Reliability analysis method of rail vehicle bogie based on dynamic Bayesian network

Abstract

The present invention relates to the technical field of rail vehicles, and specifically to a reliability analysis method for rail vehicle bogies based on a dynamic Bayesian network, including extracting a training sample set and an initial sample point, training an adaptive Kriging model, using a learning function UH to update the adaptive Kriging model, fitting the time-varying correlation between optimal state values ​​through a TV-Copula function, constructing an optimal TV-pair Copula function between two optimal state value sets through an AIC criterion, constructing a TV-Vine Copula function, as a Bayesian network DAG, constructing a TV-VC-BN between each variable, constructing a TV-VC-DBN, obtaining a failure probability, and calculating reliability. The present invention uses an active learning function UH to select the optimal sample point to optimize the adaptive Kriging proxy model, thereby improving the accuracy of the adaptive Kriging proxy model; by using the TV-Copula function to finally establish a TV-VC-DBN model, the reliability analysis is combined with the time-varying correlation, thereby improving the accuracy of the reliability analysis; by using a K-fold cross-check to judge the stopping criterion of the UH function, the accuracy of the active learning function UH in selecting the optimal sample point is improved.

Description

Technical Field

[0001] The invention relates to the technical field of rail vehicles, and in particular to a reliability analysis method for rail vehicle bogies based on a dynamic Bayesian network. Background Art

[0002] The goal of reliability analysis of rail vehicle related mechanisms is to study the internal and external causes that lead to the weak links of the overall mechanism, so as to find out the rules, propose improvement measures for the overall mechanism, and analyze the impact of the improvement on the reliability of the mechanism. The reliability analysis methods of rail vehicle bogies in the prior art mainly include fault tree analysis, reliability block diagram, failure mode and effect analysis, Markov model, Monte Carlo method and GO method, Bayesian network, etc. However, the reliability analysis methods in the prior art cannot combine the time-varying correlation problem with the reliability analysis results, resulting in a decrease in the accuracy of the reliability analysis results of rail vehicle bogies. Summary of the invention

[0003] In order to overcome the technical problem that the reliability analysis method in the prior art is difficult to combine with time-varying correlation, resulting in low accuracy of reliability analysis results, the present invention provides a rail vehicle bogie reliability analysis method based on a dynamic Bayesian network.

[0004] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a rail vehicle bogie reliability analysis method based on a dynamic Bayesian network, comprising the following steps:

[0005] S1: Determine several different groups of rail vehicle bogie real-time data and their initial design spaces, and sample initial sample points in each group of initial design spaces And training sample set , by training each set of samples Perform simulation calculations to obtain the real-time status of each group of rail vehicle bogies, and use each group of training sample sets The real-time state training of the rail vehicle bogie adaptive Kriging model is used to train the adaptive Kriging model, and each set of training sample sets Perform steps S2-S3;

[0006] S2: Use the learning function UH to extract the initial sample points from the group Select the optimal sample point and use K-fold cross validation to learn the function UH iteration stopping criterion. After the iteration stopping criterion is met, the optimal sample point is added to the current training sample set Get the sample set , and bring the optimal sample point into the current adaptive Kriging model to obtain the optimal state value ;

[0007] S3: Using the Sample Set Optimize the adaptive Kriging model and calculate the coefficient of variation to determine whether the model meets the termination condition. If the coefficient of variation does not meet the requirements, repeat steps S2-S3 and obtain the optimal state value set of the group. , is the number of optimal state values ​​of the group. If the coefficient of variation meets the requirements, the loop steps S2-S3 are stopped and each group of training sample sets Perform steps S2-S3 to obtain the optimal state value set of each group;

[0008] S4: Fit the time-varying correlation between the optimal state value sets through the time-varying Copula function TV-Copula function, construct the optimal time-varying pair Copula function TV-pair Copula function between the two optimal state value sets through the Akaike information criterion AIC criterion, and construct the time-varying Vine Copula function TV-Vine Copula function as the directed acyclic graph DAG of the Bayesian network;

[0009] S5: constructing a time-varying VineCopula Bayesian network TV-VC-BN between the variables based on the DAG of the Bayesian network obtained in step S4;

[0010] S6: Based on TV-VC-BN, a time-varying Vine Copula dynamic Bayesian network TV-VC-DBN is constructed to obtain the failure probability, and the reliability is calculated based on the failure probability;

[0011] S7: Determine whether the failure probability meets the requirement. If not, repeat steps S4-S7. If it meets the requirement, output the current reliability.

[0012] Preferably, the several groups of optimization variables include frame crack data, tread damage data, wheel rim wear data, wheel diameter deviation data, axle crack data, primary spring damage data, vertical shock absorber loose data, vertical shock absorber oil leakage data, lateral buffer stop deformation wear data, air spring scratch data, air spring burst data, lateral shock absorber oil leakage data, lateral shock absorber rubber deformation data, anti-roll torsion bar loose data, anti-roll torsion bar rubber deformation data, anti-roll torsion bar crack data, gearbox assembly case damage data, gear damage data, gearbox bearing damage data, motor bearing damage data, motor internal circuit damage data, tread brake unit failure data, belt parking brake unit failure data, brake shoe wear data, The real-time status of the rail vehicle bogie includes a frame crack status, a tread damage status, a wheel rim wear status, a wheel diameter deviation status, an axle crack status, a primary spring damage status, a vertical shock absorber loose status, a vertical shock absorber oil leakage status, a lateral buffer stop deformation and wear status, an air spring scratch status, an air spring burst status, a lateral shock absorber oil leakage status, a lateral shock absorber rubber deformation status, an anti-roll torsion bar loose status, an anti-roll torsion bar rubber deformation status, an anti-roll torsion bar crack status, a gear box assembly case damage status, a gear damage status, a gear box bearing damage status, a motor bearing damage status, a motor internal circuit damage status, a tread brake unit failure status, a belt parking brake unit failure status, and a brake shoe wear status.

[0013] Preferably, the frame crack data includes material fatigue limit value, cyclic load amplitude, and manufacturing residual stress; the tread damage data includes tread material strength, tread wear coefficient, and tread load pressure; the wheel rim wear data includes wheel material hardness, wheel rim wear coefficient, and wheel-rail contact pressure; the wheel diameter deviation data includes wheel diameter manufacturing tolerance, operating load, and wheel temperature change; the axle crack data includes axle material strength, axle operating load, and axle manufacturing defects; the primary spring damage data includes spring material stiffness, load amplitude, and primary spring service time; the vertical shock absorber loosening data includes shock absorber connection The data of vertical shock absorber oil leakage include oil seal quality, oil pressure and service life; the data of lateral buffer stop deformation and wear include buffer material hardness, frequency of use and lateral buffer stop load pressure; the data of air spring scratch include spring material strength, load amplitude and external wear; the data of air spring burst include spring material quality, internal pressure and spring temperature change; the data of lateral shock absorber oil leakage include shock absorber quality, oil pressure and shock absorber temperature change; the data of lateral shock absorber rubber deformation include rubber hardness, lateral shock absorber rubber load condition and lateral shock absorber rubber use The data of anti-roll torsion bar loosening include torsion bar connection strength, anti-roll torsion bar operating load, and vibration frequency; the data of anti-roll torsion bar rubber deformation include rubber strength, anti-roll torsion bar rubber load conditions, and anti-roll torsion bar rubber service time; the data of anti-roll torsion bar cracking include material fatigue limit, anti-roll torsion bar operating load, and anti-roll torsion bar manufacturing defects; the data of gearbox assembly housing damage include housing material strength, gear transmission load, and gearbox assembly housing manufacturing tolerance; the data of gear damage include gear material strength, gear load conditions, and gear manufacturing tolerance; the data of gearbox bearing damage include shaft Bearing material strength, bearing load, and gearbox bearing manufacturing tolerance; motor bearing damage data includes motor bearing material strength, motor load, and motor running time; motor internal circuit damage data includes motor internal voltage, circuit insulation material quality, and motor running time; tread brake unit failure data includes brake unit material strength, tread brake unit operating load, and braking frequency; parking brake unit failure data includes brake unit quality, parking brake unit braking pressure, and parking brake unit usage time; brake shoe wear data includes brake shoe material strength, brake shoe braking pressure, and brake shoe usage time.

[0014] Preferably, step S2 specifically includes the following steps:

[0015] S201: Use U function to extract the sample points Screening candidate sample point sets , select sample points with small U function values ​​and add them to the candidate sample point set , where the expression of U function is:

[0016] ;

[0017] in, is the predicted mean, is the prediction variance, is the U function value;

[0018] Candidate sample point set It is expressed as:

[0019] ;

[0020] in is the candidate sample space, is the sample data, is the U function value;

[0021] S202: Use H function to select candidate sample point set Select the sample points that contribute most to the accuracy of the adaptive Kriging model and add them to the current sample set The updated sample set is formed, where the expression of the H function is:

[0022] H ( x ) = | ln 2 π s g ^ ( x ) + 1 / 2 [ F ( 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) − F ( − 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) ] − [ 2 s g ^ ( x ) − m g ^ ( x ) 2 f ( 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) + 2 s g ^ ( x ) − m g ^ ( x ) 2 f ( − 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) ] | ;

[0023] in, is the H function value, is the predicted mean, is the prediction variance, is the cumulative distribution function CDF of the standard normal distribution, is the probability density function of the standard normal distribution;

[0024] The expression of the sample point with the largest contribution is:

[0025] ;

[0026] in, is the sample point with the largest contribution, is the candidate sample point set The sample points in For sample points The H function value of

[0027] S203: adopt the K-fold cross learning function UH iteration stopping criterion, if it is not reached, repeat steps S201-S202, if it is reached, output the sample point with the largest current contribution as the optimal sample point;

[0028] S204: Add the optimal sample point to the current training sample set Get the sample set ;

[0029] The expression of the updated sample set is:

[0030] ;

[0031] in, is the updated sample set, is the current training sample set, is the sample point with the largest contribution;

[0032] S205: Bring the optimal sample point into the current adaptive Kriging model to obtain the optimal state value .

[0033] Preferably, the use of K-fold cross-check in step S203 to determine whether the iteration stop criterion is reached includes the following steps:

[0034] S20301: Divide the sample set used by the current adaptive Kriging model into K subsets, with the A subset is used as a validation set , the remaining K-1 subsets are used as training sets , whose expression is:

[0035] ;

[0036] in, For the The training set with a subset as the validation set, For the subsets, For the The validation set when the subset is used as the validation set, For the subsets;

[0037] S20302: Using the training set Generate Kriging Proxy Model ;

[0038] S20303: Using a validation set Evaluating the Model The performance of the overall cross-validation error is calculated as follows:

[0039] ;

[0040] in: For the The validation error when the subset is used as the validation set is is the number of subsets, is the overall cross validation error;

[0041] S20304: Determine whether the iteration criterion is met. The iteration criterion expression is:

[0042] ;

[0043] ;

[0044] in, is the failure probability calculated using the Kriging surrogate model generated using all training sets, For the The failure probability calculated by the Kriging surrogate model constructed when the subset is used as the validation set, is the threshold value, for and The maximum absolute value of the difference.

[0045] Preferably, the coefficient of variation calculation expression in step S3 is:

[0046] ;

[0047] in, represents the coefficient of variation, is the failure probability calculated using the Kriging surrogate model generated by all training sets, Indicates the number of sample points.

[0048] Preferably, step S4 includes the following steps:

[0049] S401: Set two optimal state values and , and obtain their standardized variables through their respective marginal distribution functions, which are expressed as follows:

[0050] ;

[0051] ;

[0052] in, and are the optimal state values, and Represent the optimal state values and The standardized variables are obtained through their respective marginal distribution functions. and They are and The marginal distribution function of

[0053] S402: Using TV-Copula function representation and exist The joint distribution of time is expressed as:

[0054] ;

[0055] in, For time Copula function, and The optimal state values ​​are and The standardized variables are obtained through their respective marginal distribution functions. and The optimal state values ​​are and The empirical distribution function of is the joint probability;

[0056] The parameters are expressed as: ;

[0057] in, It is a function of time and changes with time;

[0058] S403: Get the final expression of the TV-Copula function:

[0059] ;

[0060] in, is a time-varying Copula function, and The optimal state values ​​are and The empirical distribution function of is a function of time, is the Copula function;

[0061] S404: Determine the TV-Copula function as the type of the TV-pair Copula function by using the AIC criterion, wherein the TV-Copula function with the smallest AIC value is used as the TV-pair Copula function, wherein the expression for calculating AIC is:

[0062] ;

[0063] in, represents the AIC value, is the number of model parameters, is the maximum likelihood estimate;

[0064] S405: Determine the primary and secondary relationship between the TV-pair Copula functions of each group by calculating the Kendall rank correlation coefficient. The expression for calculating the Kendall rank correlation coefficient is:

[0065] ;

[0066] in, is the Kendall rank correlation coefficient, is the Copula function, and The optimal state values ​​are and The empirical distribution function of

[0067] S406: Construct TV-Vine Copula function, whose expression is:

[0068] ;

[0069] in, is the TV-Vine Copula function, is the standardized variable vector, is the parameter set of the TV-Copula function, is the number of variables, For variables and The set of conditionally independent variables, is the marginal distribution function, For variables and TV-Copula function, , All are variable numbers.

[0070] Preferably, constructing the TV-VC-BN between the variables comprises the following steps:

[0071] S501: Assume sample space In The basic event is , among which Events The prior probability of ,and satisfy , , the total probability formula is as follows:

[0072] ;

[0073] in, For the Events The prior probability of For events Events that occur The conditional probability of occurrence, For events The probability of occurrence, , All are event numbers;

[0074] S502: Constructing the Bayesian formula: If the event Mutually exclusive, and these events constitute a complete event, and there are events With events The events in occur simultaneously, then the Bayesian formula is expressed as:

[0075] ;

[0076] in, For the Events The prior probability of For events Events that occur The conditional probability of occurrence, For events Probability of occurrence; For events Events that occur Conditional probability of occurrence;

[0077] S503: Substitute the total probability formula into the Bayesian formula to obtain the TV-VC-BN model expression:

[0078] ;

[0079] in, For the Events The prior probability of For events Events that occur The conditional probability of occurrence, For events Events that occur The conditional probability of occurrence, is the number of events.

[0080] Preferably, step S6 comprises the following steps:

[0081] S601: Obtain the joint probability distribution of the initial state of the system in the initial network, which is expressed as:

[0082] ;

[0083] in, is the joint probability distribution of the initial state of the system in the initial network, In the dynamic Bayesian network The value of a node at the initial moment, is the parent node of this node, is the number of nodes in the network, is probability;

[0084] S602: Obtaining the transfer network Time has come The state transition probability at time is expressed as:

[0085] ;

[0086] in, To transfer the network Time has come The state transition probability at time , In the dynamic Bayesian network Nodes in The value of the moment, is the parent node of this node, For nodes in The value of the moment, For nodes in The value of the moment, is the number of nodes in the network, is probability;

[0087] S603: Get the dynamic Bayesian network The joint probability distribution of time is expressed as:

[0088] ;

[0089] in, For dynamic Bayesian networks The joint probability distribution of time, is the joint probability distribution of the initial state of the system in the initial network, To transfer the network Time has come The state transition probability at time , is the node number, is the number of nodes in the network;

[0090] S604: construct a TV-VC-DBN model to obtain the failure probability. The expression of the TV-VC-DBN model is:

[0091] ;

[0092] in, From time arrive The joint distribution of all failure probabilities, For time The joint initial distribution of all variables at time , For in time Time, variable The conditional probability distribution given the state of its parent node and the parameters of the time-varying Vine Copula model, For in time Time, variable In a set of known parent nodes, is the set of time-varying Vine Copula model parameters;

[0093] S605: Calculate the reliability. The reliability calculation expression is:

[0094] ;

[0095] in, For reliability, From time arrive The joint distribution of all failure probabilities.

[0096] Preferably, the expression for judging whether the failure probability meets the requirement in step S7 is:

[0097] ;

[0098] in, is the failure probability of this cycle, is the failure probability of the last cycle, is the threshold value.

[0099] Compared with the prior art, the present invention has the beneficial effects of using an active learning function UH to select optimal sample points to optimize the adaptive Kriging proxy model, thereby improving the accuracy of the adaptive Kriging proxy model; finally establishing a TV-VC-DBN model by using a TV-Copula function, combining the analysis of rail vehicle bogie reliability with time-varying correlation, thereby improving the accuracy of bogie reliability analysis; and improving the accuracy of selecting the optimal sample points by the active learning function UH by using a K-fold cross-check to determine the stopping criterion of the UH function. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 The present invention is a flow chart of a rail vehicle bogie reliability analysis method based on a dynamic Bayesian network. DETAILED DESCRIPTION

[0101] The specific implementation of the rail vehicle bogie reliability analysis method based on dynamic Bayesian network of the present invention is as follows:

[0102] like Figure 1 As shown, the reliability analysis method of a rail vehicle bogie based on a dynamic Bayesian network analyzes the reliability of a rail vehicle bogie. In this embodiment, reliability refers to the probability that the rail vehicle bogie operates effectively, and whether the mechanism operates effectively can be obtained through its operating status data, including the following steps:

[0103] S1: Determine several different groups of rail vehicle bogie real-time data and their initial design spaces, and sample initial sample points in each group of initial design spaces And training sample set , by training each set of samples Perform simulation calculations to obtain the real-time status of each group of rail vehicle bogies, and use each group of training sample sets The real-time state of the rail vehicle bogie is used to train the adaptive Kriging model, and each set of training samples is Perform steps S2-S3;

[0104] Several groups of optimization variables include frame crack data, tread damage data, wheel rim wear data, wheel diameter deviation data, axle crack data, primary spring damage data, vertical shock absorber loose data, vertical shock absorber oil leakage data, lateral buffer stop deformation wear data, air spring scratch data, air spring burst data, lateral shock absorber oil leakage data, lateral shock absorber rubber deformation data, anti-roll torsion bar loose data, anti-roll torsion bar rubber deformation data, anti-roll torsion bar crack data, gearbox assembly case damage data, gear damage data, gearbox bearing damage data, motor bearing damage data, motor internal circuit damage data, tread brake unit failure data, parking brake unit failure data, brake shoe wear data; the frame crack data includes Material fatigue limit value, cyclic load amplitude, manufacturing residual stress; tread damage data includes tread material strength, tread wear coefficient, tread load pressure; wheel rim wear data includes wheel material hardness, wheel rim wear coefficient, wheel-rail contact pressure; wheel diameter deviation data includes wheel diameter manufacturing tolerance, operating load, wheel temperature change; axle crack data includes axle material strength, axle operating load, axle manufacturing defects; primary spring damage data includes spring material stiffness, load amplitude, primary spring usage time; vertical shock absorber loosening data includes shock absorber connection strength, vibration frequency, load conditions; vertical shock absorber oil leakage data includes oil seal quality, oil pressure, service life; lateral buffer stop deformation wear data includes buffer material hardness, usage frequency, lateral Load pressure of the buffer stop; air spring scratch data includes spring material strength, load amplitude, and external wear; air spring burst data includes spring material mass, internal pressure, and spring temperature change; lateral shock absorber oil leakage data includes shock absorber mass, oil pressure, and shock absorber temperature change; lateral shock absorber rubber deformation data includes rubber hardness, lateral shock absorber rubber load conditions, and lateral shock absorber rubber usage time; anti-roll torsion bar loosening data includes torsion bar connection strength, anti-roll torsion bar operating load, and vibration frequency; anti-roll torsion bar rubber deformation data includes rubber strength, anti-roll torsion bar rubber load conditions, and anti-roll torsion bar rubber usage time; anti-roll torsion bar crack data includes material fatigue limit, anti-roll torsion bar operating load, and anti-roll torsion bar manufacturing defects ; Gearbox assembly housing damage data includes housing material strength, gear transmission load, and gearbox assembly housing manufacturing tolerance; gear damage data includes gear material strength, gear load conditions, and gear manufacturing tolerance; gearbox bearing damage data includes bearing material strength, bearing load, and gearbox bearing manufacturing tolerance; motor bearing damage data includes motor bearing material strength, motor load, and motor running time; motor internal circuit damage data includes motor internal voltage, circuit insulation material quality, and motor running time; tread brake unit failure data includes brake unit material strength, tread brake unit operating load, and brake frequency; belt parking brake unit failure data includes brake unit quality, belt parking brake unit brake pressure, and belt parking brake unit usage time;Brake shoe wear data include brake shoe material strength, brake shoe braking pressure, and brake shoe usage time;

[0105] Real-time status of rail vehicle bogies, including frame crack status, tread damage status, wheel rim wear status, wheel diameter deviation status, axle crack status, primary spring damage status, vertical shock absorber loose status, vertical shock absorber oil leakage status, lateral buffer stop deformation and wear status, air spring scratch status, air spring burst status, lateral shock absorber oil leakage status, lateral shock absorber rubber deformation status, anti-roll torsion bar loose status, anti-roll torsion bar rubber deformation status, anti-roll torsion bar crack status, gearbox assembly housing damage status, gear damage status, gearbox bearing damage status, motor bearing damage status, motor internal circuit damage status, tread brake unit failure status, belt parking brake unit failure status, brake shoe wear status

[0106] S2: Use the learning function UH to extract the initial sample points from the group Select the optimal sample point and use K-fold cross validation to learn the function UH iteration stopping criterion. After the iteration stopping criterion is met, the optimal sample point is added to the current training sample set Get the sample set , and bring the optimal sample point into the current adaptive Kriging model to obtain the optimal state value ;

[0107] S201: Use U function to extract the sample points Screening candidate sample point sets , select sample points with small U function values ​​and add them to the candidate sample point set , where the expression of U function is:

[0108] ;

[0109] in, is the predicted mean, is the prediction variance, is the U function value;

[0110] Candidate sample point set It is expressed as:

[0111] ;

[0112] in is the candidate sample space, is the sample data, is the U function value;

[0113] S202: Use H function to select candidate sample point set Select the sample points that contribute most to the accuracy of the adaptive Kriging model and add them to the current sample set The updated sample set is formed, where the expression of the H function is:

[0114] H ( x ) = | ln 2 π s g ^ ( x ) + 1 / 2 [ F ( 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) − F ( − 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) ] − [ 2 s g ^ ( x ) − m g ^ ( x ) 2 f ( 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) + 2 s g ^ ( x ) − m g ^ ( x ) 2 f ( − 2 s g ^ ( x ) − m g ^ ( x ) s g ^ ( x ) ) ] | ;

[0115] in, is the H function value, is the predicted mean, is the prediction variance, is the cumulative distribution function CDF of the standard normal distribution, is the probability density function of the standard normal distribution;

[0116] The expression of the sample point with the largest contribution is:

[0117] ;

[0118] in, is the sample point with the largest contribution, is the candidate sample point set The sample points in For sample points The H function value of

[0119] S203: adopt the K-fold cross learning function UH iteration stopping criterion, if it is not reached, repeat steps S201-S202, if it is reached, output the sample point with the largest current contribution as the optimal sample point;

[0120] Using K-fold cross-validation to determine whether the iteration stopping criterion is reached includes the following steps:

[0121] S20301: Divide the sample set used by the current adaptive Kriging model into K subsets, with the A subset is used as a validation set , the remaining K-1 subsets are used as training sets , whose expression is:

[0122] ;

[0123] in, For the The training set with a subset as the validation set, For the subsets, For the The validation set when the subset is used as the validation set, For the subsets;

[0124] S20302: Using the training set Generate Kriging Proxy Model ;

[0125] S20303: Using a validation set Evaluating the Model The performance of the overall cross-validation error is calculated as follows:

[0126] ;

[0127] in: For the The validation error when the subset is used as the validation set is is the number of subsets, is the overall cross validation error;

[0128] S20304: Determine whether the iteration criterion is met. The iteration criterion expression is:

[0129] ;

[0130] ;

[0131] in, is the failure probability calculated using the Kriging surrogate model generated using all training sets, For the The failure probability calculated by the Kriging surrogate model constructed when the subset is used as the validation set, is the threshold value, for and The maximum absolute value of the difference;

[0132] S204: Add the optimal sample point to the current training sample set Get the sample set ;

[0133] The expression of the updated sample set is:

[0134] ;

[0135] in, is the updated sample set, is the current training sample set, is the sample point with the largest contribution;

[0136] S205: Bring the optimal sample point into the current adaptive Kriging model to obtain the optimal state value ;

[0137] S3: Using the Sample Set Optimize the adaptive Kriging model and calculate the coefficient of variation to determine whether the model meets the termination condition. If the coefficient of variation does not meet the requirements, repeat steps S2-S3 and obtain the optimal state value set of the group. , is the number of optimal state values ​​of the group. If the coefficient of variation meets the requirements, the loop steps S2-S3 are stopped and each group of training sample sets Perform steps S2-S3 to obtain the optimal state value set of each group;

[0138] The expression for calculating the coefficient of variation is:

[0139] ;

[0140] in, represents the coefficient of variation, is the failure probability calculated using the Kriging surrogate model generated by all training sets, Indicates the number of sample points;

[0141] S4: Fit the time-varying correlation between the optimal state value sets through the TV-Copula function, construct the optimal TV-pair Copula function between the two optimal state value sets through the AIC criterion, and construct the TV-Vine Copula function as the DAG of the Bayesian network;

[0142] S401: Set two optimal state values and , and obtain their standardized variables through their respective marginal distribution functions, which are expressed as follows:

[0143] ;

[0144] ;

[0145] in, and are the optimal state values, and Represent the optimal state values and The standardized variables are obtained through their respective marginal distribution functions. and They are and The marginal distribution function of

[0146] S402: Using TV-Copula function representation and exist The joint distribution of time is expressed as:

[0147] ;

[0148] in, For time Copula function, and The optimal state values ​​are and The standardized variables are obtained through their respective marginal distribution functions. and The optimal state values ​​are and The empirical distribution function of is the joint probability;

[0149] The parameters are expressed as: ;

[0150] in, It is a function of time and changes with time;

[0151] S403: Get the final expression of the TV-Copula function:

[0152] ;

[0153] in, is a time-varying Copula function, and The optimal state values ​​are and The empirical distribution function of is a function of time, is the Copula function;

[0154] S404: Determine the TV-Copula function as the type of the TV-pair Copula function by using the AIC criterion, wherein the TV-Copula function with the smallest AIC value is used as the TV-pair Copula function, wherein the expression for calculating AIC is:

[0155] ;

[0156] in, represents the AIC value, is the number of model parameters, is the maximum likelihood estimate;

[0157] S405: Determine the primary and secondary relationship between the TV-pair Copula functions of each group by calculating the Kendall rank correlation coefficient. The expression for calculating the Kendall rank correlation coefficient is:

[0158] ;

[0159] in, is the Kendall rank correlation coefficient, is the Copula function, and The optimal state values ​​are and The empirical distribution function of

[0160] S406: Construct TV-Vine Copula function, whose expression is:

[0161] ;

[0162] in, is the TV-Vine Copula function, is the standardized variable vector, is the parameter set of the TV-Copula function, is the number of variables, For variables and The set of conditionally independent variables, is the marginal distribution function, For variables and TV-Copula function, , All are variable numbers;

[0163] S5: constructing TV-VC-BN between variables based on the DAG of the Bayesian network obtained in step S4;

[0164] Constructing TV-VC-BN between variables includes the following steps:

[0165] S501: Assume sample space In The basic event is , among which Events The prior probability of ,and satisfy , , the total probability formula is as follows:

[0166] ;

[0167] in, For the Events The prior probability of For events Events that occur The conditional probability of occurrence, For events The probability of occurrence, , All are event numbers;

[0168] S502: Constructing the Bayesian formula: If the event Mutually exclusive, and these events constitute a complete event, and there are events With events The events in occur simultaneously, then the Bayesian formula is expressed as:

[0169] ;

[0170] in, For the Events The prior probability of For events Events that occur The conditional probability of occurrence, For events Probability of occurrence; For events Events that occur Conditional probability of occurrence;

[0171] S503: Substitute the total probability formula into the Bayesian formula to obtain the TV-VC-BN model expression:

[0172] ;

[0173] in, For the Events The prior probability of For events Events that occur The conditional probability of occurrence, For events Events that occur The conditional probability of occurrence, is the number of events;

[0174] S6: Based on TV-VC-BN, construct TV-VC-DBN, obtain the failure probability, and calculate the reliability based on the failure probability;

[0175] S601: Obtain the joint probability distribution of the initial state of the system in the initial network, which is expressed as:

[0176] ;

[0177] in, is the joint probability distribution of the initial state of the system in the initial network, In the dynamic Bayesian network The value of a node at the initial moment, is the parent node of this node, is the number of nodes in the network, is probability;

[0178] S602: Obtaining the transfer network Time has come The state transition probability at time is expressed as:

[0179] ;

[0180] in, To transfer the network Time has come The state transition probability at time , In the dynamic Bayesian network Nodes in The value of the moment, is the parent node of this node, For nodes in The value of the moment, For nodes in The value of the moment, is the number of nodes in the network, is probability;

[0181] S603: Get the dynamic Bayesian network The joint probability distribution of time is expressed as:

[0182] ;

[0183] in, For dynamic Bayesian networks The joint probability distribution of time, is the joint probability distribution of the initial state of the system in the initial network, To transfer the network Time has come The state transition probability at time , is the node number, is the number of nodes in the network;

[0184] S604: Determine the CPT between nodes across time periods, set the system stable operation period to 112 hours, construct a TV-VC-DBN model based on the unit failure density function and the maintenance density function, and obtain the failure probability. The expression of the TV-VC-DBN model is:

[0185] ;

[0186] in, From time arrive The joint distribution of all failure probabilities, For time The joint initial distribution of all variables at time , For in time Time, variable The conditional probability distribution given the state of its parent node and the parameters of the time-varying Vine Copula model, For in time Time, variable In a set of known parent nodes, is the set of time-varying Vine Copula model parameters;

[0187] The expression of the unit failure density function is:

[0188] ;

[0189] in, is the unit failure density function of the system, is the failure rate, For time;

[0190] The expression of the maintenance density function is:

[0191] ;

[0192] in, is the maintenance density function, is the maintenance rate, For time;

[0193] S605: Calculate the reliability. The reliability calculation expression is:

[0194] ;

[0195] in, For reliability, From time arrive The joint distribution of all failure probabilities;

[0196] S7: Determine whether the failure probability meets the requirement. If not, repeat steps S4-S7. If it meets the requirement, output the current reliability.

[0197] The expression for judging whether the failure probability meets the requirement is:

[0198] ;

[0199] in, is the failure probability of this cycle, is the failure probability of the last cycle, is the threshold value.

[0200] The present invention is described by way of embodiments, and those skilled in the art will appreciate that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application belong to the protection scope of the present invention.

Claims

1. A reliability analysis method for rail vehicle bogies based on dynamic Bayesian networks, characterized in that: The following steps are involved: S1: Determine several different sets of rail vehicle bogie real-time data and their initial design spaces, and sample initial sample points S and training sample sets S in each set of initial design spaces. t , by training each set of samples S t Perform simulation calculations to obtain the real-time status of each group of rail vehicle bogies, and use each group of training sample sets S t The adaptive Kriging model is used to train the real-time state of the rail vehicle bogie, and the adaptive Kriging model is used to train each training sample set S t Perform steps S2-S3; S2: Use the learning function UH to select the optimal sample point from the initial sample point S of the group, and use K-fold cross-validation to iterate the learning function UH and stop the criterion. After the iterative stop criterion is met, the optimal sample point is added to the current training sample set S t The sample set S is obtained from t+1 , and bring the optimal sample point into the current adaptive Kriging model to obtain the optimal state value Y1; S3: Use sample set S t+1 Optimize the adaptive Kriging model and calculate the coefficient of variation to determine whether the model meets the termination condition. If the coefficient of variation does not meet the requirements, repeat steps S2-S3 and obtain the optimal state value set Y = (Y1, Y2, ..., Y n ), n is the number of optimal state values ​​of the group. If the coefficient of variation meets the requirements, the loop steps S2-S3 are stopped, and each group of training sample set S t Perform steps S2-S3 to obtain the optimal state value set of each group; S4: Fit the time-varying correlation between the optimal state value sets through the time-varying Copula function TV-Copula function, construct the optimal time-varying pair Copula function TV-pair Copula function between the two optimal state value sets through the Akaike Information Criterion AIC criterion, and construct the time-varying Vine Copula function TV-Vine Copula function as the directed acyclic graph DAG of the Bayesian network; S5: constructing a time-varying Vine Copula Bayesian network TV-VC-BN between the variables based on the DAG of the Bayesian network obtained in step S4; S6: Based on TV-VC-BN, a time-varying Vine Copula dynamic Bayesian network TV-VC-DBN is constructed to obtain the failure probability, and the reliability is calculated based on the failure probability; S7: Determine whether the failure probability meets the requirement. If not, repeat steps S4-S7. If it meets the requirement, output the current reliability.

2. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 1 is characterized in that: The several groups of different rail vehicle bogie real-time data include frame crack data, tread damage data, wheel rim wear data, wheel diameter deviation data, axle crack data, primary spring damage data, vertical shock absorber loose data, vertical shock absorber oil leakage data, lateral buffer stop deformation wear data, air spring scratch data, air spring burst data, lateral shock absorber oil leakage data, lateral shock absorber rubber deformation data, anti-roll torsion bar loose data, anti-roll torsion bar rubber deformation data, anti-roll torsion bar crack data, gear box assembly case damage data, gear damage data, gear box bearing damage data, motor bearing damage data, motor internal circuit damage data, tread brake unit failure data, belt parking brake unit failure data, brake shoe wear The data includes the real-time status of the rail vehicle bogie, including the frame crack status, tread damage status, wheel rim wear status, wheel diameter deviation status, axle crack status, primary spring damage status, vertical shock absorber loose status, vertical shock absorber oil leakage status, lateral buffer stop deformation and wear status, air spring scratch status, air spring burst status, lateral shock absorber oil leakage status, lateral shock absorber rubber deformation status, anti-roll torsion bar loose status, anti-roll torsion bar rubber deformation status, anti-roll torsion bar crack status, gear box assembly case damage status, gear damage status, gear box bearing damage status, motor bearing damage status, motor internal circuit damage status, tread brake unit failure status, belt parking brake unit failure status, brake shoe wear status.

3. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 2 is characterized in that: The frame crack data includes material fatigue limit value, cyclic load amplitude, and manufacturing residual stress; tread damage data includes tread material strength, tread wear coefficient, and tread load pressure; wheel rim wear data includes wheel material hardness, wheel rim wear coefficient, and wheel-rail contact pressure; wheel diameter deviation data includes wheel diameter manufacturing tolerance, operating load, and wheel temperature change; axle crack data includes axle material strength, axle operating load, and axle manufacturing defects; primary spring damage data includes spring material stiffness, load amplitude, and primary spring usage time; vertical shock absorber loosening data includes shock absorber connection strength , vibration frequency, load conditions; vertical shock absorber oil leakage data includes oil seal quality, oil pressure, and service life; lateral buffer stop deformation and wear data includes buffer material hardness, frequency of use, and lateral buffer stop load pressure; air spring scratch data includes spring material strength, load amplitude, and external wear; air spring burst data includes spring material quality, internal pressure, and spring temperature change; lateral shock absorber oil leakage data includes shock absorber quality, oil pressure, and shock absorber temperature change; lateral shock absorber rubber deformation data includes rubber hardness, lateral shock absorber rubber load conditions, and lateral shock absorber rubber usage time. The data of anti-roll torsion bar loosening include torsion bar connection strength, anti-roll torsion bar operating load, and vibration frequency; the data of anti-roll torsion bar rubber deformation include rubber strength, anti-roll torsion bar rubber load conditions, and anti-roll torsion bar rubber service time; the data of anti-roll torsion bar cracking include material fatigue limit, anti-roll torsion bar operating load, and anti-roll torsion bar manufacturing defects; the data of gearbox assembly housing damage include housing material strength, gear transmission load, and gearbox assembly housing manufacturing tolerance; the data of gear damage include gear material strength, gear load conditions, and gear manufacturing tolerance; the data of gearbox bearing damage include bearing Material strength, bearing load, and gearbox bearing manufacturing tolerance; motor bearing damage data includes motor bearing material strength, motor load, and motor running time; motor internal circuit damage data includes motor internal voltage, circuit insulation material quality, and motor running time; tread brake unit failure data includes brake unit material strength, tread brake unit operating load, and braking frequency; parking brake unit failure data includes brake unit quality, parking brake unit braking pressure, and parking brake unit usage time; brake shoe wear data includes brake shoe material strength, brake shoe braking pressure, and brake shoe usage time.

4. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 1, characterized in that: Step S2 specifically includes the following steps: S201: Use U function to select candidate sample point set C from sample point S t , select sample points with small U function values ​​and add them to the candidate sample point set C t , where the expression of U function is: in, is the predicted mean, is the prediction variance, U(x) is the U function value; Candidate sample point set C t It is expressed as: C t ={x∈X|U(x)}; Where X is the candidate sample space, x is the sample data, and U(x) is the U function value; S202: Use H function to select candidate sample point set C t Select the sample points that contribute most to the accuracy of the adaptive Kriging model and add them to the current sample set S t The updated sample set is formed, where the expression of the H function is: Where H(x) is the value of the H function, is the predicted mean, is the prediction variance, Φ is the cumulative distribution function CDF of the standard normal distribution, and φ is the probability density function of the standard normal distribution; The expression of the sample point with the largest contribution is: in, is the sample point with the greatest contribution, and x is the candidate sample point set C t The sample points in H t (x) is the H function value of sample point x; S203: adopt the K-fold cross learning function UH iteration stopping criterion, if it is not reached, repeat steps S201-S202, if it is reached, output the sample point with the largest current contribution as the optimal sample point; S204: Add the optimal sample point to the current training sample set S t The sample set S is obtained from t+1 ; The expression of the updated sample set is: Among them, S t+1 is the updated sample set, S t is the current training sample set, is the sample point with the largest contribution; S205: Bring the optimal sample point into the current adaptive Kriging model to obtain the optimal state value Y1.

5. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 4 is characterized in that: The K-fold cross-check in step S203 to determine whether the iteration stop criterion is reached includes the following steps: S20301: Divide the sample set used by the current adaptive Kriging model into K subsets, and use the i-th subset as the validation set V i , the remaining K-1 subsets are used as training set T i , whose expression is: Among them, T i is the training set when the ith subset is used as the validation set, D j is the jth subset, V i is the validation set when the ith subset is used as the validation set, D i is the i-th subset; S20302: Use training set T i Generate Kriging surrogate model K i ; S20303: Use validation set V i Evaluate Model K i The performance of the overall cross-validation error is calculated as follows: Where: E i is the verification error when the i-th subset is used as the verification set, K is the number of subsets, E CV is the overall cross validation error; S20304: Determine whether the iteration criterion is met. The iteration criterion expression is: in, is the failure probability calculated using the Kriging surrogate model generated by all training sets, P f -i is the failure probability calculated by the Kriging surrogate model constructed when the i-th subset is used as the validation set, ε s is the threshold value, for and The maximum absolute value of the difference.

6. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 4 is characterized in that: The calculation expression of the coefficient of variation in step S3 is: in, represents the coefficient of variation, is the failure probability calculated using the Kriging surrogate model generated by all training sets, n MC Indicates the number of sample points.

7. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 4 is characterized in that: Step S4 includes the following steps: S401: Assume two optimal state values ​​X and Y, and obtain their standardized variables through their respective marginal distribution functions, the expression of which is: U=F X (X); V=F Y (Y); Among them, X and Y are the optimal state values, U and V are the standardized variables of the optimal state values ​​X and Y obtained by their respective marginal distribution functions, and F X and F Y are the marginal distribution functions of X and Y respectively; S402: Use the TV-Copula function to represent the joint distribution of U and V at time t, and its expression is: C t (u,v)=P[(U≤u,V≤v);t]; Among them, C t is the Copula function at time t, U and V are the standardized variables of the optimal state values ​​X and Y obtained by their respective marginal distribution functions, u and v are the empirical distribution functions of the optimal state values ​​X and Y, and P is the joint probability; C t The parameters are expressed as: t =f(t); Among them, θ t It is a function of time and changes with time; S403: Get the final expression of the TV-Copula function: C t [(u,v);θ t ]=C[(u,v);θ t ]; Among them, C t is a time-varying Copula function, u and v are the empirical distribution functions of the optimal state values ​​X and Y respectively, θ t is the function of time, C is the Copula function; S404: Determine the TV-Copula function as the type of the TV-pairCopula function by using the AIC criterion, wherein the TV-Copula function with the smallest AIC value is used as the TV-pairCopula function, wherein the expression for calculating AIC is: AIC = 2k-2lnL; Among them, AIC represents the AIC value, k is the number of model parameters, and L is the maximum likelihood estimate; S405: Determine the primary and secondary relationship between the TV-pair Copula functions of each group by calculating the Kendall rank correlation coefficient. The expression for calculating the Kendall rank correlation coefficient is: Among them, τ is the Kendall rank correlation coefficient, C is the Copula function, u and v are the empirical distribution functions of the optimal state values ​​X and Y respectively; S406: Construct TV-Vine Copula function, whose expression is: Among them, V t is the TV-VineCopula function, u=(u1,u2,...,u d ) is the standardized variable vector, θ t ={θ t,ij } is the parameter set of the TV-Copula function, d is the number of variables, and D(i,j) is the variable u i and u j The set of conditionally independent variables, U D(i,j) is the marginal distribution function, C t,ij is the variable u i and u j TV-Copula function, i and j are both variable numbers.

8. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 6, characterized in that: Constructing TV-VC-BN between variables includes the following steps: S501: Assume that n basic events in the sample space Φ are B1, B2, ..., B n , where the i-th event B i The prior probability of i ), and B1,B2,...,B n Meet B i ∩B j =Φ,(i≠j),P(B i )>0, i=1,2,...,n, the total probability formula is as follows: Among them, P(B i ) is the i-th event B i The prior probability, P(VB i ) is event B i The conditional probability of event V occurring when occurs, P(V) is the probability of event V occurring, i and j are both event numbers; S502: Constructing Bayesian formula: If events B1, B2, ..., B n mutually exclusive, and these events constitute a complete event, and there is event V and events B1, B2, ..., B n The events in occur simultaneously, then the Bayesian formula is expressed as: Among them, P(B i ) is the i-th event B i The prior probability, P(VB i ) is event B i The conditional probability of event V occurring when the event occurs, P(V) is the probability of event V occurring; P(B i |V) is event B when event V occurs i Conditional probability of occurrence; S503: Substitute the total probability formula into the Bayesian formula to obtain the TV-VC-BN model expression: Among them, P(B i ) is the i-th event B i The prior probability, P(VB i ) is event B i The conditional probability of event V occurring when the event occurs, P(B i |V) is event B when event V occurs i The conditional probability of occurrence, n is the number of events.

9. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 7, characterized in that: Step S6 includes the following steps: S601: Obtain the joint probability distribution of the initial state of the system in the initial network, which is expressed as: Among them, P(X0) is the joint probability distribution of the initial state of the system in the initial network, is the value of the i-th node in the dynamic Bayesian network at the initial moment, is the parent node of the node, n is the number of nodes in the network, and P is the probability; S602: Obtain the state transition probability from time t-1 to time t in the transfer network, and its expression is: Among them, P(X t |X t-1 ) is the state transition probability from time t-1 to time t in the transfer network, is the value of the ith node in the dynamic Bayesian network at time t, is the parent node of the node, X t is the value of the node at time t, X t-1 is the value of the node at time t-1, n is the number of nodes in the network, and P is the probability; S603: Obtain the joint probability distribution of the dynamic Bayesian network at time 0, 1, 2, ..., t, which is expressed as: Among them, P(X0,X1,...,X t ) is the joint probability distribution of the dynamic Bayesian network at time 0, 1, 2, ..., t, P(X0) is the joint probability distribution of the initial state of the system in the initial network, P(X t |X t-1 ) is the state transition probability from time t-1 to time t in the transfer network, i is the node number, and n is the number of nodes in the network; S604: construct a TV-VC-DBN model to obtain the failure probability. The expression of the TV-VC-DBN model is: Among them, P(X(0),X(1),...,X(T)) is the joint distribution of all failure probabilities from time t = 0 to t = T, P(X(0)) is the joint initial distribution of all variables at time t = 0, and P(X i (t+1)|Parents(X i (t+1)),{θ t,ij }) is the variable X at time t+1 i Conditional probability distribution under the condition that the state of its parent node and the time-varying VineCopula model parameters are known, Parents(X i (t+1)) is the variable X at time t+1. i In the set of known parent nodes, {θ t,ij } is the set of time-varying Vine Copula model parameters; S605: Calculate the reliability. The reliability calculation expression is: R=1-P(X(0),X(1),...,X(T)); Where R is the reliability and P(X(0),X(1),...,X(T)) is the joint distribution of all failure probabilities from time t=0 to t=T.

10. The rail vehicle bogie reliability analysis method based on dynamic Bayesian network according to claim 1, characterized in that: The expression for judging whether the failure probability meets the requirement in step S7 is: in, is the failure probability of this cycle, is the failure probability of the last cycle, and ε is the threshold.

Images