15 AND P18(CF=0.9) Rule 6: IF P6THEN P14 (CF=0.8); Rule 14: IF P15 THEN P18 (CF=0.9) Rule 7: IF P7THEN P15 (CF=0.95); Rule 15: IF P16 THEN P15 (CF=0.85) Rule 8: IF P8THEN P15 (CF=0.8); Rule 16: IF P17 THEN P18 (CF=0.85) Table 1. Meaning of each proposition in fuzzy production rules for main circuit systems P1pantograph bounce P10 nonlinear resistor sparkwear P2mechanical part damaged P11 coil/main contact sparkwear P3scratching of pantograph P12 contact in poor contact P4insulating oil damp P13 no current in pantograph P5cooling system breakdown P14 traction transformer breakdown P6transformer internal breakdown P15 pulling motor inoperation P7electrical strength reduction P16 circuit breaker inoperation P8electromotor overload P17 contactor breakdown P9isolating switch sparkwear P18 main circuit breakdown Fault Diagnosis Models for Electric Locomotive Systems 389  V  V  V  V F  V  V  V  V F  V F  5  V F  V F  5  5  V  5  V F  5  5  5  V F  5  V F  V F  5  V F  5  5  V  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  V F  5  5  5  5  3  V  V F  5  V F  V F  V F  V F  V F  V F  V F  V F  V F  V F  V F  V F  V F Fig. 3. A fault diagnosis model based on rFRSN P systems for the main circuit systems 3.2 A Fault Diagnosis Model for the Power Supply Systems Fuzzy production rules (Rules 1 to 13), describing the relationships between breakdown signals detected and candidate faulty sections, for power supply systems of electric locomotives are described as follows, where CF represents the certainty (confidence) factor of a rule, P1,...,P 17 are propositions whose meanings are shown in Table 2. According to these fuzzy production rules, a fault diagnosis model based on rFRSN P systems for power supply systems Π2=(O,σ1,...,σ 30,syn,in,out) is built, as shown in Fig. 4, where: (1) O={a}is the singleton alphabet (ais called spike); (2) σ1,...,σ 17 are proposition neurons associated with propositions P1,...,P 17, respectively; (3) σ18,...,σ 21,σ 23,σ 24,σ 26,...,σ 30 are GENERAL rule neurons associated with fuzzy production rules R1,...,R 4,R 6,R 7,R 9,...,R 13, respectively; σ22 is an OR rule neuron associated with fuzzy production rule R5;σ25 is an AND rule neuron associated with fuzzy production rule R8; (4) syn ={(1,18),(2,19),(3,20),(4,21),(5,22),(6,23),(7,24),(8,25),(9,26), (10,27),(11,22),(12,28),(13,25),(14,29),(16,30),(18,17),(19,10),(20,10), (21,11),(22,12),(23,14),(23,13),(24,13),(25,15),(26,16),(27,17),(27,11), (27,13),(27,14),(28,14),(28,17),(29,16),(30,17)}; (5) in ={σ1,...,σ 9},out ={σ15,σ 17}. Rule 1: IF P1THEN P17 (CF=0.9) Rule 2: IF P2THEN P10 (CF=0.8) Rule 3: IF P3THEN P10 (CF=0.85) Rule 4: IF P4THEN P11 (CF=0.9) Rule 5: IF P5OR P11 THEN P12 (CF=0.85) Rule 6: IF P6THEN P13 AND P14 (CF=0.8) Rule 7: IF P7THEN P13 (CF=0.95) Rule 8: IF P8AND P13 THEN P15 (CF=0.85) Rule 9: IF P9THEN P16 (CF=0.9) 390 T. Wang et al. Table 2. Meaning of each proposition in fuzzy production rules for power supply systems P1main traction invertor breakdown P9fan breakdown P2current collector breakdown P10 DC750V input breakdown P3locomotive current collector breakdown P11 110V DC/DC chopper inoperation P4110V DC/DC chopper breakdown P12 DC110V breakdown P5110V accumulator breakdown P13 280V DC/DC chopper inoperation P6auxiliary inverter breakdown P14 auxiliary inverter inoperation P7280V DC/DC chopper breakdown P15 DC280V breakdown P8280V accumulator breakdown P16 fan inoperation P17 main traction invertor inoperation  V  V  V  V F  V  V  V  V F  V F  5  V F  V  5  5  5  V F  5  V F  5  5  5  V F  5  V F  V F  5  V F  5  5  5  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  V F  V  V  V F  V F  V F  V F V  V F  V F  V F  V F  V F Fig. 4. A fault diagnosis model based on rFRSN P systems for the power supply systems Rule 10: IF P10 THEN P11 AND P13 AND P14 AND P17 (CF=0.85) Rule 11: IF P12 THEN P14 AND P17 (CF=0.8) Rule 12: IF P14 THEN P16 (CF=0.95) Rule 13: IF P16 THEN P17 (CF=0.9) 3.3 A Fault Diagnosis Model for the Traction and Braking Systems Fuzzy production rules (Rules 1 to 10), describing the relationships between breakdown signals detected and candidate faulty sections, for traction and braking systems of electric locomotives are described as follows, where CF represents the certainty (confidence) factor of a rule, P1,...,P 16 are propositions whose meanings are shown in Table 3. According to these fuzzy production rules, a fault diagnosis model based on rFRSN P systems for traction and braking systems Π3=(O,σ1,...,σ 26,syn,in,out) is built, as shown in Fig. 5, where: (1) O={a}is the singleton alphabet (ais called spike); (2) σ1,...,σ 16 are proposition neurons associated with propositions P1,...,P 16, respectively; (3) σ17,σ 18,σ 23,...,σ 26 are GENERAL rule neurons associated with fuzzy production rules R1,R 2,R 7,...,R 10, respectively; σ20,...,σ 22 are OR rule neurons associated with fuzzy production rules R4,...,R 6, respectively; (4) syn ={(1,17),(2,18),(3,19),(4,19),(5,19),(6,20),(7,20),(8,21),(9,22), (10,23),(11,22),(12,24),(13,25),(14,26),(15,21), (17,16), (18,16), (19,13), (20,14),(21,16),(22,16),(23,16),(24,16),(25,15),(26,16)}; Fault Diagnosis Models for Electric Locomotive Systems 391 (5) in ={σ1,...,σ 12},out ={σ16}. Rule 1: IF P1THEN P16 (CF=0.85) Rule 2: IF P2THEN P16 (CF=0.8) Rule 3: IF P3OR P4OR P5THEN P13 (CF=0.9) Rule 4: IF P6OR P7THEN P14 (CF=0.95) Rule 5: IF P8OR P15 THEN P16 (CF=0.9) Rule 6: IF P9OR P11 THEN P16 (CF=0.8) Rule 7: IF P10 THEN P16 (CF=0.7) Rule 8: IF P12 THEN P16 (CF=0.85) Rule 9: IF P13 THEN P15 (CF=0.95) Rule 10: IF P14 THEN P16 (CF=0.75) Table 3. Meaning of each proposition in fuzzy production rules for traction and braking systems P1DC110V breakdown P9main protective relay breakdown P2control source converter plate breakdown P10 traction power controller breakdown P3U-phase current sensor breakdown P11 A/D breakdown P4W-phase current sensor breakdown P12 25/5V breakdown P5V-phase current sensor breakdown P13 more than one among P3,P4and P5happen P6first linear electromotor group breakdown P14 linear electromotor inoperation P7second linear electromotor group breakdown P15 phase current sensor inoperation P8main traction invertor breakdown P16 traction and braking system inoperation  V  V  V  V F  V  V  V  V F  V F  5  V F  5  5  V F  5  V F  5  5  V F  5  V F  5  5  3  3  3  3  3  3  3  3  3  3  3  3  3  3  V F  3  V  V  V  V  V  V  V  V  V  5  V  V F  3 Fig. 5. A fault diagnosis model based on rFRSN P systems for the traction and braking systems 392 T. Wang et al. 3.4 A Fault Diagnosis Model for the Electric Locomotive Systems From Fig. 3to Fig. 5, we know that if there is no current in pantograph or traction transformers breakdown or pulling motors inoperation or contactors breakdown, then the main circuit system of electric locomotive systems has faults; if DC750V input breakdown or fan inoperation or main traction invertor breakdown or DC110V breakdown, then the power supply system of electric locomotive systems has faults; if DC750V input breakdown or fan inoperation or main traction invertor breakdown or DC110V breakdown, then the power supply system of electric locomotive systems has faults; if the main traction invertor breakdown or DC110V breakdown or control source converter plate breakdown or main protective relay breakdown or traction power controller breakdown or A/D breakdown or 25/5V breakdown or linear electromotor inoperation or phase current sensor inoperation, then the traction and braking system of electric locomotive systems has faults. Table 4. Meaning of each proposition in fuzzy production rules for electric locomotive systems P1no current in pantograph P10 main protective relay breakdown P2traction transformer breakdown P11 traction power controller breakdown P3pulling motor inoperation P12 A/D breakdown P4contactor breakdown P13 25/5V breakdown P5DC750V input breakdown P14 linear electromotor inoperation P6fan inoperation P15 phase current sensor inoperation P7main traction invertor breakdown P16 main circuit system has faults P8DC110V breakdown P17 power supply system has faults P9control source converter plate breakdown P18 traction and braking system has faults P19 electric locomotive systems has faults For an electric locomotive system, if one or more than one of its subsystems (main circuit systems, power supply systems, and traction and braking systems) have faults, then this electric locomotive system has faults. According to the analysis, fuzzy production rules (Rules 1 to 4) for electric locomotive systems are described as follows, where CF represents the certainty (confidence) factor of a rule, P1,...,P 19 are propositions whose meanings are shown in Table 4. According to these fuzzy production rules, a fault diagnosis model based on rFRSN P systems for electric locomotive systems Π4=(O,σ1,...,σ 23,syn,in,out)is built, as shown in Fig. 6, where: (1) O={a}is the singleton alphabet (ais called spike); (2) σ1,...,σ 19 are proposition neurons associated with propositions P1,...,P 19, respectively; (3) σ20,...,σ 23 are OR rule neurons associated with fuzzy production rules R1,...,R 4, respectively; (4) syn ={(1,20),(2,20),(3,20),(4,20),(5,21),(6,21),(7,21),(7,22),(8,21),(8,22), (9,22),(10,22),(11,22),(12,22),(13,22),(14,22),(15,22), (16,23),(17,23), (18,23),(20,16),(21,17),(22,18),(23,19)}; (5) in ={σ1,...,σ 15},out ={σ19}. Fault Diagnosis Models for Electric Locomotive Systems 393  V  V  V  V F  V  V  V  V F  V F  5  V F  V F  5  V F  V F  V F  3  3  3  3  3  3  3  3  3  3  3  3  3  3  V F  3  V F  3  V F  3  V F  3  5  5  V  3  V F  V F  V F  V F Fig. 6. A fault diagnosis model based on rFRSN P systems for the electric locomotive systems Rule 1: IF P1OR P2OR P3OR P4THEN P16 (CF=0.95) Rule 2: IF P5OR P6OR P7OR P8THEN P17 (CF=0.95) Rule 3: IF P7OR P8OR P9OR P10 OR P11 OR P12 OR P13 OR P14 OR P15 THEN P18 (CF=0.95) Rule 4: IF P16 OR P17 OR P18 THEN P19 (CF=0.98) 4 Conclusions In this study, rFRSN P systems are applied in fault diagnosis of electric locomotive systems. This study focuses on describing relationships among breakdown signals, faulty sections, faulty subsystems and faulty electric locomotive systems in the form of fuzzy production rules by using syntactical ingredients provided by rFRSN P systems. It proposes fault diagnosis models based on rFRSN P systems for SS4 electric locomotive systems. These models can visually and formally describe relationships among breakdown signals detected and candidate faulty sections or faulty systems. This work is an important theoretical basis for proposing a novel bio-inspired method for fault diagnosis of electric locomotive systems by using rFRSN P systems. To test and verify the practical implementation and scalability of the proposed method, our future work includes the development of diagnosis algorithms for the models proposed in this paper and model reduction algorithms for the models used in specific cases. Experiments with a tool we aim to develop will prove the effectiveness of these algorithms and the approach presented in this paper. Acknowledgments. This work is supported by the National Natural Science Foundation of China (61170016, 61373047, 61170030), the Program for New Century Excellent Talents in University (NCET-11-0715) and SWJTU supported project (SWJTU12CX008). The last author acknowledges the support of the project TIN 2012- 3734 of the Ministerio de Econom´ıa y Competitividad of Spain.