Reliability of the traction system is of critical importance to the safety of CRH (China Railway High-speed) high-speed train. To investigate fault propagation mechanism and predict the probabilities of component-level faults accurately for a high-speed railway traction system, a fault prognosis approach via Bayesian network and bond graph modeling techniques is proposed. The inherent structure of a railway traction system is represented by bond graph model, based on which a multilayer Bayesian network is developed for fault propagation analysis and fault prediction. For complete and incomplete data sets, two different parameter learning algorithms such as Bayesian estimation and expectation maximization (EM) algorithm are adopted to determine the conditional probability table of the Bayesian network. The proposed prognosis approach using Pearl’s polytree propagation algorithm for joint probability reasoning can predict the failure probabilities of leaf nodes based on the current status of root nodes. Verification results in a high-speed railway traction simulation system can demonstrate the effectiveness of the proposed approach.
CRH (China Railway High-speed) high-speed train traction system is a complex electromechanical coupling system, which consists of a lot of electrical and mechanical devices, such as pantograph, traction transformers, traction converters, and traction motors. Along with the growth of running time, some components in a traction system like IGBTs (insulated gate bipolar transistors) and diodes will degrade with age. These fatigued components are likely to have various abrupt faults such as short-circuit or open-circuit faults, which definitely increase the risk of serious accidents in the entire railway. Thus, fault prognosis is urgently demanded in high-speed railway traction systems.
Due to the complex structures and behaviors of electromechanical coupling traction systems, it is difficult to describe the causalities accurately through analytical models, which limits the application of the existing analytical model based fault prognosis methods [
Bond graph modeling has been widely applied to lots of engineering fields for modeling various dynamic systems. It is particularly popular for modeling electromechanical coupling systems. In bond graphs, different elements that belong to different energy domains (such as mechanical, electrical, and electromagnetic domains) can be described by the same model structure with uniform modeling language. Bond graph theory and its recent applications have been summarized in [
This paper proposes a general procedure for constructing a Bayesian network structure on the basis of bond graph modeling for fault prognosis of high-speed train traction device. The causal relationships revealed by the bond graph model are combined with the reasoning capacity of the Bayesian network. For complete and incomplete data sets, Bayesian estimation and expectation maximization (EM) algorithm are adopted, respectively, to determine the conditional probability table of the Bayesian network. Pearl’s polytree propagation algorithm is used for joint probability reasoning. The failure probabilities of the other leaf nodes are determined by the current status of root nodes. The simulation results on CRH5 traction system can verify the effectiveness of the proposed approach.
CRH5 high-speed trains are providing convenient public transportation among major cities in China. According to [
Schematic diagram of CRH5 traction system.
For simplicity, the traction system consisting of two sets of inverters and induction motors is studied in this paper. The three-phase inverter bridge circuits can realize VVVF (variable velocity variable frequency) drive of the three-phase ACIMs (alternating current induction motors). The inverter circuit, as shown in Figure
Schematic diagram of CRH5 inverter.
Open-circuit fault and short-circuit fault are two kinds of common faults in traction inverters. Switch-on failure of the transistors and breakdown of the motor phase can cause open-circuit faults, which will increase torque pulsations, copper losses or reduce mean torque and efficiency. Switch-off failure of the transistors and ground of the phase terminals can cause short-circuit faults, which will bring overload burning of the stator and rotor circuits.
Electromechanical systems are governed by many effects issued from different physical phenomena and various technological components. Bond graph, a unified and multidomain modeling and simulation approach, is well suited for such systems. Bond graph provides possibilities for both structural and behavioral system analysis [
Besides the modeling capability for electromechanical systems, bond graph approach can derive equations or information from the graph itself by using a concept called the causality. In bond graphs, a stroke is marked at one end of each bond, which indicates the direction of an effort or flow signal. Users can derive the relations or analytical expressions between system variables to understand how fault signals propagate in the system.
The converter in CRH5 unit consists of two sets of rectifiers, two sets of inverters, one set of traction control device, and cooling system. Each traction motor is controlled by one set of inverters, whose equivalent circuit is shown in Figure
Equivalent circuit of the inverter and three-phase AC motor.
Equivalent circuit for open-circuit fault.
Equivalent circuit for short-circuit fault.
According to [
Bond graph modeling of CRH5 inverter and three-phase AC motor.
Open-circuit fault and short-circuit fault are two kinds of common faults in inverter circuits. According to circuit analysis, the features of the collector-emitter average voltage of the switching tube are the same when an open-circuit fault happens on
Common faults in the bond graph model of
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Open-circuit fault ( |
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Short-circuit fault ( |
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Open-circuit fault ( |
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Short-circuit fault ( |
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Open-circuit fault ( |
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Short-circuit fault ( |
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According to the equivalent circuit shown in Figures
Bond graph modeling of B-phase inverter circuit in fault.
Since the three-phase circuits in the inverter are exactly the same, B-phase circuit is shown as an example to study the fault prognosis in this paper. Figure
Overview of the fault prognosis based on Bayesian network.
Bayesian network is a directed acyclic graph (DAG), where nodes represent the random variables. The directed edges leading from cause variables to effect variables represent the causal relations. The measurements are donated by conditional probabilities between nodes and father-nodes. According to [
A Bayesian network comprises two parts
The consistent causality description facilitates FDI or fault prognosis design because it is helpful for analyzing the fault propagation in the whole system. Causal path, a graphic representation based on the concept of causality, shows the causal relationships among the system variables. “0” and “1” controlled junctions are the multiple-ports components in bond graph based modeling. According to the definition of flow variable and effort variable, “1” junction indicates that every flow variable of the bonds connected to the junction equals the other, where the input variable is defined as the flow variable of the connected bond that has no causal stroke assigned at the junction. Similarly, a “0” junction indicates that each effort variable of the adjacently connected bonds equals the other, where the input variable is defined as the effort variable of the connected bond that has a causal stroke assigned at the “
The bond graph modeling implies the state equations describing the system dynamics. The causal relationships and power transfer between each component can be obtained clearly through the state equations coming from the bond graph. List the causal relationships of B-phase circuit in number 1 inverter as follows:
Directed graph of B-phase circuit.
The first step is to establish the directed links between variables for a causal network by using the causality derived from the bond graph model of CRH5 traction system. Secondly, use intermediate variables to obtain the conditional probability distributions (CPDs). Thirdly, specify the CPDs for each variable.
The directed graph model of B-phase circuit transforming from bond graph model is shown in Figure
Bayesian network of B-phase circuit.
Different parameter learning algorithms are used to obtain the conditional probability table of the Bayesian network for complete and incomplete data sets. For complete data sets, Bayesian estimation algorithm is used for parameter estimation. It searches the parameter value with maximum posterior probability according to the a priori knowledge when the topological structure
The probability distribution expectation of data set
In this paper, fault prognosis scheme based on Bayesian network of B-phase circuit is designed to predict fault probability of stator or rotor circuit that may cause abnormal behaviors of overall system. The Bayesian network based fault prognosis is a kind of prediction mechanism using joint probability distribution to obtain the fault probability of child nodes, when network structure, fault probabilities of the root nodes, and conditional probability table of the other nodes are given. The causal variable analysis is main application of Bayesian network when the observed statues on any of the random variables are given. Conditional probability of unobserved modes is updated through belief propagation and inference can be made about the most probable status [
Firstly, a bond graph model of CRH5 traction system is formed in the environment of 20-SIM. When open-circuit fault happens on IGBT
In this section, 10000 sets of data produced by experiments are divided into 10 groups, where 600 sets of data are for training and 400 sets of data are for test in each group. According to [
Conditional probability table of parameter learning.
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Predict the fault probability of stator or rotor circuit when short-circuit fault of IGBT components in B-phase inverter circuit happens. According to Pearl’s polytree propagation algorithm used for joint probability reasoning, the prediction results on fault probability of stator and rotor circuit through 10000 sets of complete data are shown in Figures
Fault prognosis of stator circuit.
Fault prognosis of rotor circuit.
In modern engineering systems, some values in the measurement data set are missing such that EM (expectation maximization) method, a well-known parameter estimation algorithm, is used for probabilistic reasoning, combining with Pearl’s polytree propagation algorithm. Each iteration step of EM algorithm contains two steps: the E-step (expectation) and the M-step (maximization). The procedure alternates between the two steps until convergence is achieved. It should be pointed out that the search speed will slow down when EM algorithm comes close to its convergence point.
In this simulation, 10000 sets of data are hidden randomly by
Fault prognosis of stator circuit.
Fault prognosis of rotor circuit.
According to the schematic diagram of CRH5 traction system, a bond graph based model of inverter circuit and three-phase AC motor is built. Then, a bond graph and Bayesian network based fault prognosis approach is proposed to predict the fault probability of stator and rotor circuit, when the prior fault probabilities of IGBT components are given. The bond graph based model of CRH5 traction system is used for building the Bayesian network, which can solve the problem of constructing an accurate Bayesian network structure in practice. Different parameter learning algorithms, such as Bayesian estimation and EM algorithm, are adopted to determine the conditional probability table of the Bayesian network for complete and incomplete data sets. The fault probabilities of leaf nodes (stator and rotor circuit) can be predicted by joint probability reasoning through Pearl’s polytree propagation algorithm. The simulation results can verify its effectiveness in fault prognosis for both complete and incomplete data sets. Our future works lie in the following:
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by National Natural Science Foundation of China (61490703, 61374141 and 61304112), Funding of Jiangsu Innovation Program for Graduate Education KYLX_0280, and the Fundamental Research Funds for the Central Universities (NE2014202).