Method for predicting residual life of low-voltage switching device based on comprehensive performance evaluation of model

Abstract

The invention discloses a method for predicting the residual life of a low-voltage switching device based on comprehensive performance evaluation of a model, and the method comprises the steps: building an alternative performance degradation model set in consideration of the competitive failure and degradation correlation characteristics between the characteristic quantities of the low-voltage switching device; fusing all the alternative models by using a model comprehensive performance evaluation index considering prediction capability, fitting capability and complexity, and giving a residual life prediction algorithm of the low-voltage switching device; the method provided by the invention meets actual engineering requirements, the calculation process is simple, the residual life prediction result is high in reliability, a theoretical basis is provided for the problem of residual life prediction of the low-voltage switching device, and the method has high application value.

Description

Technical Field

[0001] The invention belongs to the technical field of low-voltage switch device performance detection, and proposes a method for predicting the remaining life of a low-voltage switch electrical appliance based on comprehensive performance evaluation of a model. Background Art

[0002] Low-voltage switchgear is an important component of low-voltage power distribution systems and power equipment control systems, and plays a role in controlling and protecting the power distribution systems and control systems. If low-voltage switchgear fails, the safe and stable operation of the low-voltage power distribution system and power equipment will not be guaranteed, and may even cause serious accidents and huge economic losses. Therefore, in order to effectively guide operation and maintenance management decisions and thus improve the safety and reliability of the system, it is of great significance to accurately predict the remaining life of low-voltage switchgear.

[0003] The performance status of low-voltage switchgear is usually comprehensively characterized by a variety of characteristic quantities, such as contact mass loss, arcing energy, and arcing Joule integral, and there are characteristics of competitive failure and degradation correlation between the characteristic quantities. The condition for the normal operation of low-voltage switchgear is that each characteristic quantity does not exceed its own failure threshold. Any characteristic quantity reaching the failure threshold will cause the low-voltage switchgear to fail, which is a typical competitive failure. In addition, the arcing Joule integral of the three-phase contact of the AC contactor is taken as an example to illustrate the degradation correlation problem between the characteristic quantities. First, the timing of the three-phase contact disconnection of the AC contactor is random, and the arcing phase angle is also random under the influence of factors such as coil current continuous flow, core demagnetization, and mechanical structure transmission. At the same time, the arcing phase angle of the three-phase contact under three-phase AC meets the phase difference relationship of 120°, so the arcing phase angles of the three-phase contacts are linearly correlated. Since the arcing phase angle determines the arcing Joule integral, there is a correlation between the arcing Joule integrals of the three-phase contacts. However, most existing studies on low-voltage switchgear only consider a single characteristic quantity for remaining life prediction, ignoring the competitive failure and degradation correlation characteristics between multiple characteristic quantities. In addition, existing methods usually give the performance degradation model structure of low-voltage switchgear based on historical data or mechanism knowledge, and use the actual monitoring data of the object to update the model parameters. However, due to individual differences, fluctuations in environmental and working conditions, inaccurate mechanism cognition, etc., the model structure may be specified incorrectly. There is currently no relevant solution to the problems of competitive failure and degradation correlation characteristics of multiple characteristic quantities of low-voltage switchgear and incorrect specification of performance degradation models. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a method for predicting the remaining life of low-voltage switchgear based on comprehensive performance evaluation of the model, that is, it comprehensively considers the competitive failure and degradation correlation characteristics between multiple feature quantities, constructs a set of alternative performance degradation models, integrates all alternative models through comprehensive performance evaluation, and finally realizes the remaining life prediction. It provides a theoretical basis for the problem of predicting the remaining life of low-voltage switchgear and has strong application value.

[0005] The technical solution of the present invention to solve the technical problem is to design a method for predicting the remaining life of a low-voltage switchgear based on comprehensive performance evaluation of a model, characterized in that the method has the following operating steps:

[0006] Step 1: Establish alternative performance degradation models

[0007] Step 1.1: Build a degradation trend model

[0008] Considering five degradation trend models, namely linear, power law, exponential, logarithmic and compound exponential, the expressions are as follows:

[0009]

[0010] In the formula, t is the number of interruptions, a, b, c are model parameters, and y(t) is the degradation trend of a characteristic quantity;

[0011] Step 1.2: Build a random effects model

[0012] 1) The expression of the mixed effect model is as follows:

[0013] X(t)=y(t)+ε(t) (2)

[0014] In the formula, X(t) is a characteristic quantity and X(0) = 0, y(t) is the degradation trend, ε(t) is a random effect and is independent and identically distributed at any time with an expected value of 0 and a variance of The normal distribution of

[0015] Substituting each degradation trend model y(t) in formula (1) into the mixed effect model, five mixed effect models with different degradation trends are obtained, and X(t) obeys the normal distribution Assume its distribution function is F(x(t)), where x(t) is the characteristic data at the tth disconnection;

[0016] 2) The expression of the Wiener process model is as follows:

[0017] X(t)=aΛ(t)+σB(Λ(t)) (3)

[0018] Where a is the drift parameter, σ is the diffusion parameter, Λ(t) is the time scale function, B(·) is the standard Brownian motion, and the independent increment of the Wiener process ΔX(t)=X(t+Δt)-X(t) obeys the normal distribution N(aΔΛ(t),σ 2 ΔΛ(t)), where ΔΛ(t)=Λ(t+Δt)-Λ(t), Δt is a positive number;

[0019] Let Λ(t) = y(t) / a, substitute each degradation trend model y(t) into the Wiener process model, and get five Wiener process models with different degradation trends, and ΔX(t) obeys the normal distribution N(aΔΛ(t),σ 2 ΔΛ(t)), let its distribution function be G(Δx(t)), where Δx(t) is the increment of the characteristic data from the t-th interruption to the t+Δt-th interruption;

[0020] Step 1.3: Characterize the correlation between each feature

[0021] Assuming that there are n feature quantities in total, five Copula functions are used to characterize the correlation between the n feature quantities, namely Gaussian Copula, t Copula, Clayton Copula, Frank Copula and GumbelCopula;

[0022] First, assume that the degradation process of n feature quantities obeys the mixed effect model, which is determined by equations (1) and (2); define H as an n-dimensional random vector [X1(t),…,X i (t),…,X n (t)] T The joint cumulative distribution function of i (t) represents the i-th feature quantity, i = 1, 2, ..., n, and the corresponding marginal cumulative distribution function is F i (x i (t)), where x i (t) is the characteristic data of the i-th characteristic quantity at the t-th disconnection, and the five n-dimensional Copula functions are expressed as follows:

[0023] 1) Gaussian Copula Function

[0024]

[0025] In the formula, Φ (-1) (·) is the inverse function of the standard normal distribution function; θ=(1,ρ 12 ,…,ρ 1n ;…;ρ n1 ,ρ n2,…,1), is the correlation coefficient matrix; W=[x1(t),…,x i (t),…,x n (t)] T ;

[0026] 2) tCopula function

[0027]

[0028] Where, T v (-1) (·) is the inverse function of the univariate Student's t distribution, θ=(1,ρ 12 ,…,ρ 1n ;…;ρ n1 ,ρ n2 ,…,1), is the correlation coefficient matrix; v is the degree of freedom, W=[x1(t),…,x i (t),…,x n (t)] T ;

[0029] 3) Clayton Copula Function

[0030]

[0031] In the formula, α is the model parameter;

[0032] 4) Frank Copula Function

[0033]

[0034] In the formula, α is the model parameter;

[0035] 5) Gumbel Copula Function

[0036]

[0037] In the formula, α is the model parameter;

[0038] In addition, it is assumed that the degradation processes of the n feature quantities all obey the Wiener process model, which is determined by equations (1) and (3); the structures of the five Copula functions are the same as those of equations (4)-(8), except that H in the formula is defined as an n-dimensional random vector [ΔX1(t),…,ΔX i (t),…,ΔX n (t)] T The joint cumulative distribution function of i (t) represents the degradation increment of the i-th characteristic quantity of the Wiener process from the t-th interruption to the t+Δt-th interruption, i = 1, 2, …, n, and the corresponding marginal cumulative distribution function is Gi (Δx i (t)), where Δx i (t) is the increment of the characteristic quantity from the tth interruption to the t+Δtth interruption. Then, using G i (Δx i (t)) replaces F in equations (4)-(8) i (x i (t)) can get the Copula function under the Wiener process model;

[0039] Step 1.4: Build a collection of candidate degradation models

[0040] 1) For a single feature quantity, the process of establishing the performance degradation model is as follows:

[0041] For a characteristic quantity, substituting the five degradation trend models in formula (1) into formula (2), five performance degradation models based on mixed effect models with different degradation trends can be obtained, while substituting the five degradation trend models in formula (1) into formula (3), five performance degradation models based on Wiener process model with different degradation trends can be obtained;

[0042] 2) For n feature quantities, the process of establishing the performance degradation model is as follows:

[0043] First, assume that the degradation process of n feature quantities obeys the mixed effect model, which is determined by equations (1) and (2); each feature quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and composite exponential. There are five degradation trend models for n feature quantities. n At the same time, each characteristic quantity uses a mixed effect model as a random effect model. For n characteristic quantities, 5 n A performance degradation model combination based on a mixed effect model; furthermore, five Copula functions are used to characterize n feature quantities X i The correlation between (t) and its joint cumulative distribution function H is shown in equations (4)-(8) in step 1.3, where i = 1, 2, ..., n; a total of 5 n+1 A performance degradation model that combines a mixed effects model and a Copula function;

[0044] In addition, assuming that the degradation process of n feature quantities all obeys the Wiener process model, that is, determined by equations (1) and (3); each feature quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and composite exponential, so there are 5 degradation trend models for n feature quantities. n At the same time, each characteristic quantity uses the Wiener process model as a random effect model. For n characteristic quantities, 5 nA performance degradation model combination based on the Wiener process model is proposed; furthermore, five Copula functions are used to characterize the Wiener process degradation increment ΔX of n characteristic quantities. i (t), the joint cumulative distribution function H is as described in step 1.3, where i = 1, 2, ..., n; a total of 5 n+1 A performance degradation model combining the Wiener process model and the Copula function;

[0045] Therefore, for n features, there are 5 n+1 A performance degradation model combining mixed effect model and Copula function, and 5 n+1 A performance degradation model combining the Wiener process model and the Copula function, so the set of candidate performance degradation models constructed is 2×5 n+1 Model

[0046] Step 2: Estimate parameters of each alternative performance degradation model

[0047] For n characteristic quantities, let the total number of product disconnections up to the current moment be t k , let the data of the i-th feature quantity up to the current moment be x i (t), where i=1,2,…,n,t=1,2,…,t k ; Use the maximum likelihood estimation method to estimate the unknown parameters in each alternative performance degradation model;

[0048] 1) For a performance degradation model combining a mixed effects model and a copula function, replace the n-dimensional random vector [X1(t),…,X i (t),…,X n (t)] T Taking partial derivatives of the joint cumulative distribution function H of each variable, we can get the density function h(x1(t),…,x i (t),…,x n (t)); construct the following likelihood function:

[0049]

[0050] 2) For a performance degradation model that combines the Wiener process model and the Copula function, the n-dimensional random vector [ΔX1(t),…,ΔX i (t),…,ΔX n (t)] T Taking partial derivatives of the joint cumulative distribution function H of each variable, we can get the density function h(Δx1(t),…,Δx i (t),…,Δx n (t)), and Δx i(t) = x i (t+1)-x i (t), where i = 1, 2, ..., n and t = 1, 2, ..., t k -1; construct the following likelihood function:

[0051]

[0052] According to formulas (9) and (10), the likelihood functions of all candidate models can be obtained. For each candidate model, the target is to maximize the likelihood function, and each model parameter is used as the decision variable. The estimated value of the model parameter is obtained by using the genetic algorithm. Then, the estimated value of the model parameter of all candidate models can be obtained.

[0053] Step 3: Construct comprehensive performance evaluation indicators of the model

[0054] The pseudo-average relative error is defined to characterize the prediction ability, the log-likelihood function value is used to characterize the fitting ability, and the number of model parameters is used to characterize the complexity. The specific explanation of the pseudo-average relative error is as follows:

[0055] The data of n characteristic quantities when the product is disconnected for the tth time is recorded as x i (t), where i=1,2,…,n,t=1,2,…,t k , t k is the total number of disconnections up to the current moment; definition is the pseudo current moment, Indicates rounding down; defines the product's s breaking moments t r =t m +rΔγ, where r=1,2,…,s, s is a positive integer, and if (t k -t m ) / s is an integer, and there is exactly t m +sΔγ=t k ; Note r The data x of the i-th feature quantity at time i (t r ) is the pseudo current time t m The corresponding pseudo failure threshold d i,r , i = 1, 2, ..., n; considering the competitive failure relationship of n characteristic quantities, the number of disconnections at the pseudo current moment is t m Next, the pseudo failure threshold d i,r The corresponding pseudo-remaining life is defined as the minimum remaining number of interruptions when at least one of the n characteristic quantities reaches its pseudo-failure threshold for the first time; the true value of the pseudo-remaining life is T r = rΔγ, the estimated value of pseudo remaining life is The relative error of the estimated value is qr ; Then, the true value of pseudo remaining life, estimated value of pseudo remaining life and relative error of the jth candidate performance degradation model are T j,r , and q j,r , where j = 1, 2, ..., n0, and n0 = 2 × 5 n+1 is the total number of alternative performance degradation models; and defines the pseudo average relative error Q under this model j The expression is as follows:

[0056]

[0057] The indicators of fitting ability P, prediction ability Q and complexity R are as follows:

[0058]

[0059] In the formula, n0 is the total number of models, P j represents the log-likelihood function value of the j-th model, Q j represents the pseudo average relative error value of the jth model, R j represents the number of unknown parameters of the j-th model;

[0060] Considering the index P j , Q j , R j The value range is different, and considering P j Bigger is better and Q j and R j The smaller the better, the indicators are normalized as follows:

[0061]

[0062] Let three indicators The respective weights are 1 / 3; the comprehensive performance evaluation index of the model is ZK j , and ZK j The larger the value of is, the better the overall performance of the corresponding model is;

[0063]

[0064] Step 4: Predict remaining lifespan

[0065] At the current moment, it is t k The data corresponding to the i-th characteristic quantity is x i (t k ), the failure threshold of the i-th feature is D i, where i = 1, 2, ..., n; considering the competitive failure characteristics, the remaining life is defined as the minimum remaining breaking times when at least one characteristic quantity among the n characteristic quantities reaches its failure threshold for the first time; the expression of the remaining life T is as follows:

[0066]

[0067] The expectation of the remaining life is used as the point estimate of the remaining life; the following remaining life prediction algorithm based on Monte Carlo sampling is given:

[0068] Step 1: According to the jth performance degradation model, simulate the degradation trajectory of n characteristic quantities until equation (15) is satisfied to obtain the remaining life of a simulation, where j = 1, 2, ..., n0, and n0 = 2 × 5 n+1 is the number of alternative performance degradation models;

[0069] Step 2: Repeat step 1 M times, where M is a positive integer; then the point estimate of the remaining life under the jth performance degradation model is where τ l is the remaining life of the lth simulation;

[0070] Step 3: Calculate the jth performance degradation model N j The probability of being the true model is:

[0071]

[0072] Step 4: Record the jth model N j The cumulative distribution function of the remaining life under K is j (t), the total probability theorem is used to fuse the alternative performance degradation models to obtain the cumulative distribution function K(t) of the remaining life after fusion, and combined with the calculation formula of the expected remaining life, the point estimate of the remaining life of the product after the fusion of the performance degradation model is obtained as follows:

[0073]

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] 1) The method proposed in the present invention takes into account the competitive failure and degradation correlation characteristics between the characteristic quantities of low-voltage switchgear, establishes a set of alternative performance degradation models, and solves the degradation modeling problem of multiple characteristic quantities;

[0076] 2) The method proposed in the present invention integrates all candidate models using the comprehensive performance evaluation index of the model that takes into account the prediction ability, fitting ability and complexity, and provides a low-voltage switchgear remaining life prediction algorithm;

[0077] 3) The method proposed in the present invention meets the actual engineering needs, and the calculation process is simple, the remaining life prediction results are highly reliable, and it has strong application value in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 The present invention is an operation flow chart of an embodiment of a method for predicting the remaining life of a low-voltage switchgear based on comprehensive performance evaluation of a model.

[0079] Figure 2 It is the data of the cumulative contact mass loss of port 1 when a certain type of low-voltage DC molded case circuit breaker in Example 1 of the present invention is broken 2900 times (that is, the data of characteristic quantity 1).

[0080] Figure 3 It is the data of the cumulative contact mass loss of port 2 when a certain type of low-voltage DC molded case circuit breaker in Example 1 of the present invention is opened and closed 2900 times (that is, the data of characteristic quantity 2).

[0081] Figure 4 It is the data of the accumulated arcing energy of port 1 when a certain type of low-voltage DC molded case circuit breaker in Example 1 of the present invention is opened and closed 2900 times (that is, the data of characteristic quantity 3).

[0082] Figure 5 It is the data of the accumulated arcing energy of port 2 when a certain type of low-voltage DC molded case circuit breaker in Example 1 of the present invention is opened and closed 2900 times (that is, the data of characteristic quantity 4).

[0083] Figure 6 It is the data of the accumulated arcing Joule integral when a certain type of low-voltage DC molded case circuit breaker in Example 1 of the present invention is broken 2900 times (that is, the data of feature quantity 5).

[0084] Figure 7 It is the calculation result of the model comprehensive performance evaluation index of each model in 31250 alternative performance degradation models obtained by using the low-voltage switchgear remaining life prediction method based on model comprehensive performance evaluation of the present invention combined with the five characteristic quantity data in Example 1, wherein the models numbered 1 to 15625 are performance degradation models combining the mixed effect model and the Copula function, and the models numbered 15626 to 31250 are performance degradation models combining the Wiener process model and the Copula function.

[0085] Figure 8 The method for predicting the remaining life of a low-voltage switchgear based on comprehensive model performance evaluation of the present invention is combined with the five characteristic quantity data in Example 1 to obtain the probability that each model in the 31250 alternative performance degradation models is a true model and the corresponding remaining life prediction value under each model. DETAILED DESCRIPTION

[0086] The technical content of the present invention is described in detail below in conjunction with specific implementation methods and the accompanying drawings.

[0087] The present invention proposes a method for predicting the remaining life of low-voltage switchgear based on comprehensive performance evaluation of the model. The method comprehensively considers the competitive failure and degradation correlation characteristics among multiple characteristic quantities, constructs a set of alternative performance degradation models, and proposes a comprehensive performance evaluation index of the model that comprehensively considers the prediction ability, fitting ability and complexity to integrate all alternative performance degradation models, and finally realizes the remaining life prediction.

[0088] The present invention provides a method for predicting the remaining life of a low-voltage switchgear based on comprehensive performance evaluation of a model, and the operating steps of the method are as follows:

[0089] Step 1: Establish alternative performance degradation models

[0090] In order to establish the performance degradation model, the degradation trend model and random effect model are clarified, and the Copula function is used to characterize the degradation correlation, as follows:

[0091] Step 1.1: Build a degradation trend model

[0092] Regarding the degradation trend model, the present invention considers five degradation trend models, namely, linear, power law, exponential, logarithmic and compound exponential, and the expressions are as follows:

[0093]

[0094] Where t is the number of interruptions, a, b, c are model parameters, and y(t) is the degradation trend of a characteristic quantity.

[0095] Step 1.2: Build a random effects model

[0096] Regarding the random effect model, the present invention considers the mixed effect model and the Wiener process model respectively.

[0097] 1) The expression of the mixed effect model is as follows:

[0098] X(t)=y(t)+ε(t) (2)

[0099] In the formula, X(t) is a characteristic quantity and X(0) = 0, y(t) is the degradation trend, ε(t) is a random effect and is independent and identically distributed at any time with an expected value of 0 and a variance of The normal distribution of

[0100] Substituting each degradation trend model y(t) in formula (1) into the mixed effect model, five mixed effect models with different degradation trends can be obtained, and X(t) obeys the normal distribution Suppose its distribution function is F(x(t)), where x(t) is the data of the characteristic quantity at the tth disconnection.

[0101] 2) The expression of the Wiener process model is as follows:

[0102] X(t)=aΛ(t)+σB(Λ(t)) (3)

[0103] Where a is the drift parameter, σ is the diffusion parameter, Λ(t) is the time scale function, B(·) is the standard Brownian motion, and the independent increment of the Wiener process ΔX(t)=X(t+Δt)-X(t) obeys the normal distribution N(aΔΛ(t),σ 2 ΔΛ(t)), where ΔΛ(t)=Λ(t+Δt)-Λ(t), and Δt is a positive number.

[0104] Let Λ(t) = y(t) / a, and substitute each degradation trend model y(t) into the Wiener process model. Five Wiener process models with different degradation trends can be obtained, and ΔX(t) obeys the normal distribution N(aΔΛ(t),σ 2 ΔΛ(t)), and its distribution function is assumed to be G(Δx(t)), where Δx(t) is the increment of the characteristic data from the t-th breaking to the t+Δt-th breaking.

[0105] Step 1.3: Characterize the correlation between each feature

[0106] Assuming that there are n feature quantities in total, the present invention adopts five Copula functions to characterize the correlation between the n feature quantities, namely Gaussian Copula, tCopula, Clayton Copula, Frank Copula and Gumbel Copula.

[0107] First, assume that the degradation process of n feature quantities obeys the mixed effect model, which is determined by equations (1) and (2). Define H as an n-dimensional random vector [X1(t),…,X i (t),…,X n (t)] T The joint cumulative distribution function of i (t) represents the i-th feature quantity, i = 1, 2, ..., n, and the corresponding marginal cumulative distribution function is F i (x i (t)), where x i (t) is the characteristic data of the i-th characteristic quantity at the t-th disconnection, and the five n-dimensional Copula functions are expressed as follows:

[0108] 1) Gaussian Copula Function

[0109]

[0110] In the formula, Φ (-1) (·) is the inverse function of the standard normal distribution function; θ=(1,ρ 12 ,…,ρ 1n ;…;ρ n1 ,ρ n2 ,…,1), is the correlation coefficient matrix; W=[x1(t),…,x i (t),…,x n (t)] T .

[0111] 2) tCopula function

[0112]

[0113] Where, T v (-1) (·) is the inverse function of the univariate Student's t distribution, θ=(1,ρ 12 ,…,ρ 1n ;…;ρ n1 ,ρ n2 ,…,1), is the correlation coefficient matrix; v is the degree of freedom, W=[x1(t),…,x i (t),…,x n (t)] T .

[0114] 3) Clayton Copula Function

[0115]

[0116] In the formula, α is the model parameter.

[0117] 4) Frank Copula Function

[0118]

[0119] In the formula, α is the model parameter.

[0120] 5) Gumbel Copula Function

[0121]

[0122] In the formula, α is the model parameter.

[0123] In addition, it is assumed that the degradation processes of the n feature quantities all obey the Wiener process model, which is determined by equations (1) and (3); the structures of the five Copula functions are the same as those of equations (4)-(8), except that H in the formula is defined as an n-dimensional random vector [ΔX1(t),…,ΔX i (t),…,ΔX n (t)] T The joint cumulative distribution function of i (t) represents the degradation increment of the i-th characteristic quantity of the Wiener process from the t-th interruption to the t+Δt-th interruption, i = 1, 2, …, n, and the corresponding marginal cumulative distribution function is G i (Δx i (t)), where Δx i (t) is the increment of the data of the i-th characteristic quantity from the t-th interruption to the t+Δt-th interruption characteristic quantity. i (Δx i (t)) replaces F in equations (4)-(8) i (x i (t)) can get the Copula function under the Wiener process model.

[0124] Step 1.4: Build a collection of candidate degradation models

[0125] 1) For a single feature quantity, the process of establishing the performance degradation model is as follows:

[0126] For one characteristic quantity, substituting the five degradation trend models in formula (1) into formula (2), five performance degradation models based on the mixed effect model with different degradation trends can be obtained, while substituting the five degradation trend models in formula (1) into formula (3), five performance degradation models based on the Wiener process model with different degradation trends can be obtained.

[0127] 2) For n feature quantities, the process of establishing the performance degradation model is as follows:

[0128] First, assume that the degradation process of n feature quantities all obeys the mixed effect model, which is determined by equations (1) and (2). Each feature quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and composite exponential. There are five total degradation trend models for n feature quantities. n At the same time, each feature quantity uses a mixed effect model as a random effect model, so for n feature quantities, 5 n A performance degradation model combination based on a mixed effect model. Furthermore, five Copula functions are used to characterize n feature quantities X iThe correlation between (t) and its joint cumulative distribution function H is shown in equations (4)-(8) in step 1.3, where i = 1, 2, ..., n. A total of 5 n+1 A performance degradation model that combines a mixed effects model and a copula function.

[0129] In addition, it is assumed that the degradation process of n feature quantities all obeys the Wiener process model, which is determined by equations (1) and (3). Each feature quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and composite exponential. There are 5 degradation trend models for n feature quantities. n At the same time, each characteristic quantity uses the Wiener process model as a random effect model, so for n characteristic quantities, 5 n A performance degradation model combination based on the Wiener process model is proposed. Furthermore, five Copula functions are used to characterize the degradation increment ΔX of n characteristic quantities. i (t), the joint cumulative distribution function H is as described in step 1.3, where i = 1, 2, ..., n. A total of 5 n+1 A performance degradation model combining the Wiener process model and the Copula function.

[0130] Therefore, for n features, there are 5 n+1 A performance degradation model combining mixed effect model and Copula function, and 5 n+1 A performance degradation model combining the Wiener process model and the Copula function, so the set of candidate performance degradation models constructed is 2×5 n+1 Model.

[0131] Step 2: Estimate parameters of each alternative performance degradation model

[0132] For n characteristic quantities, let the total number of product disconnections up to the current moment be t k , let the data of the i-th feature quantity up to the current moment be x i (t), where i=1,2,…,n,t=1,2,…,t k The maximum likelihood estimation method is used to estimate the unknown parameters in each alternative performance degradation model.

[0133] 1) For a performance degradation model combining a mixed effects model and a copula function, replace the n-dimensional random vector [X1(t),…,X i (t),…,X n (t)] T Taking partial derivatives of the joint cumulative distribution function H of each variable, we can get the density function h(x1(t),…,x i (t),…,x n(t)). Construct the following likelihood function:

[0134]

[0135] 2) For a performance degradation model that combines the Wiener process model and the Copula function, the n-dimensional random vector [ΔX1(t),…,ΔX i (t),…,ΔX n (t)] T Taking partial derivatives of the joint cumulative distribution function H of each variable, we can get the density function h(Δx1(t),…,Δx i (t),…,Δx n (t)), and Δx i (t) = x i (t+1)-x i (t), where i = 1, 2, ..., n and t = 1, 2, ..., t k -1. Construct the following likelihood function:

[0136]

[0137] According to formulas (9) and (10), the likelihood function of all candidate models can be obtained. For each candidate model, the target is to maximize the likelihood function, and each model parameter is used as a decision variable. The estimated value of the model parameter is obtained by using a genetic algorithm. As an embodiment, the estimated value of the model parameter is obtained according to the genetic algorithm used in the reference "Wang Haoran. Reliability evaluation method of AC contactor considering competitive failure [J]. Chinese Journal of Scientific Instruments, 2023, 44(04): 40-45.". Then, the estimated values ​​of the model parameters of all candidate models can be obtained.

[0138] Step 3: Construct comprehensive performance evaluation indicators of the model

[0139] The present invention constructs a comprehensive performance evaluation index of the model by considering the prediction ability, fitting ability and complexity of the model. The pseudo-average relative error is defined to characterize the prediction ability, the log-likelihood function value is used to characterize the fitting ability, and the number of model parameters is used to characterize the complexity.

[0140] The specific explanation of the pseudo-average relative error is as follows:

[0141] The data of n characteristic quantities when the product is disconnected for the tth time is recorded as x i (t), where i=1,2,…,n,t=1,2,…,t k , t k It is the total number of interruptions up to the current moment. Definition is the pseudo current moment, Indicates rounding down. Define the product's s breaking moments t r =t m +rΔγ, where r=1,2,…,s, s is a positive integer, and if (t k -t m ) / s is an integer, and there is exactly t m +sΔγ=t k . Remember r The data x of the i-th feature quantity at time i (t r ) is the pseudo current time t m The corresponding pseudo failure threshold d i,r , i = 1, 2, ..., n. Considering the competitive failure relationship of n characteristic quantities, the number of disconnections at the pseudo current moment is t m Next, the pseudo failure threshold d i,r The corresponding pseudo remaining life is defined as the minimum remaining number of interruptions when at least one of the n characteristic quantities reaches its pseudo failure threshold for the first time. The true value of the pseudo remaining life is T r = rΔγ, the estimated value of pseudo remaining life is The relative error of the estimated value is q r Then, the true value of pseudo remaining life, the estimated value of pseudo remaining life and the relative error of the jth candidate performance degradation model are T j,r , and q j,r , where j = 1, 2, ..., n0, and n0 = 2 × 5 n+1 is the total number of alternative performance degradation models. And define the pseudo average relative error Q under this model j The expression is as follows:

[0142]

[0143] The indicators of fitting ability, predictive ability and complexity are as follows:

[0144]

[0145] In the formula, n0 is the total number of models, P j represents the log-likelihood function value of the j-th model, Q j represents the pseudo average relative error value of the jth model, R j Represents the number of unknown parameters of the j-th model.

[0146] Considering the index P j , Q j , R j The value range is different, and considering P j Bigger is better and Q j and Rj The smaller the better, the indicators are normalized as follows:

[0147]

[0148] Let three indicators The respective weights are 1 / 3. The comprehensive performance evaluation index of the model is ZK j , and ZK j The larger the value is, the better the overall performance of the corresponding model is.

[0149]

[0150] Step 4: Predict remaining lifespan

[0151] At the current moment, it is t k The data corresponding to the i-th characteristic quantity is x i (t k ), the failure threshold of the i-th feature is D i , where i = 1, 2, ..., n. Considering the competitive failure characteristics, the remaining life is defined as the minimum remaining breaking times when at least one of the n characteristic quantities reaches its failure threshold for the first time. The expression of the remaining life T is as follows:

[0152]

[0153] The expectation of the remaining life is used as the point estimate of the remaining life. The model constructed by the present invention is relatively complex, and there is no analytical solution for the expectation of the remaining life. Therefore, the present invention provides the following remaining life prediction algorithm based on Monte Carlo sampling:

[0154] Step 1: According to the jth performance degradation model, simulate the degradation trajectory of n characteristic quantities until equation (15) is satisfied to obtain the remaining life of a simulation, where j = 1, 2, ..., n0, and n0 = 2 × 5 n+1 is the number of alternative performance degradation models.

[0155] Step 2: Repeat step 1 M times, where M is a positive integer. Then the point estimate of the remaining life under the jth performance degradation model is where τ l is the remaining life of the lth simulation.

[0156] Step 3: Calculate the jth performance degradation model N j The probability that it is the true model is

[0157]

[0158] Step 4: Record the jth model N j The cumulative distribution function of the remaining life under K isj (t), the total probability theorem is used to fuse the alternative performance degradation models to obtain the cumulative distribution function K(t) of the remaining life after fusion, and combined with the calculation formula of the expected remaining life, the point estimate of the remaining life of the product after the fusion of the performance degradation model is obtained as follows:

[0159]

[0160] Example 1

[0161] This embodiment provides a method for predicting the remaining life of a low-voltage switchgear based on comprehensive performance evaluation of a model, the method comprising the following steps:

[0162] Step 1: Establish performance degradation model

[0163] In this embodiment, there are 5 characteristic quantities, namely, the cumulative contact mass loss of port 1 (characteristic quantity 1), the cumulative contact mass loss of port 2 (characteristic quantity 2), the cumulative arcing energy of port 1 (characteristic quantity 3), the cumulative arcing energy of port 2 (characteristic quantity 4), and the cumulative arcing Joule integral (characteristic quantity 5); firstly, for the 5 characteristic quantities, the linear type is used as the degradation trend model, and the mixed effect model is used as the random effect model, and a performance degradation model combining the mixed effect model and the Gaussian Copula function is established.

[0164] The expressions of the degradation trend model of the five characteristic quantities are as follows:

[0165]

[0166] Substituting the degradation trend model into the mixed effect model, we obtain

[0167]

[0168] Where, X i (t) is the i-th feature quantity and X i (0) = 0, and X i (t) follows normal distribution Let its distribution function be F i (x i (t)), i=1,2,…,5.

[0169] The Gaussian Copula function is used to characterize the correlation between the five feature quantities. The expression of the joint cumulative distribution function is as follows:

[0170]

[0171] In the formula, Φ (-1) (·) is the inverse function of the standard normal distribution function, θ=(1,ρ12 ,…,ρ 15 ;…;ρ 51 ,ρ 52 ,…,1) is the correlation coefficient matrix, W=[x1(t),x2(t),…,x5(t)] T .

[0172] The above five characteristic quantities all use the linear type as the degradation trend model, and the mixed effect model as the random effect model. Taking this as an example, a performance degradation model combining the mixed effect model and the Gaussian Copula function is established as the result display.

[0173] Assume that the degradation process of the five characteristic quantities all obeys the mixed effect model. Each characteristic quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and compound exponential. 5 At the same time, each characteristic quantity uses a mixed effect model as a random effect model, so for 5 characteristic quantities, 5 5 A performance degradation model combination based on the mixed effect model. Furthermore, five Copula functions are used to characterize the five characteristic quantities X i (t), a total of 5 6 A performance degradation model combining a mixed effect model and a Copula function, where i = 1, 2, …, 5.

[0174] Assume that the degradation process of the five characteristic quantities all obeys the Wiener process model. Each characteristic quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and compound exponential. 5 At the same time, each characteristic quantity uses the Wiener process model as a random effect model, so for the five characteristic quantities, we can get five 5 A performance degradation model combination based on the Wiener process model is proposed. Furthermore, five Copula functions are used to characterize the degradation increments ΔX of five characteristic quantities. i (t), a total of 5 6 A performance degradation model combining the Wiener process model and the Copula function, where i = 1, 2, …, 5.

[0175] Therefore, for 5 features, there are 5 6 A performance degradation model combining mixed effect model and Copula function, and 5 6 A performance degradation model combining the Wiener process model and the Copula function. The set of candidate performance degradation models constructed is 2×5 6 Model.

[0176] Step 2: Estimate performance degradation model parameters

[0177] In this embodiment, the total number of product disconnections up to the current moment is 2900 times. For the five characteristic quantities, the linear type is first used as the degradation trend model, and the mixed effect model is used as the random effect model to establish a performance degradation model combining the mixed effect model and the Gaussian Copula function. For this performance degradation model, based on the data of the five characteristic quantities up to the current moment, the maximum likelihood estimation method is used to estimate the unknown parameters in the performance degradation model. Taking the partial derivative of the joint cumulative distribution function H(x1(t),…,x2(t),…,x5(t)) with respect to each variable, the probability density function h(x1(t),…,x2(t),…,x5(t)) can be obtained, and then the likelihood function is as follows:

[0178]

[0179] An optimization problem is constructed with the maximization of the likelihood function as the optimization objective and all unknown parameters in the model as decision variables. The constructed optimization problem is solved using the genetic algorithm used in the reference "Wang Haoran. Reliability evaluation method of AC contactor considering competitive failure [J]. Chinese Journal of Scientific Instruments, 2023, 44(04): 40-45." to obtain the maximum likelihood estimates of all unknown parameters. The estimation results are shown in Table 1.

[0180] Table 1. Estimated values ​​of unknown parameters

[0181]

[0182]

[0183] For the above five characteristic quantities, the linear type is first used as the degradation trend model, and the mixed effect model is used as the random effect model. A performance degradation model combining the mixed effect model and the Gaussian Copula function is established. Taking this model as an example, the estimation results of all parameters in the model are calculated as the result display.

[0184] For this example, there are 2×5 6 Similarly, the parameter estimation results of all other alternative performance degradation models can be obtained.

[0185] Step 3: Construct comprehensive performance evaluation indicators of the model

[0186] In this implementation, the total number of product interruptions up to the current moment is 2900, and the data of the five characteristic quantities are as follows: Figure 2-6 As shown, the pseudo current time t mis 1450 times. If s = 5, then Δγ = 290 times, t r =1740,2030,2320,2610,2900 times. r Data x of 5 feature quantities at time i (t r ) is the pseudo failure threshold d corresponding to 1450 times at the pseudo current moment i,r , where i = 1, 2, ..., 5, d i,r As shown in Table 2.

[0187] Table 2 Pseudo failure threshold

[0188]

[0189] For the five characteristic quantities, the linear type is used as the degradation trend model, the mixed effect model is used as the random effect model, and a performance degradation model combining the mixed effect model and the Gaussian Copula function is established. Then, the pseudo average relative error of the product is calculated as follows:

[0190] According to the above pseudo current time t m and the pseudo failure threshold d i,r , estimate the pseudo remaining life of the product. The pseudo remaining life is the minimum remaining number of interruptions when at least one of the five characteristic quantities reaches its pseudo failure threshold for the first time, and then the five pseudo remaining life estimates are obtained. They are 282, 586, 872, 1154 and 1443 times respectively, and the true value of the pseudo remaining life is T r They are 290, 580, 870, 1160 and 1450 times respectively. Then the pseudo average relative error Q of the performance degradation model is

[0191]

[0192] The corresponding log-likelihood function value P of the model is 147785.86, and the number of unknown parameters R is 20.

[0193] Similarly, the log-likelihood function value P, pseudo-average relative error Q, and number of unknown parameters R of each other model can be obtained. 6 The comprehensive performance evaluation index of the model is as follows: Figure 7 shown.

[0194] Step 4: Predict remaining lifespan

[0195] At the current moment, when the circuit breaker is disconnected for the 2900th time, the expression for the remaining life is:

[0196] T=inf{τ|{X1(2900+τ)≥394510.43|263006.95}∪{X2(2900+τ)≥365997.18|243998.12}∪{X3(2900+τ)≥11 76701.82|784467.88}∪{X4(2900+τ)≥1097549.45|731699.63}∪{X5(2900+τ)≥2771057.16|1847371.44}}

[0197] according to Figure 7 The comprehensive performance evaluation index results of the model can be used to calculate the probability that the jth performance degradation model is the true model using the following formula, where j = 1, 2, ..., 2 × 5 6 .

[0198]

[0199] Using the expected remaining life as the point estimate of the remaining life, 500 remaining life simulations are performed, and the point estimate of the remaining life under the jth performance degradation model is The probability that the alternative model is the true model P(N j ) (the sum of the probabilities of each model is 1) and the corresponding remaining life prediction value like Figure 8 shown.

[0200] The expression of the remaining life point estimate of the product after the fusion of the performance degradation model is:

[0201]

[0202] The remaining life prediction of the available products is Second-rate.

[0203] The present invention proposes a method for predicting the remaining life of low-voltage switchgear based on comprehensive performance evaluation of the model, which meets the actual needs of engineering. It comprehensively analyzes the competitive failure and degradation correlation characteristics between multiple characteristic quantities, first establishes a set of alternative performance degradation models, and then provides a parameter estimation method for the alternative model and a calculation method for the comprehensive performance evaluation index of the model. Finally, it realizes the fusion of all alternative models and the prediction of the remaining life of low-voltage switchgear. The analysis process of the proposed method is scientific and reasonable, convenient for engineering and technical personnel to use, and has strong application value.

[0204] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A method for predicting the remaining life of low-voltage switchgear based on comprehensive performance evaluation of the model, characterized in that: The steps of this method are as follows: Step 1: Establish alternative performance degradation models Step 1.1: Build a degradation trend model Considering five degradation trend models, namely linear, power law, exponential, logarithmic and compound exponential, the expressions are as follows: In the formula, t is the number of interruptions, a, b, c are model parameters, and y(t) is the degradation trend of a characteristic quantity; Step 1.2: Build a random effects model 1) The expression of the mixed effect model is as follows: X(t)=y(t)+ε(t)(2) In the formula, X(t) is a characteristic quantity and X(0) = 0, y(t) is the degradation trend, ε(t) is a random effect and is independent and identically distributed at any time with an expected value of 0 and a variance of The normal distribution of Substituting each degradation trend model y(t) in formula (1) into the mixed effect model, five mixed effect models with different degradation trends are obtained, and X(t) obeys the normal distribution Assume its distribution function is F(x(t)), where x(t) is the characteristic data at the tth disconnection; 2) The expression of the Wiener process model is as follows: X(t)=aΛ(t)+σB(Λ(t))(3) Where a is the drift parameter, σ is the diffusion parameter, Λ(t) is the time scale function, B(·) is the standard Brownian motion, and the independent increment of the Wiener process ΔX(t)=X(t+Δt)-X(t) obeys the normal distribution N(aΔΛ(t), σ 2 ΔΛ(t)), where ΔΛ(t)=Λ(t+Δt)-Λ(t), Δt is a positive number; Let Λ(t) = y(t) / a, substitute each degradation trend model y(t) into the Wiener process model, and obtain five Wiener process models with different degradation trends, and ΔX(t) obeys the normal distribution N(aΔΛ(t), σ 2 ΔΛ(t)), let its distribution function be G(Δx(t)), where Δx(t) is the increment of the characteristic data from the t-th interruption to the t+Δt-th interruption; Step 1.3: Characterize the correlation between each feature Assuming that there are n feature quantities in total, five Copula functions are used to characterize the correlation between the n feature quantities, namely Gaussian Copula, t Copula, Clayton Copula, Frank Copula and GumbelCopula; First, assume that the degradation process of n feature quantities obeys the mixed effect model, which is determined by equations (1) and (2); define H as an n-dimensional random vector [X1(t), …, X i (t),…,X n (t)] T The joint cumulative distribution function of i (t) represents the i-th feature quantity, i = 1, 2, ..., n, and the corresponding marginal cumulative distribution function is F i (x i (t)), where x i (t) is the characteristic data of the i-th characteristic quantity at the t-th disconnection, and the five n-dimensional Copula functions are expressed as follows: 1) Gaussian Copula Function Where Φ(-1)(·) is the inverse function of the standard normal distribution function; θ=(1,ρ 12 ,…,ρ 1n ;…;ρ n1 , ρ n2 ,…,1), is the correlation coefficient matrix; W=[x1(t),…,x i (t), …, x n (t)] T ; 2)t Copula function Where, T v (-1) (·) is the inverse function of the univariate Student's t distribution, θ = (1, ρ 12 ,…,ρ 1n ;…;ρ n1 , ρ n2 ,…,1), is the correlation coefficient matrix; v is the degree of freedom, W=[x1(t),…,x i (t), …, x n (t)] T ; 3) Clayton Copula Function In the formula, α is the model parameter; 4) Frank Copula Function In the formula, α is the model parameter; 5) Gumbel Copula Function In the formula, α is the model parameter; In addition, it is assumed that the degradation processes of the n feature quantities all obey the Wiener process model, which is determined by equations (1) and (3); the structures of the five Copula functions are the same as those of equations (4)-(8), except that H in the formula is defined as an n-dimensional random vector [ΔX1(t), …, ΔX i (t),…,ΔX n (t)] T The joint cumulative distribution function of i (t) represents the degradation increment of the i-th characteristic quantity of the Wiener process from the t-th interruption to the t+Δt-th interruption, i = 1, 2, ..., n, and the corresponding marginal cumulative distribution function is G i (Δx i (t)), where Δx i (t) is the increment of the characteristic quantity from the tth interruption to the t+Δtth interruption. Then, using G i (Δx i (t)) replaces F in equations (4)-(8) i (x i (t)) can get the Copula function under the Wiener process model; Step 1.4: Build a collection of candidate degradation models 1) For a single feature quantity, the process of establishing the performance degradation model is as follows: For a characteristic quantity, substituting the five degradation trend models in formula (1) into formula (2), five performance degradation models based on mixed effect models with different degradation trends can be obtained, while substituting the five degradation trend models in formula (1) into formula (3), five performance degradation models based on Wiener process model with different degradation trends can be obtained; 2) For n feature quantities, the process of establishing the performance degradation model is as follows: First, assume that the degradation process of n feature quantities obeys the mixed effect model, which is determined by equations (1) and (2); each feature quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and composite exponential, so there are 5n degradation trend model combinations for n feature quantities; at the same time, each feature quantity adopts the mixed effect model as the random effect model, so for n feature quantities, 5 can be obtained. n A performance degradation model combination based on a mixed effect model; furthermore, five Copula functions are used to characterize n feature quantities X i The correlation between (t) and its joint cumulative distribution function H is shown in equations (4)-(8) in step 1.3, where i = 1, 2, ..., n; a total of 5 n+1 A performance degradation model that combines a mixed effects model and a Copula function; In addition, assuming that the degradation process of n feature quantities all obeys the Wiener process model, that is, determined by equations (1) and (3); each feature quantity can adopt five degradation trend models, namely linear, power law, exponential, logarithmic and composite exponential, so there are 5 degradation trend models for n feature quantities. n At the same time, each characteristic quantity uses the Wiener process model as a random effect model. For n characteristic quantities, 5 n A performance degradation model combination based on the Wiener process model is proposed; furthermore, five Copula functions are used to characterize the Wiener process degradation increment ΔX of n characteristic quantities. i (t), the joint cumulative distribution function H is as described in step 1.3, where i = 1, 2, ..., n; a total of 5 n+1 A performance degradation model combining the Wiener process model and the Copula function; Therefore, for n features, there are 5 n+1 A performance degradation model combining mixed effect model and Copula function, and 5 n+1 A performance degradation model combining the Wiener process model and the Copula function, so the set of candidate performance degradation models constructed is 2×5 n+1 Model Step 2: Estimate parameters of each alternative performance degradation model For n characteristic quantities, let the total number of product disconnections up to the current moment be t k , let the data of the i-th feature quantity up to the current moment be x i (t), where i=1,2,…,n,t=1,2,…,t k ; Use the maximum likelihood estimation method to estimate the unknown parameters in each alternative performance degradation model; 1) For a performance degradation model combining a mixed effects model and a copula function, transform the n-dimensional random vector [X1(t), …, X i (t),…,X n (t)] T Taking partial derivatives of the joint cumulative distribution function H of each variable, we can get the density function h(x1(t),…,x i (t), …, x n (t)); construct the following likelihood function: 2) For a performance degradation model combining the Wiener process model and the Copula function, the n-dimensional random vector [ΔX1(t), …, ΔX i (t),…,ΔX n (t)] T Taking partial derivatives of the joint cumulative distribution function H of each variable, we can get the density function h(Δx1(t),…,Δx i (t),…,Δx n (t)), and Δx i (t) = x i (t+1)-x i (t), where i = 1, 2, ..., n and t = 1, 2, ..., t k -1; construct the following likelihood function: According to formulas (9) and (10), the likelihood functions of all candidate models can be obtained. For each candidate model, the target is to maximize the likelihood function, and each model parameter is used as the decision variable. The estimated value of the model parameter is obtained by using the genetic algorithm. Then, the estimated value of the model parameter of all candidate models can be obtained. Step 3: Construct comprehensive performance evaluation indicators of the model The pseudo-average relative error is defined to characterize the prediction ability, the log-likelihood function value is used to characterize the fitting ability, and the number of model parameters is used to characterize the complexity. The specific explanation of the pseudo-average relative error is as follows: The data of n characteristic quantities when the product is disconnected for the tth time is recorded as x i (t), where i=1,2,…,n,t=1,2,…,t k , t k is the total number of disconnections up to the current moment; definition is the pseudo current moment, Indicates rounding down; defines the product's s breaking moments t r =t m +rΔγ, where r=1, 2, …, s, s is a positive integer, and if (t k -t m ) / s is an integer, and there is exactly t m +sΔγ=t k ; Note r The data x of the i-th feature quantity at time i (t r ) is the pseudo current time t m The corresponding pseudo failure threshold d i，r , i = 1, 2, ..., n; considering the competitive failure relationship of n characteristic quantities, the number of disconnections at the pseudo current moment is t m Next, the pseudo failure threshold d i,r The corresponding pseudo-remaining life is defined as the minimum remaining number of interruptions when at least one of the n characteristic quantities reaches its pseudo-failure threshold for the first time; the true value of the pseudo-remaining life is T r = rΔγ, the estimated value of pseudo remaining life is The relative error of the estimated value is q r ; Then, the true value of pseudo remaining life, estimated value of pseudo remaining life and relative error of the jth candidate performance degradation model are T j,r , and q j,r , where j = 1, 2, ..., n0, and n0 = 2 × 5 n+1 is the total number of alternative performance degradation models; and defines the pseudo average relative error Q under this model j The expression is as follows: The indicators of fitting ability P, prediction ability Q and complexity R are as follows: In the formula, n0 is the total number of models, P j represents the log-likelihood function value of the j-th model, Q j represents the pseudo average relative error value of the jth model, R j represents the number of unknown parameters of the j-th model; Considering the index P j , Q j , R j The value range is different, and considering P j Bigger is better and Q j and R j The smaller the better, the indicators are normalized as follows: Let three indicators The respective weights are 1 / 3; the comprehensive performance evaluation index of the model is ZK j , and ZK j The larger the value of is, the better the overall performance of the corresponding model is; Step 4: Predict remaining lifespan At the current moment, it is t k The data corresponding to the i-th characteristic quantity is x i (t k ), the failure threshold of the i-th feature is D i , where i = 1, 2, ..., n; considering the competitive failure characteristics, the remaining life is defined as the minimum remaining breaking times when at least one characteristic quantity among the n characteristic quantities reaches its failure threshold for the first time; the expression of the remaining life T is as follows: The expectation of the remaining life is used as the point estimate of the remaining life; the following remaining life prediction algorithm based on Monte Carlo sampling is given: Step 1: According to the jth performance degradation model, simulate the degradation trajectory of n characteristic quantities until equation (15) is satisfied to obtain the remaining life of a simulation, where j = 1, 2, ..., n0, and n0 = 2 × 5 n+1 is the number of alternative performance degradation models; Step 2: Repeat step 1 M times, where M is a positive integer; then the point estimate of the remaining life under the jth performance degradation model is where τ l is the remaining life of the lth simulation; Step 3: Calculate the jth performance degradation model N j The probability of being the true model is: Step 4: Record the jth model N j The cumulative distribution function of the remaining life under K is j (t), the total probability theorem is used to fuse the alternative performance degradation models to obtain the cumulative distribution function K(t) of the remaining life after fusion, and combined with the calculation formula of the expected remaining life, the point estimate of the remaining life of the product after the fusion of the performance degradation model is obtained as follows:

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