A method for fault detection and detectability analysis of high-speed train traction motors

Abstract

This invention discloses a fault detection and detectability analysis method for high-speed train traction motors, belonging to the field of fault diagnosis technology. The method first constructs the nominal system of the traction motor using T-S fuzzy dynamic modeling technology, then establishes a stable kernel representation / stable image representation and an orthogonal projection residual generator to achieve effective detection of multiplicative faults, and combines an adaptive threshold strategy to improve robustness to changes in control input. Subsequently, based on the traction motor fault system under closed-loop control that is inherently affected by multiplicative faults, the dynamic characteristics of the residuals are analyzed using a time-varying K-Gap metric, and a quantitative evaluation index for detectability is proposed, thus forming a complete technical system from detection method to detectability assessment. This invention not only achieves efficient multiplicative fault detection but also provides theoretical analysis and quantitative basis for its detectability performance, exhibiting significant advantages in computational efficiency and engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis technology, specifically relating to a fault detection and detectability analysis method for a high-speed train traction motor. Background Technology

[0002] Currently, significant progress has been made in fault diagnosis research for induction traction motors. However, existing research suffers from two significant shortcomings: Firstly, in fault detection, traditional methods typically assume motor faults to be additive, utilizing mature observer- or filter-based diagnostic frameworks. However, typical faults in traction motors, such as rotor bar breakage, stator winding inter-turn short circuits, and air gap eccentricity, are essentially multiplicative faults caused by changes in system parameters. Existing observer- or filter-based diagnostic schemes struggle to effectively handle the deep coupling between multiplicative faults and the system's nominal dynamics. Furthermore, as a high-order, nonlinear, and strongly coupled complex system, the traction motor's operating environment exhibits significant model uncertainties. These uncertainties severely affect the residual signal, leading to high false alarm and missed alarm rates in model-based fault detection systems. Secondly, existing research largely focuses on the design and optimization of fault detection algorithms, often assuming fault detectability during the design process, but lacking a systematic analysis of fault detectability, particularly a quantitative evaluation method for the detectability of multiplicative faults under complex dynamic coupling.

[0003] At the theoretical research level, although gap-metric methods provide a basic framework for performance evaluation of linear time-invariant or linear time-varying systems, these methods are difficult to apply to traction motors with nonlinear and strongly coupled characteristics. Classical gap metrics cannot be directly used to analyze the detectability of traction motor faults, especially lacking effective tools for quantitatively evaluating the detectability of motor faults within a time-varying framework. Meanwhile, while orthogonal projection methods can effectively separate nominal dynamics from abnormal dynamics, their application in nonlinear traction motor systems still requires further research. Therefore, it is urgent to establish a theoretical system for fault detectability analysis applicable to the nonlinear characteristics of high-speed train traction motors and to develop effective fault detection methods. This has significant theoretical and engineering value for improving the scientific rigor and reliability of fault diagnosis system design. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a fault detection and detectability analysis method for high-speed train traction motors. First, fault detection based on orthogonal projection is performed to detect multiplication faults, effectively addressing the shortcomings of the nonlinear dynamic coupling characteristics of high-speed train traction motors. Then, fault detectability analysis based on time-varying K-Gap metric is conducted, forming a complete technical system from fault detection to quantitative assessment of detectability.

[0005] The technical solution of the present invention is as follows:

[0006] A method for fault detection and detectability analysis of traction motors in high-speed trains includes the following steps:

[0007] Step 1: Establish the nominal system of high-speed train traction motors using the TS fuzzy dynamic modeling method, and construct a traction motor system based on TS fuzzy modeling that includes model uncertainties.

[0008] Step 2: Based on the nominal system of the high-speed train traction motor, construct the left coprime decomposition and the right coprime decomposition, and establish stable image representation, stable kernel representation, as well as image subspace and kernel subspace;

[0009] Step 3: Construct an orthogonal projection operator on the image subspace, and design a residual generator based on the orthogonal projection operator;

[0010] Step 4: Based on the traction motor system with model uncertainty and TS fuzzy modeling, analyze the residual dynamics to construct an adaptive threshold, and determine whether the induction traction motor has failed based on the fault detection logic.

[0011] Step 5: Establish a traction motor fault system affected by multiplicative faults, and use time-varying K-Gap metrics to analyze the residual dynamic characteristics under closed-loop control. Based on this, establish a fault detectability evaluation index to quantitatively characterize the detection capability of the detection scheme for multiplicative faults.

[0012] Furthermore, the specific process of step 1 is as follows:

[0013] Step 1.1: Based on the voltage equation, flux linkage equation, torque equation, and motion equation of the traction motor, establish a continuous-time dynamic mathematical model of the traction motor:

[0014] ;

[0015] In the formula, and These represent the d-axis and q-axis stator currents of the traction motor, respectively. and These represent the rotor flux linkages on the d-axis and q-axis of the traction motor, respectively. For mechanical rotation speed; , , , , They are respectively , , , , The first derivative; and These represent the stator resistance and the rotor resistance, respectively. , and These represent the stator self-inductance, rotor self-inductance, and mutual inductance between the stator and rotor, respectively. The leakage flux coefficient; Synchronous speed; The number of magnetic pole pairs; and These represent the stator voltages of the d-axis and q-axis of the traction motor, respectively. The electromagnetic time constant; The moment of inertia of the rotor; The damping coefficient;

[0016] Step 1.2: Establish a discrete-time system model:

[0017] ;

[0018] In the formula, For discrete-time index, indicating the first... Each sampling time; , and These represent the state variables, input variables, and measured output variables of the traction motor nominal system, respectively; where, , ; It is the transpose symbol; and These represent the discretized system matrix and input matrix, respectively; , , A parameter matrix representing the nominal system state of the traction motor;

[0019] Step 1.3: Select the d-axis current, q-axis current, and speed of the traction motor stator as the antecedent variables for the fuzzy rule, and establish the IF...THEN fuzzy rule. Fuzzy rules for:

[0020] ;

[0021] In the formula, For the antecedent of the fuzzy rule; The conclusion of the fuzzy rule; That is true; For and; For the first The sampling time of the first sampling moment One preceding variable, ; Indicates the first The fuzzy subsets corresponding to each antecedent variable; and Indicates the first Local linearization subsystem The fuzzy term, the index of the locally linearized subsystem The sequence number of the fuzzy rule Correspondingly;

[0022] Step 1.4: Establish a nominal system for high-speed train traction motors based on TS fuzzy modeling.

[0023] ;

[0024] In the formula, and These are the state matrix and input matrix of the global TS fuzzy model obtained after weighted defuzzification.

[0025] Step 1.5: Construct a traction motor system based on TS fuzzy modeling that includes model uncertainties:

[0026] ;

[0027] In the formula, , All of these indicate model uncertainty caused by deviations of motor parameters from nominal values.

[0028] Furthermore, the specific process of step 2 is as follows:

[0029] Step 2.1: Establish a residual generator based on the TS fuzzy observer:

[0030] ;

[0031] In the formula, To represent the first observer A fuzzy rule; and Representing state variables respectively Measurement output variables The estimated value; Indicates new information; This is the residual signal; and They represent the first The gain matrix and post-filter of each local observer; the index of the local observer and the index of the fuzzy rule. Correspondingly;

[0032] The global TS fuzzy observer is:

[0033] ;

[0034] In the formula, and These represent the gain matrix and post-filter of the global TS fuzzy observer, respectively;

[0035] Step 2.2: Construct the left coprime decomposition of the traction motor nominal system based on TS fuzzy modeling as follows:

[0036] ;

[0037] ;

[0038] In the formula, , These are two left-coprime factorization terms; It is a parameter matrix related to the system matrix and the output matrix;

[0039] Step 2.3: Establish a TS fuzzy controller:

[0040] ;

[0041] In the formula, It is the first Local controllers The gain, the serial number of the local controller The sequence number of the fuzzy rule Correspondingly; Indicates the first An invertible matrix of a local controller; For reference signal;

[0042] The global TS controller is:

[0043] ;

[0044] In the formula, and These are the gain and invertible matrix of the global TS controller, respectively;

[0045] The global closed-loop dynamics of the nominal traction motor system of a high-speed train based on TS fuzzy modeling are as follows:

[0046] ;

[0047] Step 2.4: Construct the right coprime decomposition of the nominal system of high-speed train traction motors based on TS fuzzy modeling as follows:

[0048] ;

[0049] ;

[0050] In the formula, , These are two right-coprime factorization terms; The parameter matrix is ​​related to the system matrix and the input matrix;

[0051] Step 2.5: Construct the stable kernel representation and stable image representation of the nominal system of high-speed train traction motor based on TS fuzzy modeling:

[0052] ;

[0053] ;

[0054] In the formula, , These are the first operator and the second operator, respectively.

[0055] Step 2.6: Construct the image subspace With nuclear space They are respectively:

[0056] ;

[0057] ;

[0058] In the formula, Let Hilbert space be the space of square-summable sequences.

[0059] Furthermore, the specific process of step 3 is as follows:

[0060] Step 3.1: Perform standardized left-right coprime decomposition:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] In the formula, , These are two standardized left coprime factorization terms; , These are two right-coprime factorization terms that have been standardized. , , , , , These are all parameter matrices related to the system matrix, input matrix, and output matrix, and their formulas are as follows:

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] In the formula, It is a 5th order identity matrix; and These are solutions to the two Riccati equations:

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] In the formula, This represents the total number of discrete time steps;

[0078] Constructing a standardized and stable kernel characterization of the nominal system of high-speed train traction motors based on TS fuzzy modeling and standardized stable image characterization :

[0079] ;

[0080] ;

[0081] Step 3.2: Construct the image subspace orthogonal projection operator on :

[0082] ;

[0083] In the formula, Compound operators for mapping; for The adjoint operator;

[0084] Step 3.3: Design based on image subspace The residual generator of orthogonal projection produces residuals. for:

[0085] ;

[0086] Step 3.4: Define the residual evaluation function for:

[0087] ;

[0088] In the formula, Represents a discrete time interval. Indicates the start time. Indicates the termination time; This represents the residual generated through the normalized stable kernel characterization.

[0089] Furthermore, the specific process of step 4 is as follows:

[0090] Step 4.1: Based on the traction motor system with model uncertainty established in Step 1.5, analyze the residual dynamic characteristics obtained by the residual generator of image subspace orthogonal projection constructed in Step 3.3. Combining the properties of the orthogonal projection operator, construct an adaptive threshold. for:

[0091] ;

[0092] In the formula, Representing an uncertain system and nominal system The bound of the gap metric between them satisfies: ; For uncertain systems Image subspace;

[0093] Step 4.2: Based on the fault detection logic, compare the residual evaluation function and the adaptive threshold to determine whether a fault has occurred.

[0094] ;

[0095] When the residual evaluation function is greater than or equal to the set adaptive threshold, it indicates that a fault has occurred and an alarm is triggered; otherwise, it indicates that no fault has occurred and no alarm is triggered.

[0096] Furthermore, the specific process of step 5 is as follows:

[0097] Step 5.1: Analyze typical faults of induction traction motors, including rotor bar breakage faults, stator winding inter-turn short circuit faults, and air gap eccentricity faults. The traction motor fault system affected by multiplicative faults, constructed after analysis, is as follows:

[0098] ;

[0099] ;

[0100] In the formula, Operators representing faulty systems; , , These are the system matrix, input matrix, and output matrix of the faulty system, respectively.

[0101] Step 5.2: For any two time-varying control systems and In the formula, For the system The two left-coprime factorization terms, For the system Given two left coprime decomposition terms, the kernel subspace of these two time-varying control systems is defined as:

[0102] ;

[0103] In the formula, For the first The core space of a time-varying control system; , For the first Two left coprime decomposition terms of a time-varying control system;

[0104] The time-varying K-Gap metric between nucleus subspaces is constructed as follows:

[0105] ;

[0106] In the formula, For the kernel space of the first time-varying control system The kernel space of the second time-varying control system A time-varying K-Gap metric; To from nuclear space To nuclear space The directed K-Gap metric, To from nuclear space To nuclear space The directed K-Gap metric;

[0107] Step 5.3, the calculation method for the time-varying directed K-Gap metric is as follows:

[0108] ;

[0109] In the formula, The supremum; Represents a time series; From arrive The directed K-Gap metric; The infimum; For space To space The set of causal bounded operators; To optimize variables;

[0110] Step 5.4: Based on Bezout's equation, the dynamic representation of the faulty system under closed-loop configuration is as follows:

[0111] ;

[0112] In the formula, and For parametric feedback controller Two right-coprime factorization terms; For parametric feedback controller A left coprime factorization term; For unit mapping operators; For weighted operators; and There are two operators;

[0113] Step 5.5: Based on the dynamics of the faulty system under closed-loop configuration, the dynamics of the residuals under closed-loop control satisfy the following:

[0114] ;

[0115] In the formula, The standardized kernel space of the nominal system under closed-loop configuration. To the standardized kernel space of the faulty system The time-varying directed K-Gap metric; The norm bounds satisfied by the standardized stability kernel representation of a faulty system; , These are the core space of the faulty system and the core space of the nominal system under closed-loop configuration, respectively.

[0116] Step 5.6: Based on the definition of time-varying directed K-Gap metric, construct a time-varying directed K-Gap metric as the fault detectability evaluation index for the traction motor system based on TS fuzzy modeling. , The larger the value, the easier it is to detect the current fault, and for any given threshold... If the following expression is satisfied:

[0117] ;

[0118] Explanation at the threshold The current fault cannot be detected.

[0119] The beneficial technical effects of this invention are as follows: This invention proposes a fault detection scheme based on orthogonal projection, combining TS fuzzy modeling technology and an adaptive threshold strategy. This effectively solves the detection problem caused by the deep coupling between multiplicative faults and the nominal dynamics of the system in high-speed train traction motors, significantly improving the detection performance of the fault detection system under conditions of model uncertainty. Furthermore, for the first time, a theoretical framework for quantitative evaluation of fault detectability based on time-varying K-Gap metric is constructed, achieving accurate quantitative analysis of the detectability of multiplicative faults in high-speed train traction motors. This overcomes the theoretical limitation that traditional gap measurement methods are only applicable to linear time-invariant or linear time-varying systems. This invention forms a complete technical system from fault detection engineering practice to detectability theoretical analysis. It not only provides strong technical support for the safe and reliable operation of high-speed train traction systems through a real-time and efficient fault detection mechanism, but also provides prior theoretical guidance for the design of traction motor fault diagnosis systems. It is applicable to real-time fault monitoring and diagnosis of high-speed train traction motors in complex operating environments. Attached Figure Description

[0120] Figure 1 This is a flowchart of the fault detection and detectability analysis method for high-speed train traction motors according to the present invention.

[0121] Figure 2 This is a graph showing the residual evaluation results under rotor bar breakage fault in the experiment of this invention.

[0122] Figure 3 This is a graph showing the residual evaluation results under inter-turn short-circuit faults in the stator winding during the experiment of this invention.

[0123] Figure 4 This is a graph showing the residual evaluation results under the condition of speed sensor failure in the experiment of this invention. Detailed Implementation

[0124] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0125] like Figure 1 As shown, the present invention includes the following steps:

[0126] Step 1: Based on the voltage equation, flux linkage equation, torque equation, and motion equation, a nominal system of the high-speed train traction motor is established using the Takagi-Sugeno (TS) fuzzy dynamic modeling method. Furthermore, considering unmodeled dynamics or modeling errors caused by complex operating conditions, a traction motor system based on TS fuzzy modeling, incorporating model uncertainties, is constructed. The specific process is as follows:

[0127] Step 1.1: Based on physical principles and electromechanical energy conversion principles, and according to the voltage equation, flux linkage equation, torque equation, and motion equation of the traction motor, a continuous-time dynamic mathematical model of the traction motor is established, described as follows:

[0128] ;

[0129] In the formula, and These represent the d-axis and q-axis stator currents of the traction motor, respectively. and These represent the rotor flux linkages on the d-axis and q-axis of the traction motor, respectively. For mechanical rotation speed; , , , , They are respectively , , , , The first derivative; and These represent the stator resistance and the rotor resistance, respectively. , and These represent the stator self-inductance, rotor self-inductance, and mutual inductance between the stator and rotor, respectively. The leakage flux coefficient; Synchronous speed; The number of magnetic pole pairs; and These represent the stator voltages of the d-axis and q-axis of the traction motor, respectively. The electromagnetic time constant; The moment of inertia of the rotor; The damping coefficient;

[0130] Step 1.2: Establish a state-space model and, through discretization, establish a discrete-time system model, as described below:

[0131] ;

[0132] In the formula, For discrete-time index, indicating the first... Each sampling time, expressed as: , For continuous time variables, The sampling period is discretized. , and These represent the state variables, input variables, and measured output variables of the traction motor nominal system, respectively; where, , ; It is the transpose symbol; and Let these represent the discretized system matrix and input matrix, respectively; where, , ; It is a 5th order identity matrix. , , The parameter matrix related to the nominal system state of the traction motor is as follows:

[0133] ;

[0134] ;

[0135] ;

[0136] Step 1.3: Select the d-axis current, q-axis current, and speed of the traction motor stator as the antecedent variables for the fuzzy rules, and establish the IF...THEN fuzzy rules. Each fuzzy rule in the formula has the same form but is independent of the others. Fuzzy rules The description is as follows:

[0137] ;

[0138] In the formula, For fuzzy rules, it represents the preconditions for each rule; The conclusion of the fuzzy rule represents the result of the model established in step 1.2 after fuzzy linearization. Local linearization subsystem superscript The index of the locally linearized subsystem The sequence number of the fuzzy rule Correspondingly; That is true; For and; For the first The sampling time of the first sampling moment There are several antecedent variables, which belong to a fuzzy subset. ( Indicates the first (a fuzzy subset corresponding to each antecedent variable), the universe of discourse is , ,in Represents the predecessor variable The minimum value, Represents the predecessor variable The maximum value; and Indicates the first Local linearization subsystem The fuzzy terms are determined by the fuzzy rules, specifically:

[0139] ;

[0140] ;

[0141] In the formula, , The first Fuzzy rules The three different values ​​of the antecedent variable are calculated as follows:

[0142] ;

[0143] ;

[0144] ;

[0145] Step 1.4: Establish a nominal system for high-speed train traction motors based on TS fuzzy modeling, as described below:

[0146] ;

[0147] In the formula, and The state matrix and input matrix of the global TS fuzzy model, obtained after weighted defuzzification, are calculated using the following equations:

[0148] ;

[0149] ;

[0150] In the formula, Indicates the first A fuzzy membership function, the index of the fuzzy membership function and the index of the locally linearized subsystem. , fuzzy rule number Correspondingly, it is defined as:

[0151] ;

[0152] In the formula, Indicates the first Antecedent variables in a fuzzy subset membership degree Its satisfaction It is given by the following equation:

[0153] ;

[0154] ;

[0155] In the formula, For the first One preceding variable;

[0156] Step 1.5: Construct a traction motor system based on TS fuzzy modeling that includes model uncertainties:

[0157] ;

[0158] In the formula, , All of these indicate model uncertainty caused by deviations of motor parameters from nominal values.

[0159] Step 2: Based on the nominal system of high-speed train traction motors based on TS fuzzy modeling, construct left coprime decomposition and right coprime decomposition, and establish stable image representation / stable kernel representation (SIR / SKR) and its image subspace and kernel subspace; the specific process is as follows:

[0160] Step 2.1: Establish a residual generator based on the TS fuzzy observer:

[0161] ;

[0162] In the formula, To represent the first observer A fuzzy rule; and Representing state variables respectively Measurement output variables The estimated value; Indicates new information, ; This is the residual signal; and They represent the first The gain matrix and post-filter of each local observer; the index of the local observer and the index of the fuzzy rule. Correspondingly;

[0163] The global TS fuzzy observer is:

[0164] ;

[0165] In the formula, and Let represent the gain matrix and post-filter of the global TS fuzzy observer, respectively, and their calculation formulas are as follows:

[0166] ;

[0167] ;

[0168] Step 2.2: Construct the left coprime decomposition of the traction motor nominal system based on TS fuzzy modeling as follows:

[0169] ;

[0170] ;

[0171] In the formula, , These are two left-coprime factorization terms, which form a left-coprime pair; These are parameter matrices related to the system matrix and output matrix, specifically: ;

[0172] Step 2.3: Establish the following TS fuzzy controller:

[0173] ;

[0174] In the formula, It is the first Local controllers The gain is used to ensure system stability; the serial number of the local controller. The sequence number of the fuzzy rule Correspondingly; Indicates the first An invertible matrix of a local controller; For reference signal;

[0175] The global TS controller is:

[0176] ;

[0177] In the formula, and Here, represents the gain and invertible matrix of the global TS controller, respectively, and the calculation formula is as follows:

[0178] ;

[0179] ;

[0180] The global closed-loop dynamics of the nominal traction motor system of a high-speed train based on TS fuzzy modeling are as follows:

[0181] ;

[0182] Step 2.4: Construct the right coprime decomposition of the nominal system of high-speed train traction motors based on TS fuzzy modeling as follows:

[0183] ;

[0184] ;

[0185] In the formula, , These are two right-coprime factorization terms, which form a right-coprime pair; The parameter matrix is ​​related to the system matrix and the input matrix, specifically: .

[0186] Step 2.5: Construct the SKR and SIR of the high-speed train traction motor nominal system based on TS fuzzy modeling, which are respectively constructed using two operators. and Represented as:

[0187] ;

[0188] ;

[0189] In the formula, , These are the first operator and the second operator, respectively. Let Hilbert space be the space of square-summable sequences;

[0190] Step 2.6: Construct the image subspace and kernel subspace respectively:

[0191] ;

[0192] ;

[0193] In the formula, For image subspace; For nucleon space.

[0194] Step 3: Construct an orthogonal projection operator on the image subspace, and design a residual generator based on this; the specific process is as follows:

[0195] Step 3.1: Perform standardized left-right coprime decomposition:

[0196] ;

[0197] ;

[0198] ;

[0199] ;

[0200] In the formula, , These are two standardized left coprime factorization terms; , These are two right-coprime factorization terms that have been standardized. , , , , , These are all parameter matrices related to the system matrix, input matrix, and output matrix, and their specific formulas are as follows:

[0201] ;

[0202] ;

[0203] ;

[0204] ;

[0205] ;

[0206] ;

[0207] and These are the solutions to the following two Riccati equations:

[0208] ;

[0209] ;

[0210] ;

[0211] ;

[0212] In the formula, This represents the total number of discrete time steps;

[0213] The standardized SKR and SIR for the nominal system of high-speed train traction motors based on TS fuzzy modeling are as follows:

[0214] ;

[0215] ;

[0216] In the formula, For standardized stable kernel characterization; For standardized stable image characterization;

[0217] Step 3.2: Based on the standardized right coprime decomposition established in Step 3.1, construct the image subspace. orthogonal projection operator on :

[0218] ;

[0219] In the formula, Compound operators for mapping; for The adjoint operator;

[0220] Step 3.3: Design based on image subspace The residual generator of orthogonal projection produces residuals. for:

[0221] ;

[0222] Step 3.4: To avoid solving high-dimensional fuzzy weighted orthogonal projection operators and reduce computational requirements, a residual evaluation function is defined. for:

[0223] ;

[0224] In the formula, Represents a discrete time interval. Indicates the start time. Indicates the termination time; This represents the residual generated through the normalized stable kernel characterization.

[0225] Step 4: Based on the traction motor system with model uncertainty and TS fuzzy modeling, analyze the residual dynamics to construct an adaptive threshold, and determine whether the induction traction motor has failed based on fault detection logic; the specific process is as follows:

[0226] Step 4.1: Based on the traction motor system with model uncertainty established in Step 1.5, analyze the residual dynamic characteristics obtained by the residual generator of image subspace orthogonal projection constructed in Step 3.3. Combining the properties of the orthogonal projection operator, construct an adaptive threshold. for:

[0227] ;

[0228] In the formula, Representing an uncertain system and nominal system The bound of the gap metric between them satisfies: ; For uncertain systems Image subspace;

[0229] Step 4.2: Based on the fault detection logic, compare the residual evaluation function constructed in step 3.4 with the adaptive threshold constructed in step 4.1 to determine whether a fault has occurred, as described below:

[0230] ;

[0231] When the residual evaluation function exceeds the set adaptive threshold, it indicates a fault and triggers an alarm; otherwise, it indicates no fault has occurred and no alarm is triggered.

[0232] Step 5: Establish a traction motor fault system affected by multiplicative faults, and analyze the residual dynamic characteristics under closed-loop control using a time-varying K-Gap metric; based on this, establish a fault detectability evaluation index to quantitatively characterize the detection capability of the proposed detection scheme for multiplicative faults. The specific process is as follows:

[0233] Step 5.1: Analyze typical faults of induction traction motors and construct a fault system;

[0234] One of the typical faults of induction traction motors is rotor bar breakage, which damages the physical structure of the rotor bars, leading to a change in rotor resistance.

[0235] ;

[0236] In the formula, and These represent the rotor resistance values ​​before and after the fault occurred, respectively. Indicates the increment of rotor resistance; and These represent the total number of rotor bars and the number of broken rotor bars per phase, respectively.

[0237] The second typical fault is the stator winding inter-turn short circuit fault. Due to the reduction in the effective number of turns, this fault directly affects the stator resistance and also has a slight impact on the stator self-inductance and the mutual inductance between the stator and rotor. A common model for describing this fault is through the following stator resistance change:

[0238] ;

[0239] In the formula, and These represent the stator resistance values ​​before and after the fault occurred, respectively. This indicates the change in stator resistance. and These represent the number of turns and the number of short-circuit turns in each phase winding of the stator, respectively.

[0240] The third typical fault is the air gap eccentricity fault, which causes uneven magnetic induction intensity and distribution in the motor, resulting in changes in inductance parameters including stator self-inductance, rotor self-inductance and mutual inductance between stator and rotor.

[0241] Constructing a traction motor fault system affected by multiplicative faults:

[0242] ;

[0243] ;

[0244] In the formula, Operators representing faulty systems; , , These are the system matrix, input matrix, and output matrix of the faulty system, respectively, and the specific calculation formula is as follows:

[0245] ;

[0246] ;

[0247] ;

[0248] In the formula, and These represent the changes in the system matrix and input matrix caused by typical faults, respectively. This indicates the change in the output matrix caused by sensor malfunction.

[0249] Step 5.2: For any two time-varying control systems and In the formula, For the system The two left-coprime factorization terms, For the system Given two left coprime decomposition terms, the kernel subspace of these two time-varying control systems is defined as:

[0250] ;

[0251] In the formula, For the first The core space of a time-varying control system; , For the first Two left coprime decomposition terms of a time-varying control system;

[0252] The time-varying K-Gap metric between nucleus subspaces is constructed as follows:

[0253] ;

[0254] In the formula, For the kernel space of the first time-varying control system The kernel space of the second time-varying control system A time-varying K-Gap metric; To from nuclear space To nuclear space The directed K-Gap metric, To from nuclear space To nuclear space The directed K-Gap metric is calculated as follows:

[0255] ;

[0256] ;

[0257] In the formula, The supremum; Represents a time series; From arrive The directed K-Gap metric; The infimum; , They are respectively and Elements in; and These are the following subspaces:

[0258] ;

[0259] ;

[0260] In the formula, It is an operator matrix, specifically:

[0261] ,

[0262] In the formula, For unit mapping operators; The truncation operator is specifically represented as follows:

[0263] ;

[0264] In the formula, Represents any sequence, This indicates the first [number]th ... One portion, ;

[0265] Step 5.3: The calculation method for the time-varying directed K-Gap metric is given as follows:

[0266] ;

[0267] In the formula, From arrive The directed K-Gap metric; For space To space The set of causal bounded operators, where the operators are... The norm is defined as:

[0268] ;

[0269] In the formula, For space Elements in; To optimize variables;

[0270] Step 5.4: Based on Bezout's equation, the dynamic representation of the faulty system under closed-loop configuration is as follows:

[0271] ;

[0272] In the formula, and For parametric feedback controller Two right-coprime factorization terms; and For parametric feedback controller The two left coprime factorization terms satisfy the following condition: ; For weighted operators, it is represented as: ; and There are two operators, and the calculation formulas are as follows:

[0273] ;

[0274] ;

[0275] ;

[0276] In the formula, A standardized stable kernel characterization for faulty systems; and These are two left-coprime factorization terms;

[0277] Step 5.5: Based on the dynamics of the faulty system under closed-loop configuration, the dynamics of the residuals under closed-loop control satisfy the following:

[0278] ;

[0279] In the formula, The standardized kernel space of the nominal system under closed-loop configuration. To the standardized kernel space of the faulty system The time-varying directed K-Gap metric; The norm bound satisfied by the normalized stability kernel representation of a faulty system, i.e. ; , The core space of the faulty system and the core space of the nominal system under closed-loop configuration are represented as follows:

[0280] ;

[0281] ;

[0282] Step 5.6: Based on the definition of time-varying directed K-Gap metric, construct a time-varying directed K-Gap metric as the fault detectability evaluation index for the traction motor system based on TS fuzzy modeling. ,Right now The larger the value, the easier the fault is to detect, and for any given threshold... If the following expression is satisfied:

[0283] ;

[0284] Explanation at the threshold The fault cannot be detected under these conditions.

[0285] To demonstrate the feasibility and superiority of this invention, this invention takes the MT205 three-phase squirrel-cage asynchronous motor equipped on the China Railway High-speed No.2 (CRH2) EMU as an example, and detects rotor bar breakage fault, stator winding inter-turn short circuit and speed sensor gain fault respectively. The relevant parameters of the MT205 traction motor are given in Table 1.

[0286] Table 1. Parameters of MT205 Traction Motor

[0287] .

[0288] The simulation sampling period was set to 10 μs. The occurrence times of rotor bar breakage fault, stator winding inter-turn short circuit, and speed sensor fault were set to 3 × 10 μs respectively. 4 4×10 4 5×10 4 The fault detection method proposed in this invention is applied. The adaptive threshold is calculated in step 4.1, and the detection results are obtained by... Figure 2 , Figure 3 and Figure 4 Provided. Figures 2-4 In the graph, the horizontal axis represents the simulation step size, and the vertical axis represents the curves of the residual evaluation function and the adaptive threshold. The dashed line represents the residual evaluation function for fault detection, and the solid line represents the adaptive threshold selected for the residual evaluation. Figures 2-4 The detection results demonstrate that the fault detection method proposed in this invention can effectively detect several typical faults of high-speed train traction motors under the presence of model uncertainties, and has high real-time performance.

[0289] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for fault detection and detectability analysis of traction motors in high-speed trains, characterized in that, Includes the following steps: Step 1: Establish the nominal system of high-speed train traction motors using the TS fuzzy dynamic modeling method, and construct a traction motor system based on TS fuzzy modeling that includes model uncertainties. Step 2: Based on the nominal system of the high-speed train traction motor, construct the left coprime decomposition and the right coprime decomposition, and establish stable image representation, stable kernel representation, as well as image subspace and kernel subspace; Step 3: Construct an orthogonal projection operator on the image subspace, and design a residual generator based on the orthogonal projection operator; the specific process is as follows: Step 3.1: Perform standardized left-right coprime decomposition: ； ； ； ； In the formula, , These are two standardized left coprime decomposition terms; , These are two right-coprime factorization terms that have been standardized. , , , , , These are all parameter matrices related to the system matrix, input matrix, and output matrix, and their formulas are as follows: ； ； ； ； ； ； In the formula, It is a 5th order identity matrix; and These are solutions to the two Riccati equations: ； ； ； ； In the formula, Indicates the total number of discrete time steps; Constructing a standardized and stable kernel characterization of the nominal system of high-speed train traction motors based on TS fuzzy modeling and standardized stable image characterization : ； ； Step 3.2: Construct the image subspace orthogonal projection operator on : ； In the formula, Compound operators for mapping; for The adjoint operator; Step 3.3: Design based on image subspace The residual generator of orthogonal projection produces residuals. for: ； Step 3.4: Define the residual evaluation function for: ； In the formula, Represents a discrete time interval. Indicates the start time. Indicates the end time; This represents the residual generated through standardized stable kernel characterization; Step 4: Based on the traction motor system with model uncertainty and TS fuzzy modeling, analyze the residual dynamics to construct an adaptive threshold, and determine whether the induction traction motor has failed based on the fault detection logic. Step 5: Establish a traction motor fault system affected by multiplicative faults, and analyze the residual dynamic characteristics under closed-loop control using time-varying K-Gap metrics. Based on this, establish a fault detectability evaluation index to quantitatively characterize the detection capability of the detection scheme for multiplicative faults. The specific process is as follows: Step 5.1: Analyze typical faults of induction traction motors, including rotor bar breakage faults, stator winding inter-turn short circuit faults, and air gap eccentricity faults. The traction motor fault system affected by multiplicative faults, constructed after analysis, is as follows: ； ； In the formula, Operators representing faulty systems; , , These are the system matrix, input matrix, and output matrix of the faulty system, respectively. Step 5.2: For any two time-varying control systems and In the formula, For the system The two left-coprime factorization terms, For the system Given two left coprime decomposition terms, the kernel subspace of these two time-varying control systems is defined as: ； In the formula, For the first The core space of a time-varying control system; , For the first Two left coprime decomposition terms of a time-varying control system; The time-varying K-Gap metric between nucleus subspaces is constructed as follows: ； In the formula, For the kernel space of the first time-varying control system The kernel space of the second time-varying control system Time-varying K-Gap metric; To from nuclear space To nuclear space The directed K-Gap metric, To from nuclear space To nuclear space The directed K-Gap metric; Step 5.3, the calculation method for the time-varying directed K-Gap metric is as follows: ； In the formula, The supremum; Represents a time series; From arrive The directed K-Gap metric; The infimum; For space To space The set of causal bounded operators; To optimize variables; Step 5.4: Based on Bezout's equation, the dynamic representation of the faulty system under closed-loop configuration is as follows: ； In the formula, and For parametric feedback controller Two right-coprime factorization terms; For parametric feedback controller A left coprime factorization term; For unit mapping operators; For weighted operators; and There are two operators; Step 5.5: Based on the dynamics of the faulty system under closed-loop configuration, the dynamics of the residuals under closed-loop control satisfy the following: ； In the formula, The standardized kernel space of the nominal system under closed-loop configuration. To the standardized kernel space of the faulty system The time-varying directed K-Gap metric; The norm bounds satisfied by the standardized stability kernel representation of a faulty system; , These are the core space of the faulty system and the core space of the nominal system under closed-loop configuration, respectively. Step 5.6: Based on the definition of time-varying directed K-Gap metric, construct a time-varying directed K-Gap metric as the fault detectability evaluation index for the traction motor system based on TS fuzzy modeling. , The larger the value, the easier it is to detect the current fault, and for any given threshold... If the following expression is satisfied: ； Explanation at the threshold The current fault cannot be detected.

2. The fault detection and detectability analysis method for high-speed train traction motors according to claim 1, characterized in that, The specific process of step 1 is as follows: Step 1.1: Based on the voltage equation, flux linkage equation, torque equation, and motion equation of the traction motor, establish a continuous-time dynamic mathematical model of the traction motor: ； In the formula, and These represent the d-axis and q-axis stator currents of the traction motor, respectively. and These represent the rotor flux linkages on the d-axis and q-axis of the traction motor, respectively. For mechanical rotation speed; , , , , They are respectively , , , , The first derivative; and These represent the stator resistance and the rotor resistance, respectively. , and These represent the stator self-inductance, rotor self-inductance, and mutual inductance between the stator and rotor, respectively. The leakage flux coefficient; Synchronous speed; The number of magnetic pole pairs; and These represent the stator voltages of the d-axis and q-axis of the traction motor, respectively. The electromagnetic time constant; The moment of inertia of the rotor; The damping coefficient; Step 1.2: Establish a discrete-time system model: ； In the formula, For discrete-time index, indicating the first... Each sampling time; , and These represent the state variables, input variables, and measured output variables of the traction motor nominal system, respectively; where, , ; It is the transpose symbol; and These represent the discretized system matrix and input matrix, respectively; , , A parameter matrix representing the nominal system state of the traction motor; Step 1.3: Select the d-axis current, q-axis current, and speed of the traction motor stator as the antecedent variables for the fuzzy rule, and establish the IF...THEN fuzzy rule. Fuzzy rules for: ； In the formula, For the antecedent of the fuzzy rule; The conclusion of the fuzzy rule; That is true; For and; For the first The sampling time of the first sampling moment One preceding variable, ; Indicates the first The fuzzy subsets corresponding to each antecedent variable; and Indicates the first Local linearization subsystem The fuzzy term, the index of the locally linearized subsystem The sequence number of the fuzzy rule Correspondingly; Step 1.4: Establish a nominal system for high-speed train traction motors based on TS fuzzy modeling. ； In the formula, and These are the state matrix and input matrix of the global TS fuzzy model obtained after weighted defuzzification. Step 1.5: Construct a traction motor system based on TS fuzzy modeling that includes model uncertainties: ； In the formula, , All of these indicate model uncertainty caused by deviations of motor parameters from nominal values.

3. The fault detection and detectability analysis method for high-speed train traction motors according to claim 2, characterized in that, The specific process of step 2 is as follows: Step 2.1: Establish a residual generator based on the TS fuzzy observer: ； In the formula, To represent the first observer A fuzzy rule; and Representing state variables respectively Measurement output variables The estimated value; Indicates new information; This is the residual signal; and They represent the first The gain matrix and post-filter of each local observer; the index of the local observer and the index of the fuzzy rule. Correspondingly; The global TS fuzzy observer is: ； In the formula, and These represent the gain matrix and post-filter of the global TS fuzzy observer, respectively; Step 2.2: Construct the left coprime decomposition of the traction motor nominal system based on TS fuzzy modeling as follows: ； ； In the formula, , These are two left-coprime factorization terms; It is a parameter matrix related to the system matrix and the output matrix; Step 2.3: Establish a TS fuzzy controller: ； In the formula, It is the first Local controllers The gain, the serial number of the local controller The sequence number of the fuzzy rule Correspondingly; Indicates the first An invertible matrix of a local controller; For reference signal; The global TS controller is: ； In the formula, and These are the gain and invertible matrix of the global TS controller, respectively; The global closed-loop dynamics of the nominal traction motor system of a high-speed train based on TS fuzzy modeling are as follows: ； Step 2.4: Construct the right coprime decomposition of the nominal system of high-speed train traction motors based on TS fuzzy modeling as follows: ； ； In the formula, , These are two right-coprime factorization terms; The parameter matrix is ​​related to the system matrix and the input matrix; Step 2.5: Construct the stable kernel representation and stable image representation of the nominal system of high-speed train traction motor based on TS fuzzy modeling: ； ； In the formula, , These are the first operator and the second operator, respectively. Step 2.6: Construct the image subspace With nuclear space They are respectively: ； ； In the formula, Let Hilbert space be the space of square-summable sequences.

4. The fault detection and detectability analysis method for high-speed train traction motors according to claim 3, characterized in that, The specific process of step 4 is as follows: Step 4.1: Based on the traction motor system with model uncertainty established in Step 1.5, analyze the residual dynamic characteristics obtained from the residual generator of the image subspace orthogonal projection constructed in Step 3.

3. Combining the properties of the orthogonal projection operator, construct an adaptive threshold. for: ； In the formula, Representing an uncertain system and nominal system The bound of the gap metric between them satisfies: ; For uncertain systems Image subspace; Step 4.2: Based on the fault detection logic, compare the residual evaluation function and the adaptive threshold to determine whether a fault has occurred. ； When the residual evaluation function is greater than or equal to the set adaptive threshold, it indicates a fault and triggers an alarm; Otherwise, it indicates that no fault has occurred and no alarm will be triggered.

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