Accelerated degradation test method based on Tweedie index performance index correlation

Abstract

The invention relates to an accelerated degradation test method based on Tweedie index performance index, which belongs to the field of electrical digital data processing, and includes: constructing a binary constant stress accelerated degradation test model based on the Tweedie index diffusion process and using a stress acceleration model; assuming that the product has two related performance degradation characteristics; determining the Copula function; solving the unknown parameters of the model; obtaining a binary constant stress accelerated degradation test optimization design model based on the estimated values ​​of the unknown parameters of the model, combined with constraints and optimization goals; using the optimization design model and using a particle swarm optimization algorithm to search for the optimal constant stress accelerated degradation test scheme. The invention takes into account the influence of binary performance degradation characteristics, takes maximizing the determinant of the Fisher information matrix as the optimization goal, ensures the parameter estimation accuracy of the product degradation model, and provides a theoretical basis for test cost control, degradation data collection, life prediction and reliability evaluation.

Description

Technical Field

[0001] The invention belongs to the technical field of electrical digital data processing, and in particular relates to an accelerated degradation test method based on Tweedie index performance index correlation. Background Art

[0002] Constant stress accelerated degradation test is an effective mechanical modeling method that collects more reliability-related information in a shorter time by conducting a more rigorous test environment than normal operating conditions. Constant stress accelerated degradation test is widely used to obtain quality characteristic information, and its degradation data is related to life, because degradation is the accumulation of product damage time. At present, the research on constant stress accelerated degradation test mainly focuses on performance degradation model, statistical analysis method of degradation data, and optimization design of constant stress accelerated degradation test.

[0003] Among the basic assumptions of optimal design, the following conditions are assumed for the accelerated degradation model: 1) product degradation is irreversible; 2) an accelerated degradation model corresponds to a degradation process, mechanism or failure mode; 3) the degradation of sample performance before the start of the accelerated degradation test can be ignored; 4) the degradation or failure mechanism under high stress levels is consistent with the degradation or failure mechanism under design or conventional use stress. At present, most accelerated degradation models only consider the situation where the product has a single performance degradation feature. In fact, some high-reliability and long-life products may have two or more performance degradation features, or a system may be composed of multiple components. For example, the performance degradation of the rubidium atomic lamp, a key component of the rubidium atomic frequency standard, can be described by the consumption of rubidium or the decrease in light intensity. A lighting system may be composed of multiple different types of bulbs. Due to the different designs and characteristics of various types of bulbs, there may be multiple degradation mechanisms that cause the entire lighting system to fail. Therefore, the product may have multiple degradation trajectories, which may be independent or related. Degradation modeling for only one of the performance degradation features may cause certain deviations in reliability analysis and prediction. In independent cases, they can be modeled separately. Crk (Crk V. Reliability assessment from degradation data. Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055), Los Angeles, CA, USA, 2000: 155-161. https: / / doi.org / 10.1109 / RAMS.2000.816300) represents each degradation mechanism by a unique model with random, correlated and stress-dependent parameters to address situations where high-reliability components, subsystems or systems fail due to one or more performance degradation characteristics.Wang and Coit (Peng Wang and DWCoit. Reliability prediction based on degradation modeling for systems with multiple degradation measures. Annual Symposium Reliability and Maintainability, 2004 - RAMS, Los Angeles, CA, USA, 2004: 302-307. https: / / doi.org / 10.1109 / RAMS.2004.1285465) used multivariate normal distribution for modeling and proposed a general reliability prediction modeling and analysis method based on degradation modeling. Xu and Zhao (D. Xu and W. Zhao. Reliability prediction using multivariate degradation data. Annual Reliability and Maintainability Symposium, 2005. Proceedings., Alexandria, VA, USA, 2005:337-341. https: / / doi.org / 10.1109 / RAMS.2005.1408385) proposed a state space model that combines degradation dynamics and random stress effects to describe the evolution of the degradation process. Although the above research works involve binary degradation modeling problems, most of them assume that the performance degradation characteristics are independent of each other. When it comes to correlation, they also assume that they have two-dimensional normality or that the degradation process is a simple deterministic degradation form, which is often inconsistent with actual engineering. Therefore, taking the binary problem as a special case of the multivariate problem, assuming that the product has two related performance degradation characteristics, in order to study the importance of the correlation of performance degradation characteristics.

[0004] The most widely used performance degradation models are Wiener process, Gamma process and inverse Gaussian process. However, in some engineering applications, these three most commonly used random processes are not the most appropriate degradation models. If there is no true model among the candidate models, the reliability analysis results based on the commonly used models may be poor. The degradation model is selected from the candidate models by the Akaike information criterion. As we know, the disadvantage of selecting a model by the Akaike information criterion is that if all candidate models are not suitable, the Akaike information criterion will not give any warning. Then the results of reliability analysis based on the selected inappropriate model may be poor. Therefore, considering the diversity of products, a more general and widely used degradation model is needed to more accurately describe the real degradation data.

[0005] In order to improve the adaptability of modeling methods to degradation data, the Tweedie exponential diffusion process is proposed to describe the degradation path of certain products, and the Wiener process, Gamma process and IG process are taken as special cases. The Tweedie exponential diffusion process has been shown to provide a more suitable degradation model to describe the degradation path of products. Zhou and Xu (Zhou S, Xu A.Exponential dispersion process for degradation analysis. IEEE Transactions onReliability, 2019; 68(2): 398–409. https: / / doi.org / 10.1109 / TR.2019.2895352) proposed using the Tweedie exponential diffusion process to describe the degradation path of physical or chemical properties of products. They used the maximum likelihood estimation method and the Bootstrap method to obtain point estimates and interval estimates of model parameters. In data analysis, they found that the degradation model constructed using the Tweedie exponential diffusion process fits the data better than the commonly used degradation model. Lee and Tseng (Lee IC, Tseng ST, Hong Y. Global planning of accelerated degradation tests based on exponential dispersion degradation models. Naval ResearchLogistics, 2020; 67(6): 469–83. https: / / doi.org / 10.1002 / nav.21923) proposed a semi-analytical method to determine the total sample size, accelerated stress level, number of measurements, and measurement frequency under the Tweedie exponential diffusion process degradation model. Chen and Xia (Chen Z, Xia T, Li Y, Pan E. Tweedie exponential diffusion processes for degradation modeling, prognostic, and accelerated degradation test planning. IEEE Transactions on Reliability, 2019; 69(3):887–902. https: / / doi.org / 10.1109 / TR.2019.2955596) discussed the Tweedie exponential diffusion process degradation model with random effects and measurement errors, considering individual heterogeneity and observation errors.Yan (Yan WA, Xu XF, Bigaud D and Cao WQ. Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process. Reliability Engineering and System Safety, 2022; 230: 108917. https: / / doi.org / 10.1016 / j.ress.2022.108917) et al. obtained the optimal test scheme based on the Tweedie exponential diffusion process and compared the effects of different optimization criteria, different total sample sizes and different total number of measurements on the optimal test scheme. Although the research work including the above articles is dedicated to the statistical inference and optimal design of accelerated degradation tests under the Tweedie exponential diffusion process, these accelerated degradation models only consider the situation where the product has a single performance degradation feature. There are few related studies on the design of the optimal binary constant stress accelerated degradation test scheme under the Tweedie exponential diffusion process, which deserves further study. Summary of the invention

[0006] The purpose of the present invention is to provide an accelerated degradation test method based on the Tweedie index performance index, which can more comprehensively design an optimal constant stress accelerated degradation test scheme for the factors affecting product degradation data, so as to solve the technical problems mentioned in the above background technology.

[0007] To achieve the above purpose, the present invention provides a specific technical solution of an accelerated degradation test method based on Tweedie index performance index as follows:

[0008] The present invention provides a Tweedie index performance index-related accelerated degradation test method, which mainly includes the following steps:

[0009] Step S1: constructing a binary constant stress accelerated degradation test model based on the Tweedie exponential diffusion process and using the stress acceleration model;

[0010] Step S2: constructing a binary constant stress accelerated degradation test optimization design model for the product;

[0011] Step S201: Assume that the product has two related performance degradation characteristics;

[0012] Step S202: Determine the Copula function;

[0013] Step S203: solving unknown parameters of the model;

[0014] Step S204: Based on the estimated values ​​of the unknown parameters of the model, combined with the constraint conditions and the optimization objectives, an optimization design model for the binary constant stress accelerated degradation test is obtained;

[0015] Step S3: adopting the binary constant stress accelerated degradation test optimization design model and using the particle swarm optimization algorithm to search for the optimal constant stress accelerated degradation test scheme.

[0016] Furthermore, in step S1, the binary constant stress accelerated degradation test model is:

[0017] ;

[0018] in, represents the drift parameter of the Tweedie exponential diffusion process, Indicated in is the standardized stress value at each stress level, and a and b are coefficients.

[0019] Furthermore, in step S201, the specific assumptions are as follows:

[0020] 1) The degradation trajectories of the two performance degradation features are both calculated using the drift parameter The diffusion parameter is The Tweedie exponential diffusion process is modeled. ;

[0021] 2) At each stress level, there is a correlation between the two performance degradation characteristics, and the correlation between the two performance degradation characteristics is described by the Copula function;

[0022] 3) The degradation observation times of the two performance degradation features are consistent.

[0023] Furthermore, in step S202, the Copula function specifically uses the Frank Copula function in the Archimedean Copula function family that can describe the correlation between two performance degradation characteristics:

[0024] ;

[0025] Among them, α represents the correlation parameter, ; For any variable ,satisfy and ; for each ,have , , .

[0026] Furthermore, the specific operation process of step S203 is as follows:

[0027] Assume that the constant stress accelerated degradation test is The test was carried out at a stress level, namely , For normal stress level, is the maximum stress level; at stress level Next, there is The samples were used for the constant stress accelerated degradation test. Secondary performance measurement; in the Tweedie exponential diffusion process, the drift parameter represents the degradation rate. When the stress level is different, the degradation rate will change significantly. According to the above assumptions, at the standardized stress level Next, The initial degradation value of the performance of samples is , No. The measured value is The corresponding measurement time is , , , , ; Stress level The experimental degradation data matrix under is expressed as:

[0028] ;

[0029] Indicates stress level The experimental degradation data matrix under , according to the properties of Tweedie exponential diffusion process (TED): , ,in, represents the measurement time interval, For the The measurement time, Indicates The measurement time, Represents category parameters;

[0030] According to Sklar's theorem, there exists a Copula function C such that in the time interval The degradation increments of the next two performance degradation characteristics The joint distribution function of is:

[0031] ;

[0032] in:

[0033] , ;

[0034] In the formula, and They represent the degradation increments of the two performance degradation characteristics respectively, Degenerate increment The standardized value of and Denote the degradation increment and degenerate increment The standardized value of and Respectively and The standard normal distribution of The drift coefficients representing the two performance degradation characteristics, represents the diffusion parameter of the Tweedie exponential diffusion process;

[0035] set up Indicates that the associated parameter is The probability density function of the Copula function is obtained at the stress level The log-likelihood function of the test data under is:

[0036] ;

[0037] in, are the corresponding model parameters, Indicated at the standardized stress level Next, The pth performance characteristic of the sample is The degradation increment under the measurement; The expression is as follows:

[0038] ;

[0039] The unit deviation function is represented and the Gibbs sampling is implemented using Matlab for model parameter evaluation to solve the unknown parameters of the binary constant stress accelerated degradation test model.

[0040] Furthermore, in each iteration of Gibbs sampling, each variable is updated sequentially, and each update is performed given the current values ​​of other variables to ensure that each variable is sampled from its conditional distribution during the entire sampling process; after Gibbs sampling converges, the mean, standard deviation, confidence interval and median of the posterior distribution of the model parameters are obtained.

[0041] Furthermore, the specific operation process of step S204 is as follows:

[0042] Assume Fisher information matrix The specific calculation formula is:

[0043] ;

[0044] Where E represents expectation, L represents log-likelihood function, a1, a2, b1 and b2 represent coefficients in the relationship between drift coefficient and stress, α represents the correlation parameter, λ1 and λ2 represent diffusion coefficients;

[0045] Assume that the constant stress accelerated degradation test is The test was carried out at stress levels. Next, there is The samples were used for the constant stress accelerated degradation test. Each sample at each stress level The performance degradation value is measured once per unit time, and a total of Second-rate, , then the test cost is:

[0046]

[0047] in, , and They represent the cost of each sample, the cost per unit time of operating the test equipment, and the cost of making one measurement, respectively.

[0048] Furthermore, the D optimization criterion is used to maximize the determinant of the Fisher information matrix, and the optimization objective function is:

[0049] ;

[0050] Among them, Max represents the maximum value, det represents the determinant, represents the Fisher information matrix.

[0051] Furthermore, in step S204, the constraint condition is:

[0052] 1) The total cost of the experiment is less than the budgeted cost ;

[0053] 2) Number of stress levels Greater than 2;

[0054] 3) The normalized stress values ​​at all stress levels range from 0 to 1.

[0055] Furthermore, the mathematical expression of the binary constant stress accelerated degradation test optimization design model is:

[0056] ;

[0057] in, represents the Fisher information matrix, represents the total cost of the experiment, Indicates the stress level The number of samples used for the constant stress accelerated degradation test, t is the total test time, represents the number of times the performance is measured for each sample, represents the budget cost, represents the number of stress levels, , , , Both represent stress levels.

[0058] The beneficial effects of the present invention are:

[0059] The present invention develops a constant stress accelerated degradation test optimization design method based on the binary performance degradation characteristics of the Tweedie exponential diffusion process. Compared with the existing work, the main advantages of the present invention are:

[0060] 1) In view of the situation where high-reliability, long-life products have two related performance degradation characteristics, the present invention adopts the Tweedie exponential diffusion process to describe their degradation failure process, and uses the Copula function to describe the correlation between the two, and then establishes a binary constant stress accelerated degradation test optimization design model based on the Tweedie exponential diffusion process under constant stress acceleration. The present invention uses the Tweedie exponential diffusion process to describe the degradation trajectory of the product, comprehensively considers the influence of the correlation of the binary performance degradation characteristics, takes maximizing the determinant of the Fisher information matrix as the optimization goal, and ensures the parameter estimation accuracy of the product degradation model;

[0061] 2) Without destroying the failure mechanism of the product, the present invention proposes an optimal constant stress accelerated degradation test scheme under constant stress acceleration, and provides an analysis method for the impact of model parameters, total sample number, and total test times on the optimal test scheme, in order to solve the optimal design problem of binary degradation tests under constant accelerated stress. At the same time, the corresponding optimal constant stress accelerated degradation test scheme was designed through the rubidium spectrum lamp engineering case, and parameter comparison analysis, model comparison analysis, constraint condition analysis, and parameter sensitivity analysis were carried out to verify the feasibility of the theoretical model. The present invention fully considers the related impacts of the binary performance degradation characteristics of the product, and provides a theoretical basis for test cost control, degradation data collection, life prediction, and reliability evaluation;

[0062] 3) The optimal constant stress accelerated degradation test design scheme obtained by the Tweedie index performance index-related accelerated degradation test method of the present invention shows good robustness when the model parameters fluctuate. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is the cumulative consumption diagram of rubidium in the rubidium spectrum lamp;

[0064] Figure 2 This is the lamp flux maintenance rate diagram of the rubidium spectrum;

[0065] Figure 3 The comparison chart of the optimal CSADT design scheme under two different conditions of performance degradation characteristics: correlated and independent;

[0066] Figure 4 The comparison chart of the optimal CSADT design scheme under a single performance degradation feature. DETAILED DESCRIPTION

[0067] The present invention provides a Tweedie index performance index-related accelerated degradation test method, which specifically includes the following steps:

[0068] Step S1: constructing a binary constant stress accelerated degradation test model based on the Tweedie exponential diffusion process and using the stress acceleration model;

[0069] Stochastic processes are widely used to simulate degradation phenomena, and the degradation path is modeled using the Tweedie exponential diffusion process. Y(t) represents the degradation value of a product that conforms to the Tweedie exponential diffusion process. When the degradation value of a product exceeds a preset critical threshold, the product is considered to have failed. Currently, the basic Tweedie exponential diffusion process has the following three characteristics:

[0070] 1) ;

[0071] 2) With smooth independent increments;

[0072] 3) Increment The probability density function of is:

[0073] ;

[0074] in is the regularization function; is the diffusion parameter; is the cumulative function; is the drift parameter; represents the time interval of measurement, and , For the The measurement time, Indicates The measurement time. and are independent of each other, and the mean and variance of Y(t) are and Where , , . is the variance function, and They are about The first and second derivatives of .

[0075] The Tweedie exponential diffusion process model is an important type of exponential diffusion model, and the relationship between its variance function and mean is a power function, that is:

[0076] , ;

[0077] In the formula is the category parameter. Obviously The expression depends only on The value of The values ​​represent different degradation models; when , the Tweedie exponential diffusion process model is simplified to the Wiener process model; when , the Tweedie exponential diffusion process model is simplified to the Gamma process model; when , the Tweedie exponential diffusion process model is simplified to the inverse Gaussian process model; when , the Tweedie exponential diffusion process model is simplified to a compound Poisson process model.

[0078] Table 1 shows the relationship between the Tweedie exponential diffusion process model (TED) and common random process models. It can be seen that compared with other random process models, the Tweedie exponential diffusion process model can describe the more complex and diverse degradation processes of many products and has a wider range of applications. Therefore, the present invention mainly uses the Tweedie exponential diffusion process model for research.

[0079] Table 1 Relationship between Tweedie exponential diffusion process model and common random process models

[0080] .

[0081] However, for the Tweedie exponential diffusion process model, except for some special cases, the function There is no specific expression. According to existing research, the saddle point approximation method provides a high-precision approximation for the Tweedie exponential diffusion process model, which can be expressed as:

[0082] ;

[0083] in:

[0084] ;

[0085] The stress acceleration model used in the present invention takes into account the influence of stress factors on product performance degradation, and accordingly establishes a mathematical relationship model, which is as follows:

[0086] 1) Arrhenius model;

[0087] When temperature is used as the working stress in accelerated tests, such as electronic components and insulators, Arrhenius proposed the following model in 1880, as shown in the following formula:

[0088] ;

[0089] Where: is the characteristic life span, such as median life span; is a constant and ; E is the activation energy, which is mainly related to the material of the product; is the Boltzmann constant, ; is the absolute temperature;

[0090] 2) Inverse power law model;

[0091] When electrical stress is used as the working stress in the accelerated test, such as voltage and current, the following model of the relationship between life and stress is proposed through multiple tests and demonstrations, as shown in the following formula:

[0092] ;

[0093] Where: is the characteristic life span, such as median life span; is a constant and ; is a positive constant related to the activation energy is the voltage stress;

[0094] 3) Eyring model;

[0095] When temperature is used as the working stress in the accelerated test, in addition to the Arrhenius model, the Eyring model can also be selected. The degree of fit between the two models is used to determine which model is more suitable. The model expression is shown in the following formula:

[0096] ;

[0097] Where: is the characteristic life span, such as median life span; and All are undetermined constants; is the Boltzmann constant, ; T is absolute temperature.

[0098] In the Tweedie exponential diffusion process, the drift parameter represents the degradation rate, which varies significantly when the stress level is different. The relationship between the degradation rate and the stress level can follow one of the following three functions:

[0099] 1) Arrhenius function: ;

[0100] 2) Exponential function: ;

[0101] 3) Power law function: .

[0102] Among them, in Standardized stress value at each stress level for:

[0103] ;

[0104] Therefore, under standardization, we have , For normal stress level, is the maximum stress level, and the unique relationship between the degradation rate and the stress level, namely the binary constant stress accelerated degradation test model, is:

[0105] ;

[0106] in, represents the drift parameter of the Tweedie exponential diffusion process, Indicated in The standardized stress value at each stress level, a and b are coefficients;

[0107] Step S2: constructing a binary constant stress accelerated degradation test optimization design model for the product;

[0108] Step S201: Assume that the product has two related performance degradation characteristics;

[0109] 1) The degradation trajectories of the two performance degradation features are both calculated using the drift parameter The diffusion parameter is The Tweedie exponential diffusion process is modeled. ;

[0110] 2) At each stress level, there is a correlation between the two performance degradation characteristics, and the correlation between the two performance degradation characteristics is described by the Copula function;

[0111] 3) The degradation observation times of the two performance degradation features are consistent.

[0112] Step S202: Determine the Copula function;

[0113] The Copula function is a function that connects the joint distribution of multidimensional random variables with their one-dimensional marginal distributions. It has many excellent properties and is an effective tool for characterizing dependencies.

[0114] The following is a brief introduction to the relevant contents of the Copula function. Since the present invention mainly discusses the binary degradation modeling problem, only the two-dimensional Copula function is introduced below.

[0115] Function C: It is called a two-dimensional Copula function. ,satisfy and For each ,have , , .

[0116] Assume that the joint distribution function H has two marginal cumulative distribution functions and , according to Sklar's theorem, there exists a Coplua function C for any ,have:

[0117] ;

[0118] According to different data distribution forms, a more appropriate Coplua function that describes the correlation structure between data is often used for expression, and the range of the correlation parameter will be given accordingly. Among the many Coplua function families, the Gaussian Copula function family and the Archimedean Copula function family are the most common and widely used Copula function families. However, the Gaussian Copula function family cannot accurately characterize the correlation between variables. The commonly used Coplua function family is the Archimedean Copula function family. The following mainly introduces several common Archimedean Copula functions:

[0119] 1) Clayton Copula function:

[0120] ;

[0121] Among them, the associated parameters .

[0122] 2) FGM Copula function:

[0123] ;

[0124] Among them, the associated parameters .

[0125] 3) Frank Copula function:

[0126] ;

[0127] in ,when , the marginal distributions are independent.

[0128] From the associated parameters From the range of values, the Frank Copula function is more flexible and has a wider range of related parameters. The value of can be positive or negative and has symmetry. Among them, the associated parameter of the Frank Copula function is It may be unrelated to stress or it may be related to stress. If it is related, the correlation can be described by a simple linear function:

[0129] ;

[0130] in, Indicated in The standardized stress value at each stress level is ; c, z, r and d are coefficients.

[0131] Therefore, the present invention mainly uses the Frank Copula function in the Archimedean Copula function family that can accurately characterize the correlation between variables to describe the correlation between two performance degradation characteristics.

[0132] Step S203: solving unknown parameters of the model;

[0133] Assume that the constant stress accelerated degradation test is The test was carried out at a stress level, namely ,in, For normal stress level, is the maximum stress level; at stress level Next, there is The samples were used for the constant stress accelerated degradation test. performance measurement (measurement time is negligible); in the Tweedie exponential diffusion process, the drift parameter It represents the degradation rate. When the stress level is different, the degradation rate will change significantly. According to the properties of the Tweedie exponential diffusion process, it can be seen that: , ,in, represents the measurement time interval, For the The measurement time, Indicates The measurement time, Represents a category parameter.

[0134] According to the binary constant stress accelerated degradation test model constructed in step S1, at the stress level Next, The initial degradation value of the performance of samples is , No. The measured value is The corresponding measurement time is , , , , ; At stress level The experimental degradation data matrix under can be expressed as:

[0135] ;

[0136] Indicates stress level The experimental degradation data matrix under .

[0137] make , then:

[0138] , ;

[0139] According to the properties of Tweedie exponential diffusion process (TED), , .when hour, and Independent of each other.

[0140] According to Sklar's theorem, there exists a Copula function C such that in the time interval Under the condition that the degradation increments of the two performance degradation characteristics are assumed to be Under this condition, the correlation between the two performance degradation characteristics in different measurement time periods can be ignored, that is, for any The joint distribution function of is:

[0141] ;

[0142] in:

[0143] , ;

[0144] In the formula, and They represent the degradation increments of the two performance degradation characteristics respectively, Degenerate increment The standardized value of and Denote the degradation increment and degenerate increment The standardized value of and Respectively and The standard normal distribution of The drift coefficients representing the two performance degradation characteristics, Represents the diffusion parameter of the Tweedie exponential diffusion process.

[0145] set up Indicates that the associated parameter is The probability density function of the Copula function is obtained at the stress level The log-likelihood function of the test data under is:

[0146] ;

[0147] in, are the corresponding model parameters, Indicated at the standardized stress level Next, The pth performance characteristic of the sample is The degradation increment under the measurement; The expression is as follows:

[0148] ;

[0149] represents the unit deviation function, which is given by It can be seen from the log-likelihood function of the test data under that the optimization design model of the binary constant stress accelerated degradation test is quite complex, so it is not easy to estimate the model parameters. Therefore, the present invention uses Matlab to implement Gibbs sampling for model parameter evaluation and solves the unknown parameters of the binary constant stress accelerated degradation test model.

[0150] Parameter estimation is one of the key techniques in statistics. It infers unknown population parameters through sample data, providing a basis for scientific research and decision-making. It is widely used in various fields, and the choice of estimation method directly affects the accuracy and credibility of the results. For the complex accelerated degradation model proposed in this invention, the MCMC method is used to simulate and solve the parameters, and the maximum likelihood estimate of the parameters is obtained. The two most popular MCMC algorithms are Gibbs sampling and Metropolis-Hastings sampling. Gibbs sampling is a Monte Carlo integration method. Its basic idea is to use the distribution to sample high-dimensional or complex populations. The conditional distribution family is used to construct an irreducible recurrent Markov chain, so that it It is a special case of Metropolis-Hastings sampling. Its essence is to replace the suggestion distribution in Metropolis-Hastings sampling with a completely conditional distribution and accept the suggestion value with probability 1.

[0151] Suppose a random vector , its conditional probability distribution , represents the rth random variable, represents the sth random variable, , It is sampleable. The specific Gibbs sampling steps are as follows:

[0152] 1) First, generate a random vector based on the prior distribution Initial value of ,Right now ;

[0153] 2) For each iteration ( is the number of iterations):

[0154] a. Sampling each variable:

[0155] For each variable , from its conditional probability distribution Draw a sample from

[0156] b. Update the value of the variable:

[0157] Assign the obtained new sample value to the corresponding variable, that is ;

[0158] 3) Repeat step 2) until the predetermined number of iterations is reached Or the convergence condition is met.

[0159] In each iteration of Gibbs sampling, each variable is updated in sequence, and each update is performed under the condition of the current values ​​of other variables to ensure that each variable in the entire sampling process is sampled from its conditional distribution; after Gibbs sampling converges, the mean, standard deviation, confidence interval, median and other information of the posterior distribution of the model parameters are obtained. Among them, in the model parameter solution of the present invention, the prior distribution of the parameters is set as an uninformative prior, and the model parameter evaluation is performed only based on the data obtained from the experiment or simulation, so the selection and construction of the prior distribution of the parameters are not discussed.

[0160] Step S204: Based on the estimated values ​​of the unknown parameters of the model, combined with the constraint conditions and the optimization objectives, an optimization design model for the binary constant stress accelerated degradation test is obtained;

[0161] Due to the parameters The Fisher information matrix may be singular, so the inverse matrix cannot be calculated, so the parameter is not considered. The impact on the Fisher information matrix is ​​replaced by the estimated value. Therefore, the Fisher information matrix The specific calculation formula is:

[0162] ;

[0163] Where E represents expectation, L represents log-likelihood function, a1, a2, b1 and b2 represent coefficients in the relationship between drift coefficient and stress, α represents association parameter, and λ1 and λ2 represent diffusion coefficients.

[0164] Assume that the constant stress accelerated degradation test is The test was carried out at stress levels. Next, there is The samples were used for the constant stress accelerated degradation test. Each sample at each stress level The performance degradation value is measured once per unit time, and a total of Second-rate, , then the test cost is:

[0165] ;

[0166] in, , and They represent the cost of each sample, the cost per unit time of operating the test equipment, and the cost of making one measurement, respectively.

[0167] Considering the influence of the limited conditions of special samples on the estimation accuracy of model parameters in the prediction test, the present invention pays more attention to the estimation accuracy of model parameters and adopts the D optimization criterion, that is, maximizing the determinant of the Fisher information matrix. Then the optimization objective function is:

[0168] ;

[0169] Among them, Max represents the maximum value, det represents the determinant, represents the Fisher information matrix.

[0170] Therefore, the optimization goal of the constant stress accelerated degradation test is to determine the best stress level, as well as the number of samples assigned to each level and the test duration according to certain optimization criteria.

[0171] The constraints are set as follows:

[0172] 1) The total cost of the experiment is less than the budgeted cost ;

[0173] 2) Number of stress levels Greater than 2;

[0174] 3) The normalized stress values ​​at all stress levels range from 0 to 1;

[0175] The mathematical expression of the optimization design model of the binary constant stress accelerated degradation test is:

[0176] ;

[0177] in, represents the Fisher information matrix, represents the total cost of the experiment, Indicates the stress level The number of samples used for the constant stress accelerated degradation test, t is the total test time, represents the number of times the performance is measured for each sample, represents the budget cost, represents the number of stress levels, , , , Both represent stress levels.

[0178] Step S3: adopting the binary constant stress accelerated degradation test optimization design model and using the particle swarm optimization algorithm to search for the optimal constant stress accelerated degradation test scheme.

[0179] The particle swarm optimization algorithm is a swarm intelligence algorithm proposed by Kennedy and Eberhart in 1995 based on the foraging behavior of bird flocks. In the particle swarm optimization algorithm, each particle represents a potential solution in the optimization space and has a fitness value determined by the function being optimized. In each iterative evolution, the particle updates the current speed and position through its own and the group's historical optimal position. After the iteration is completed, the optimal constant stress accelerated degradation test plan can be obtained. The specific steps are described as follows:

[0180] 1) Initialize particle population: particles The position vector is , the velocity vector is , after random initialization, calculate the fitness function value of each particle and select the optimal fitness function value of the individual from the candidate values And the optimal fitness function value of the population ;

[0181] 2) Given the number of iterations , let the current ;

[0182] 3) Update each individual velocity vector: ;in, represents the inertia weight, and represent individual cognitive factors and group cognitive factors, respectively. and Both represent random numbers in the interval [0,1].

[0183] 4) Update each individual position vector: ;

[0184] 5) Update the optimal fitness function value of individuals and populations and ;

[0185] 6) When the number of iterations reaches , then it is considered that the current is the optimal value; otherwise, repeat step 3).

[0186] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0187] Constant stress accelerated degradation test is an effective means to evaluate product reliability. In existing scheme design, degradation models based on specific random processes are usually adopted, and only the situation where the product has a single performance degradation feature is considered, or the performance degradation features are considered to be independent. This approach may affect the accuracy of product reliability evaluation. Therefore, it is particularly necessary to seek a binary constant stress accelerated degradation test optimization design model with wide applicability to accurately describe multivariate performance degradation information. In order to solve this problem, the present invention uses the Tweedie exponential diffusion process to construct a binary constant stress accelerated degradation test model. This process converts the common random process into a special case of the Tweedie exponential diffusion process, and uses binary degradation as a special case of multivariate degradation. The Copula function is introduced to describe the correlation between the two performance degradation features, and the influence of the correlation between the performance degradation features on the model parameters and the test optimization design is studied.

[0188] The present invention specifically conducts case analysis based on two performance degradation characteristics of rubidium content and luminous flux of rubidium spectrum lamps, designs a constant stress accelerated degradation test scheme related to binary performance degradation characteristics based on Tweedie exponential diffusion process, and makes comparative analysis with the optimal constant stress accelerated degradation test scheme designed under the conditions of two independent performance degradation characteristics and a single performance degradation characteristic, verifies the necessity of considering the correlation of binary performance degradation characteristics, and conducts a detailed analysis of the sensitivity of test constraints and model parameters to verify the robustness of the proposed binary constant stress accelerated degradation test optimization design model. The binary constant stress accelerated degradation test optimization design model established by the present invention fully examines the general applicability of random processes, the multivariate performance degradation characteristics of products, and the correlation between performance degradation characteristics, etc., provides a theoretical basis for further obtaining product degradation data, predicting product service life, and reducing detection costs, and points out the direction of improvement for further improving the optimization design of multivariate accelerated degradation tests.

[0189] The specific test process of the present invention is as follows:

[0190] 1. Numerical example:

[0191] The model and method of the present invention are illustrated by a set of degradation data of a rubidium spectrum lamp. The life of a rubidium spectrum lamp can be characterized by the rubidium consumption or the attenuation of the light intensity. In fact, the attenuation of the light flux is closely related to the consumption of the rubidium. The less rubidium in the lamp, the weaker the light flux. When the rubidium in the rubidium spectrum lamp is consumed to only 100%, the light intensity will decrease. Or if the luminous flux drops by 50%, the lamp is considered to be unable to work normally, that is, degradation failure occurs.

[0192] In the experiment, six samples were placed at room temperature for testing, and the rubidium content and luminous flux were measured once every 480 hours, for a total of 30 measurements. The stage of rubidium reaction with impurities was not considered, and only the diffusion process of rubidium and its corresponding light intensity maintenance were modeled. The cumulative rubidium consumption and luminous flux maintenance rate data of the six rubidium spectrum lamps collected from the experiment are shown in Figure 1. Figure 1 and Figure 2 As shown. Figure 1 As shown in Figure 2, the cumulative consumption of rubidium increases with time; Figure 2 As shown, the luminous flux maintenance rate of rubidium decreases with time.

[0193] Estimating model parameters using MCMC methods , and estimated the mean, standard deviation, MCMC error and quantile of the model parameters. Table 2 lists the evaluation results of the model parameters.

[0194] Table 2 Model parameter estimation results

[0195] .

[0196] At the same time, if the correlation between rubidium consumption and luminous flux maintenance rate is not considered, the degradation process is modeled using the Tweedie exponential diffusion process, and the evaluation results of the corresponding model parameters are shown in Table 3.

[0197] Table 3 Model parameter estimation results under independent conditions

[0198] .

[0199] It can be seen from Tables 2 and 3 that if the correlation between rubidium consumption and luminous flux maintenance rate is ignored, the evaluation results of the model parameters will be different. For example, when the correlation between rubidium consumption and luminous flux maintenance rate is considered, the parameter The mean and standard deviation of are greater than those without considering the correlation, and from the perspective of quantiles, the parameters when considering the correlation between rubidium consumption and luminous flux maintenance rate are The probability of being less than 0.312 is 2.5%, and the probability of being greater than 0.397 is 97.5%, which is larger than the case when the correlation is not considered. Therefore, if the correlation between rubidium consumption and luminous flux maintenance rate is arbitrarily ignored, it may cause distortion of model parameter estimation, thus affecting the subsequent experimental design. According to Table 2, the model parameters are The numerical comparison of the log-likelihood function and AIC value of the proposed Tweedie exponential diffusion process model with the Wiener, Gamma, and IG process models is shown in Table 4. The AIC calculation formula is:

[0200] ;

[0201] Among them, K represents the number of model parameters to be calculated. Represents the log-likelihood function. Models with larger log-likelihood function values ​​and smaller AIC values ​​are more suitable for describing the data.

[0202] Table 4 Comparison of model parameters between the Tweedie exponential diffusion process and three common random processes

[0203] .

[0204] It can be seen from Table 4 that when When , the log-likelihood function value of the proposed Tweedie exponential diffusion process model is the largest. Therefore, based on the log-likelihood function criterion, it can be considered that The Tweedie exponential diffusion process model is the most suitable degradation model for the degradation data of rubidium spectral lamp. The log-likelihood function value obtained by the Gamma process ranks second, and the smallest is based on The log-likelihood function value obtained by the Wiener process. In addition, since the Tweedie exponential diffusion process model has one more parameter than the Gamma process model , so although the log-likelihood function value of the Tweedie exponential diffusion process is greater than that of the Gamma process, the AIC value of the Gamma process is the smallest, followed by the Tweedie exponential diffusion process, and the AIC value of the Wiener process is the largest. It is very close to 2, indicating that the Gamma process is an approximation of the real degradation process, while the Tweedie exponential diffusion process can more accurately describe the real degradation process. Therefore, although the Gamma process is a good choice from the perspective of AIC value, considering flexibility and wide applicability, the present invention chooses to use the Tweedie exponential diffusion process to characterize this set of data.

[0205] 2. Comparative analysis:

[0206] Assume that there are N rubidium spectral lamps used for constant stress accelerated degradation test, and the excitation power is used as the accelerating stress. samples, a total of Second performance degradation value, The excitation power of the rubidium spectrum lamp during normal operation is , when the excitation power is 5W, the temperature of the rubidium spectrum lamp is 200℃. Since the consumption rate of rubidium is increased without changing the main consumption mechanism, the temperature of the rubidium spectrum lamp must be kept below 200℃, so the limit excitation power is set to The cost coefficient in the experiment is assumed to be Without losing generality, refer to Zheng et al. (Zheng BK, Chen C, Lin YG, et al. Optimal design of step-stress accelerated degradation test oriented by nonlinear and distributed degradation process[J]. Reliability Engineering and SystemSafety, 2022, 217: 108087. https: / / doi.org / 10.1016 / j.ress.2021.108087) on the selection of accelerated stress values ​​under different stress levels. Assume Between 0 and 0.8, , Based on the above assumptions, the optimization design model of binary constant stress accelerated degradation test can be expressed as:

[0207] ;

[0208] In order to investigate the influence of performance degradation characteristics on the optimal constant stress accelerated degradation test design scheme under two different conditions, namely, correlated and independent, the PSO algorithm was used. In combination with the research on PSO by Acitas et al. (Acitas S, Aladag HC, Senoglu BA new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An Application to the Strengths of Glass FibreData[J]. Reliability Engineering and System Safety, 2018, 183: 116-127.https: / / doi.org / 10.1016 / j.ress.2018.07.024) and the determination of initial parameters of PSO, according to the model parameter estimation results in Tables 2 and 3, the optimal constant stress accelerated degradation test design scheme was proposed. When the value is 10000, the optimal constant stress accelerated degradation test design scheme for performance degradation characteristics in two different cases of correlation and independence is obtained, as shown in Table 5 and Figure 3 shown.

[0209] Table 5 Optimal constant stress accelerated degradation test design schemes for performance degradation characteristics under two different conditions: dependent and independent

[0210] .

[0211] By analyzing Table 5 and Figure 3 Sample size distribution under each stress level , and It can be seen that the results when the two performance degradation characteristics of rubidium content and luminous flux are correlated are (5, 3, 3), and the results when the two performance degradation characteristics are independent are (4, 4, 3). This shows that when considering the correlation of the two performance degradation characteristics, the number of samples allocated to the lower acceleration stress increases, reducing the impact of the equivalent uncertainty of the degradation mechanism caused by the increase in the acceleration factor as the stress level increases. Distribution of the number of measurements at each stress level , and Similar to the change in sample size allocation, indicating that the two performance degradation characteristics are correlated will also increase the number of measurements allocated to the lower accelerated stress. From the perspective of test cost, the result when two performance degradation characteristics are related is ( , 9938), the result when the two performance degradation characteristics are independent is ( , 9926). This shows that the parameter estimation accuracy and test cost utilization rate when the two performance degradation characteristics are related are better than when the two performance degradation characteristics are independent. Therefore, the correlation between performance degradation characteristics cannot be ignored. Ignoring the correlation between the two will affect the accuracy of subsequent test data.

[0212] For a single performance degradation feature, that is, considering only one of the two performance degradation features of rubidium content or luminous flux on the optimal constant stress accelerated degradation test design, different optimal constant stress accelerated degradation test design schemes are given to illustrate the necessity of considering the binary performance degradation features, as shown in Table 6 and Figure 4 shown.

[0213] Table 6 Optimal constant stress accelerated degradation test design scheme under single performance degradation characteristics

[0214] .

[0215] As shown in Table 6 and Figure 4 As shown, the sample distribution at each stress level in three different situations , and In the comparison results, the number of samples allocated to the low stress level when considering the rubidium amount alone is 7, which is more than the number of samples allocated to the low stress level when two performance degradation characteristics are related, while the number of samples allocated to each stress level when considering the light flux alone is basically the same as when two performance degradation characteristics are related. Analysis of the distribution of measurement times at each stress level under three different situations , and It can be seen that the number of measurements allocated to the higher stress level when considering the luminous flux alone is (13, 9), which is higher than the number of measurements allocated to the higher stress level when the two performance degradation characteristics are related, while the number of measurements allocated to each stress level when considering the rubidium amount alone is lower than when the two performance degradation characteristics are related. Comparison of the stress level values ​​under three different situations , and When considering the light flux alone, the excitation powers of the first and second stress levels are 2.9W and 3.4W, respectively, which are higher than the case when the two performance degradation characteristics are related, while the opposite is true when considering the rubidium amount alone.

[0216] By analyzing the comparison of the decision variables under the above different situations, it can be seen that the test scheme that only considers the rubidium content design focuses on the sample test data at low stress levels, and the test scheme that only considers the luminous flux design focuses on the sample test data at high stress levels. Figure 4 The determinant of the Fisher information matrix under different circumstances Although the test cost utilization rate is higher when considering the rubidium content and luminous flux separately than when the two performance degradation characteristics are related, the comprehensive consideration of and test cost utilization rate. The optimal test scheme designed with two performance degradation characteristics is better than the test scheme designed with a single performance degradation characteristic. This shows that the test scheme designed by only modeling one of the performance degradation characteristics may cause certain deviations in reliability analysis and prediction. It is necessary to design the test scheme with two performance degradation characteristics in mind.

[0217] In order to investigate the influence of the total test cost on the optimal constant stress accelerated degradation test design, different budget costs were used to The optimal constant stress accelerated degradation test design scheme under the condition of 2.5 % and 1.5 % are compared and analyzed. The results are shown in Table 7. From the comparison of the optimization results, it can be seen that the test scheme changes with the change of cost constraints. The higher the cost, the better the test plan. The higher the value, the better the evaluation effect.

[0218] Table 7 Cost constraints are The optimal experimental design when

[0219] .

[0220] It can be seen from Table 7 that the sample size under the first stress level With the number of measurements More than other stress levels. The increase in the sample size of the first stress level The fastest growth, while the sample size of the 2nd and 3rd stress levels and Slower growth and sometimes no change, e.g. , hour, Always equal to 2. The time interval measured and the number of measurements at each stress level , and Also with the budget Increases as the test duration increases It can be seen that the test duration increases with the number of measurements or the time interval between measurements. The optimal stress value for each stress level is , and No budget costs In addition, the determinant of the Fisher information matrix is Increases with the increase of budget. The higher the budget, the longer the test time and the larger the test sample size. This means that increasing the test sample size or extending the test time can provide more information about the degradation process. More information about the degradation process helps improve the accuracy of subsequent product life assessment.

[0221] Below Taking the example of the influence of experimental constraint changes on the optimal constant stress accelerated degradation test design, the design scheme is explored based on the constraints of different total sample numbers and total test times. and The specific changes are shown in Tables 8 and 9.

[0222] Table 8 Optimal constant stress accelerated degradation test design schemes under different total measurement number constraints

[0223] .

[0224] Table 9 Optimal constant stress accelerated degradation test design schemes under different total sample number constraints

[0225] .

[0226] It can be seen from Tables 8 and 9 that with the increase of the total sample size N and the total number of measurements M, the determinants of the Fisher information matrix of all design schemes increase. The difference in the determinants of different design schemes increases with the increase of N or M. When the total sample size N or the total number of measurements M is small, that is, or , the determinant value of the Fisher information matrix grows relatively slowly, and the difference between the determinant values ​​is small; when the total sample size N or the total number of measurements M is large, that is, or , the determinant value of the Fisher information matrix grows faster, and the difference between the determinant values ​​is relatively large. It can be seen that the D optimization criterion is sensitive to the total sample size N and the total number of measurements M.

[0227] 3. Parameter sensitivity analysis:

[0228] The optimal constant stress accelerated degradation test design scheme obtained by the present invention using historical test data is based on model parameters In fact, errors are inevitably introduced in the actual model parameter evaluation. Therefore, it is necessary to analyze the sensitivity of the optimal constant stress accelerated degradation test design scheme to the model parameters, so as to examine the robustness of the optimal constant stress accelerated degradation test design scheme.

[0229] In order to quickly and effectively implement sensitivity analysis, the present invention adopts an orthogonal experimental strategy. For example, There are 8 factors, each with three levels. Sensitivity analysis is performed using an orthogonal table. The analysis results are shown in Table 10.

[0230] Table 10 Results of model parameter sensitivity analysis

[0231] .

[0232] It can be seen from Table 10 that the optimal constant stress accelerated degradation test design scheme of the present invention has good robustness. The change of model parameters has little effect on the number of test samples and stress values, but has a certain effect on the number of measurements and the time interval of measurements at each stress level. Among all the optimal constant stress accelerated degradation test design schemes, and The volatility ratio and In general, all the optimal constant stress accelerated degradation test design schemes deviate moderately from the actual situation, which proves that the optimal constant stress accelerated degradation test design scheme designed by the present invention has good robustness under model parameter fluctuations.

[0233] The present invention obtains the following conclusions through the optimization design study of the constant stress accelerated degradation test related to the binary performance degradation characteristics based on the Tweedie exponential diffusion process:

[0234] 1) Starting from the definition of Tweedie exponential diffusion process, this paper introduces the basic concepts of Tweedie exponential diffusion process model and its relationship with common random process models, and gives the probability density function when the product performance degradation process is Tweedie exponential diffusion process. On this basis, assuming that the product has two related performance degradation characteristics, combined with the two-dimensional Copula function, a binary constant stress accelerated degradation test model based on Tweedie exponential diffusion process and a model parameter estimation method are proposed.

[0235] 2) In the numerical analysis, the proposed model and method are applied to model the degradation process of rubidium content and luminous flux in rubidium spectral lamp, and the model parameters are evaluated. The results show that if the correlation between rubidium content and luminous flux is ignored, the evaluation results of model parameters will be different. By comprehensively analyzing the log-likelihood function criterion and the AIC criterion, it is found that the Tweedie exponential diffusion process is a better model than the Wiener process, the Gamma process and the IG process.

[0236] 3) In the test scheme analysis, the optimal constant stress accelerated degradation test design schemes designed when two performance degradation characteristics are correlated, two performance degradation characteristics are independent, and a single performance degradation characteristic are compared. The results show that the constant stress accelerated degradation test design scheme designed when the two performance degradation characteristics are correlated is optimal. Ignoring the correlation between the performance degradation characteristics will reduce the sample size and the distribution of low stress levels. Considering only a single performance degradation characteristic will reduce the reliability of the test data results and affect the accuracy of subsequent test data results. The analysis results of the test constraints and model parameter sensitivity show that the D optimization criterion is very sensitive to the total sample size and the total number of measurements. The optimal constant stress accelerated degradation test design scheme obtained by the present invention shows good robustness under the condition of model parameter fluctuations.

[0237] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art 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 by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. Accelerated degradation test method based on Tweedie index performance index, It is characterized in that The following steps are involved: Step S1: constructing a binary constant stress accelerated degradation test model based on the Tweedie exponential diffusion process and using the stress acceleration model; Step S2: constructing a binary constant stress accelerated degradation test optimization design model for the product; Step S201: Assume that the product has two related performance degradation characteristics; Step S202: Determine the Copula function; Step S203: solving unknown parameters of the model; Assume that the constant stress accelerated degradation test is carried out at l stress level, that is, S 0 ≤S 1 <…<S k <…<S l ≤S Max , S 0 is the normal stress level, S Max is the maximum stress level; at stress level S k Next, there are N k Samples were used for constant stress accelerated degradation test. Each sample was subjected to M k Secondary performance measurement; According to the above assumptions, at the stress level S k Under this condition, the initial degradation value of the performance of the i-th sample is Y ip (t 0 |S k )=(Y i1 (t 0 |S k ),Y i2 (t 0 |S k )), the jth measurement value is Y ip (t j |S k )=(Y i1 (t j |S k ),Y i2 (t j |S k )), the corresponding measurement time is t j ,k=1,...,l,i=1,...,N,j=1,...M,t 1 <t j <t M ; Stress level S k The experimental degradation data matrix under is expressed as: According to the properties of Tweedie exponential diffusion process TED, ΔY ip (t j |S k )~TED(η p (S k )Δt,λ p ,ρ),Δt=t j -t j-1 , where Δt represents the measurement time interval, t j is the jth measurement time, t j-1 represents the j-1th measurement time, ρ represents the category parameter; According to Sklar's theorem, there exists a Copula function C such that the degradation increment ΔY of two performance degradation characteristics at the time interval Δt is ip (t j |S k )=(ΔY i1 (t j |S k ),ΔY i2 (t j |S k The joint distribution function of )) is: H(ΔY i1 (t j |S k ),ΔY i2 (t j |S k ))=C(Φ(U kij1 ),Φ(U kij2 )); in: In the formula, ΔY i1 (t j |S k ) and ΔY i2 (t j |S k ) represent the degradation increments of the two performance degradation characteristics, U kijp Degradation increment ΔY ip (t j |S k ), U kij1 and U kij2 Denote the degradation increment ΔY i1 (t j |S k ) and degradation increment ΔY i2 (t j |S k ), Φ(U kij1 ) and Φ(U kij2 ) represent U kij1 and U kij2 The standard normal distribution of The drift coefficients representing the two performance degradation characteristics, λ p represents the diffusion parameter of the Tweedie exponential diffusion process; η p represents the drift parameter of the Tweedie exponential diffusion process; Let c(u,v|α) represent the probability density function of the Copula function with the associated parameter α, and obtain k The log-likelihood function of the test data under is: Where θ=(a 1 ,a 2 ,b 1 ,b 2 ,λ 1 ,λ 2 ,α,ρ) are the corresponding model parameters, a 1 、a 2 , b 1 and b 2 Both represent the coefficients in the relationship between drift coefficient and stress, λ 1 and λ 2 Both represent diffusion coefficients; Δy kijp Indicates that at stress level S k The degradation increment of the pth performance characteristic of the i-th sample under the j-th measurement; d(Δy kijp η p ) is expressed as follows: d(Δy kijp |η p ) represents the unit deviation function, and Matlab is used to implement Gibbs sampling for model parameter evaluation and solve the unknown parameters of the binary constant stress accelerated degradation test model; Step S204: Based on the estimated values ​​of the unknown parameters of the model, combined with the constraint conditions and the optimization objectives, an optimization design model for the binary constant stress accelerated degradation test is obtained; The mathematical expression of the binary constant stress accelerated degradation test optimization design model is: Where I(θ) represents the Fisher information matrix, TC({N k ,t,M k }| k＝1,2,...,l ) represents the total cost of the experiment, t is the total experiment time, C b represents the budget cost; Step S3: Adopting the binary constant stress accelerated degradation test optimization design model and searching for the optimal constant stress accelerated degradation test scheme.

2. The accelerated degradation test method based on Tweedie index performance index correlation according to claim 1, It is characterized in that In step S1, the binary constant stress accelerated degradation test model is: Among them, a and b are coefficients.

3. The accelerated degradation test method based on Tweedie index performance index correlation according to claim 1, It is characterized in that In step S201, the specific assumptions are as follows: 1) The degradation trajectories of the two performance degradation characteristics are both calculated with a drift parameter η p , the diffusion parameter is λ p The Tweedie exponential diffusion process is modeled, p = 1, 2; 2) At each stress level, there is a correlation between the two performance degradation characteristics, and the correlation between the two performance degradation characteristics is described by the Copula function; 3) The degradation observation times of the two performance degradation characteristics are consistent.

4. The Tweedie index performance index-related accelerated degradation test method according to claim 1, It is characterized in that In step S202, the Copula function specifically uses the Frank Copula function in the Archimedean Copula function family that can describe the correlation between two performance degradation characteristics: Among them, α∈(-∞,0)U(0,+∞); for any variables u,v∈[0,1], C(u,1)=u and C(1,v=v are satisfied; for each u 1 ,u 2 ,v 1 ,v 2 ∈[0,1], there is u 1 ≤u 2 , v 1 ≤v 2 ,C(u 2 ,v 2 )-C(u 2 ,v 1 )-C(u 1 ,v 2 )+C(u 1 ,v 1 )≥0.

5. The Tweedie index performance index-related accelerated degradation test method according to claim 1, It is characterized in that In each iteration of Gibbs sampling, each variable is updated sequentially, and each update is performed given the current values ​​of other variables to ensure that each variable is sampled from its conditional distribution during the entire sampling process; after Gibbs sampling converges, the mean, standard deviation, confidence interval and median of the posterior distribution of the model parameters are obtained.

6. The Tweedie index performance index-related accelerated degradation test method according to claim 1, It is characterized in that The specific operation process of step S204 is as follows: Assume that the specific calculation formula of Fisher information matrix I(θ) is: Among them, E represents expectation; Assume that the constant stress accelerated degradation test is carried out at stress level l. k Next, there are N k Samples are used for constant stress accelerated degradation test. For each sample under the kth stress level, the performance degradation value is measured every Δt unit time, and a total of M samples are measured. k times, k=1,...,l, then the test cost is: Among them, C s , C o and C m They represent the cost of each sample, the cost per unit time of operating the test equipment, and the cost of making one measurement, respectively.

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