Component accelerated degradation modeling method considering multi-stress working condition coupling effect, storage medium and equipment

Abstract

The invention discloses a component accelerated degradation modeling method considering a multi-stress working condition coupling effect, a storage medium and equipment, and belongs to the technical field of component accelerated degradation analysis. The problem that the accuracy of an accelerated degradation modeling result is low due to the fact that the influence of multi-stress working condition coupling on a component accelerated degradation model is considered technically is solved. According to the method, a main effect function form of a kth acceleration stress variable is determined based on failure physics and statistical correlation judgment criteria, and an acceleration model considering the coupling effect of the multi-stress working conditions and used for representing the influence of the multi-stress working conditions on component degradation characteristic parameters is further obtained; a multi-stress accelerated degradation model is established in combination with a random effect Wiener process model; component multi-stress accelerated degradation tests of different multi-stress working condition combinations are carried out, multi-stress accelerated degradation model parameter estimation is carried out, and to-be-estimated parameters of a multi-stress accelerated degradation model are obtained through a log-likelihood function corresponding to the likelihood function obtained through the joint distribution function.

Description

Technical Field

[0001] The present invention belongs to the technical field of accelerated degradation analysis of components, and particularly relates to a method for modeling accelerated degradation of components, a storage medium, and a device. Background Art

[0002] An accelerated degradation test of components is to accelerate the degradation process of a product by setting multiple test stresses higher than the working stress level on the premise of ensuring the same degradation mechanism, so as to obtain sufficient degradation data within a short test cycle. Accelerated degradation modeling quantitatively analyzes the accelerated degradation test data by establishing a functional relationship between performance parameters and time and stress conditions, so as to realize the prediction and extrapolation of the performance parameters of "high reliability, long life" products at different times and different stress conditions. Components working in a switching power supply are long-term affected by the coupling action of multiple stress conditions such as electricity, heat, and random vibration. However, most of the existing accelerated degradation modeling methods only consider single stress conditions or double stress conditions, and few modeling methods considering three or more stress conditions can effectively characterize the coupling action mechanism of multiple stress conditions, thus resulting in low accuracy of the accelerated degradation modeling results. Summary of the Invention

[0003] The present invention aims to solve the problem of low accuracy of the accelerated degradation modeling results caused by the influence of the coupling of multiple stress conditions on the accelerated degradation model of components.

[0004] An accelerated degradation modeling method for components considering the coupling action of multiple stress conditions includes:

[0005] S1. Assume that there are N D acceleration stress variables in the accelerated degradation test of components, denoted as element S k as the k-th acceleration stress variable; the main effect function of each acceleration stress variable is denoted as μ k (S k ) = α k h k (S k , β k ); in the formula, μ k (S k ) is the main effect function of the k-th acceleration stress variable, and the main effect function refers to the relationship that quantitatively affects the degradation characteristic parameters of components when each stress variable acts alone; α k is a parameter, h k (·) is the form of the main effect function of the k-th acceleration stress variable determined based on the physics of failure and the statistical correlation criterion; β k is a constant related to the activation energy of component failure;

[0006] Furthermore, an acceleration model considering the coupling action of multiple stress conditions is obtained: where μ(S) is the influence of the multi-stress condition on the degradation characteristic parameters of the component; λ, β k represent the unknown parameters to be estimated in the acceleration model, and λ corresponds to the adjustment parameter; γ k represents the unknown parameter to be estimated in the acceleration model, corresponding to the parameter in the coupling function corresponding to the acceleration stress variable; g k (·) is the form of the coupling function corresponding to the k-th acceleration stress variable, and it has multiple alternative forms;

[0007] S2. Establish a multi-stress accelerated degradation model:

[0008] Y(t, S) = X(t, S) + ε = X0 + υ(S)Λ(t) + σ B (S)B(Λ(t)) + ε

[0009]

[0010] where Y(t, S) is the measured value of the performance parameter degradation amount of the component at time t under the multi-stress condition S; X(t, S) is the true value of the performance parameter degradation amount of the component at time t under the multi-stress condition S; υ(S) is the degradation rate under the multi-stress condition S, and i.e., it follows a normal distribution with a mean of μ υ (S) and a variance of ; σ B (S) is the diffusion coefficient under the multi-stress condition S, indicating the degree of fluctuation in the degradation process of the component under this stress condition; ξ1 and ξ2 represent the correlation coefficients, Λ(t) = t b is the time scale function, b is the time scale parameter; ε is the measurement error, independently following a normal distribution with a mean of 0 and a standard deviation of σ ε ;

[0011] S202. Estimation of multi-stress accelerated degradation model parameters:

[0012] In the multi-stress accelerated degradation test of the component, there are a total of L groups of different multi-stress condition combinations; under each group of test stress conditions, n samples are put in, and each sample is tested m times in the test; t i1l , t i2l ,..., t iml represents the test time of the i-th sample under the l-th stress condition, and Y il = (Y i1l , Y i2l ,..., Y iml )' represents the degradation amount of the performance parameter measured at the corresponding time, and the time scale function matrix is defined as T il = (T i1l , Ti2l ,...,T iml )', where According to the properties of the Wiener process, Y il follows a multivariate normal distribution;

[0013] Considering the degradation correlation of U performance parameters of the component, the parameters to be estimated in the multi-stress accelerated degradation model include U marginal accelerated degradation model parameters Ω u and the correlation parameter θ1 of the Copula function, u = 1,..., U, where is the λ corresponding to the parameter corresponding to the u-th performance parameter σ , β k , γ k , b, ξ1, ξ2, σ ε ; Based on the degradation increments of U performance parameters of the i-th sample under the l-th stress condition within the interval between the (j - 1)-th test and the j-th test the likelihood function is obtained from the joint distribution function:

[0014]

[0015] In the formula, F ΔY (·) and f ΔY (·) are the marginal distribution function and its probability density function of the degradation increment of the u-th performance parameter; c(·) represents the probability density function;

[0016] Its log-likelihood function is expressed as:

[0017]

[0018] where θ1 is the parameter to be determined in the copula;

[0019] Taking the maximization of the log-likelihood function as the objective function, determine the optimal form of the coupling function and the estimated values of U marginal accelerated degradation model parameters Ω u and the correlation parameter θ1 of the Copula function; thus realizing the accelerated degradation modeling of the component considering the coupling effect of multi-stress conditions.

[0020] Furthermore, in the process of determining the form of the main effect function h k (·) of the k-th accelerated stress variable through the failure physics and statistical correlation discrimination criteria, first, multiple single-stress acceleration models determined based on the failure physics laws are used as alternative forms of the main effect function in the multi-stress acceleration model, and then the form of the main effect function is determined based on the correlation coefficient ρ, where the correlation coefficient ρ is the coefficient determined based on the statistical correlation discrimination criteria;

[0021] The statistical correlation discrimination criteria are as follows:

[0022]

[0023] In the formula, E(·) is the expectation function; D(·) is the variance function; ψ(S) is the function form related to the degradation rate of components in the single-stress acceleration model, S represents stress, and represents temperature stress T and electrical stress E; ω(S) is the function form related to the stress variable in the single-stress acceleration model.

[0024] Furthermore, in the process of determining the main effect function form based on the correlation coefficient ρ, the single-stress acceleration model with |ρ| closest to 1 is selected as the main effect function.

[0025] Furthermore, the process of obtaining the acceleration model considering the coupling effect of multi-stress conditions includes the following steps:

[0026] Without considering the coupling effect, the influence of multi-stress conditions on the degradation characteristic parameters of components is expressed as:

[0027]

[0028] The parameter α k is further expressed as a function of other stress variables except the stress variable S k as follows:

[0029] α k (S\{S k ) = λ k g k ((S\{S k}), γ k )

[0030] In the formula, α k (S\{S k}) is the coupling function term corresponding to the kth acceleration stress variable; S\{S k} is other stress variables except the stress S k ; g k (·) is the coupling function form corresponding to the kth acceleration stress variable; λ k , γ k are the unknown parameters to be estimated in the coupling function term corresponding to the kth acceleration stress variable;

[0031] Combined with the alternative form of the coupling function corresponding to the kth acceleration stress variable, the acceleration model form considering the coupling effect of multi-stress conditions is obtained:

[0032]

[0033] In the formula, λ, β k , γ kDenote the unknown parameters to be estimated in the acceleration model; g k (·) is the coupling function form corresponding to the k-th acceleration stress variable, and there are multiple alternative forms for it.

[0034] Furthermore, the alternative forms of the coupling function corresponding to the k-th acceleration stress variable include the following function forms:

[0035]

[0036] In the formula, γ k is the parameter in the coupling function corresponding to the acceleration stress variable, and it is an unknown parameter to be estimated when reflected in the acceleration model.

[0037] Furthermore, Y il obeys a multivariate normal distribution in the following form:

[0038]

[0039] In the formula, The variance of the represented multivariate normal distribution is the covariance matrix, T' il represents the transpose of T il and S l is the acceleration stress variable S under the l-th stress condition; I m represents the m-order identity matrix,

[0040] Furthermore, the degradation increment of the U performance parameters of the i-th sample under the l-th stress condition within the interval between the (j - 1)-th test and the j-th test is:

[0041]

[0042] In the formula, C(·) represents the Copula function.

[0043] Furthermore, the marginal distribution function F ΔY (·) and its probability density function f ΔY (·) are as follows:

[0044]

[0045]

[0046] Among them, represents the degradation increment of the U performance parameters of the i-th sample under the l-th stress condition within the interval between the (j - 1)-th test and the j-th test; the subscript u in the parameter represents the parameter corresponding to the u-th performance parameter, represents σ corresponding to the u-th performance parameterB ; ΔΛ u represents ΔΛ corresponding to the u-th performance parameter, where ΔΛ represents the change in the time scale Λ; Φ represents the standard normal distribution function.

[0047] A computer storage medium stores at least one instruction, and the at least one instruction is loaded and executed by a processor to implement the method for accelerating component degradation modeling considering the coupling effect of multiple stress conditions.

[0048] An apparatus for accelerating component degradation modeling considering the coupling effect of multiple stress conditions, the apparatus includes a processor and a memory, and the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the method for accelerating component degradation modeling considering the coupling effect of multiple stress conditions.

[0049] Beneficial effects:

[0050] In the present invention, the main effect function of the acceleration model is constructed through the failure physics and statistical correlation discrimination criteria. Based on the acceleration degradation model represented by the random effect Wiener process model, the quantitative influence relationship of the coupling effect of multiple stress conditions on the component performance degradation process is derived through the consistency analysis of the degradation mechanism and the invariant criterion of the acceleration factor, and a multi-stress acceleration degradation model of components is established. The failure distribution function and the log-likelihood function corresponding to the multi-stress acceleration degradation model are derived, and an algorithm for estimating model parameters is given. Based on numerical simulation examples, the accuracy of the optimal coupling function form adaptive identification and parameter estimation in the proposed model is verified. In 1000 simulations, the identification accuracy of the optimal coupling function reaches 99.1%, which fully shows that the proposed acceleration degradation model can accurately characterize the coupling effect mechanism of multiple stress conditions. Multifactor variance analysis is carried out on the degradation data of the capacitance value and equivalent series resistance of a certain filter capacitor under voltage, temperature and random vibration stress conditions, and it is clear that the coupling effect between various stresses is relatively significant, indicating the necessity of considering the coupling effect of multiple stress conditions when carrying out acceleration degradation modeling. The verification results show that compared with the existing model, the multi-stress acceleration degradation model proposed by the present invention has the smallest AIC value, and under 3 groups of different verification stress conditions, the mean square error of the reliability evaluation results obtained based on the model proposed by the present invention is reduced by at least 46.67%, indicating that accurately characterizing the coupling effect mechanism of multiple stress conditions can significantly improve the accuracy of multi-stress acceleration degradation modeling. Description of the Drawings

[0051] Figure 1 Flowchart for establishing an acceleration model considering the coupling effect of multiple stress conditions.

[0052] Figure 2 Comparison diagram of expressions for different models.

[0053] Figure 3 is a random vibration stress loading platform.

[0054] Figure 4 is a voltage, temperature stress loading and parameter automatic testing platform.

[0055] Figure 5 is the degradation trajectory of the capacitor capacitance value under different stress conditions.

[0056] Figure 6 is the degradation trajectory of the equivalent series resistance of the capacitor under different stress conditions.

[0057] Figure 7 is the interaction diagram of the multi-factor variance analysis of the capacitance degradation data.

[0058] Figure 8 is the interaction diagram of the multi-factor variance analysis of the equivalent series resistance degradation data.

[0059] Figure 9 is the reliability curve of the capacitor based on different edge accelerated degradation models under the stress conditions of 333K, 8Grms, and 175V.

[0060] Figure 10 is the reliability curve of the capacitor based on different edge accelerated degradation models under the stress conditions of 353K, 12Grms, and 300V.

[0061] Figure 11 is the reliability curve of the capacitor based on different edge accelerated degradation models under the stress conditions of 373K, 20Grms, and 100V. Specific implementation method

[0062] In view of the problems in the background technology, the present invention proposes a method for accelerating the degradation modeling of components considering the coupling effect of multi-stress conditions. First, based on the physics of failure and statistical correlation discrimination criteria, the main effect function of the multi-stress acceleration model is constructed, and an adaptive coupling function is constructed based on the maximum likelihood optimization criterion. On this basis, an acceleration model considering the coupling effect of multi-stress conditions is established to accurately characterize the coupling mechanism of multi-stress conditions. Then, based on the random effect Wiener process model, the quantitative influence relationship of the coupling effect of multi-stress conditions on the performance degradation process of components is derived based on the consistency analysis of degradation mechanisms and the invariant criterion of acceleration factors, and a multi-stress accelerated degradation model is established. The failure distribution function and log-likelihood function of the multi-stress accelerated degradation model are derived, and an algorithm for estimating model parameters is given. Finally, the effectiveness of the proposed model is verified based on numerical simulation examples and a multi-stress accelerated degradation example of a certain filter capacitor. Specific implementation method one:

[0064] A method for accelerating degradation modeling of components considering the coupling effect of multi-stress conditions according to this embodiment includes the following steps:

[0065] S1. Establishment of an acceleration model considering the coupling effect of multi-stress conditions:

[0066] The acceleration model is a mathematical model that describes the quantitative relationship between characteristic parameters such as the degradation rate of a product and stress conditions. Components in key fields such as aerospace and industrial automation serve under multi-stress conditions such as electricity, heat, and random vibration for a long time, and the acceleration effects of multi-stress conditions on the degradation process of components are not independent of each other and often have coupling. Therefore, when establishing a multi-stress acceleration model, the influence of multi-stress conditions on characteristic parameters such as the degradation rate of components is divided into two parts, one is the main effect function of each stress variable within the condition, and the other is the coupling function between stress variables;

[0067] S101. In the constructed multi-stress acceleration model, the main effect function is defined as the quantitative influence relationship of each stress variable acting alone on characteristic parameters such as the degradation rate of components. Here, two discrimination criteria are proposed to determine the specific form of the main effect function in the multi-stress acceleration model: (1) the failure physics discrimination criterion; (2) the statistical correlation discrimination criterion.

[0068] (1) The failure physics discrimination criterion:

[0069] Most single-stress acceleration models such as the Arrhenius model and the Eyring model are derived based on failure physics laws and empirical knowledge. According to the definition of the main effect function, single-stress acceleration models can be used as alternative forms of the main effect function in the multi-stress acceleration model. Some typical forms of single-stress acceleration models are shown in Table 1, where μ(S) represents characteristic parameters such as the degradation rate of components under the action of a single stress variable S. In addition to the models listed in Table 1, if more accurate failure mechanisms can be further analyzed in engineering practice, more applicable alternative forms of the main effect function can be adopted.

[0070] Table 1 Alternative forms of the main effect function based on the failure physics discrimination criterion

[0071]

[0072] (2) The statistical correlation discrimination criterion:

[0073] In engineering practice, the form of the main effect function of most stress variables can be determined by referring to Table 1. In addition, for some stress variables, if there is more than one alternative form of the main effect function corresponding to them, or there is no clear corresponding failure physics law in the current research, it is necessary to further use the statistical correlation discrimination criterion to determine.

[0074] For example, as can be seen from Table 1, both the Arrhenius model and the Eyring model can describe the quantitative relationship between the degradation rate of components and temperature stress, so they can both be used as the main effect function of temperature stress. Similarly, the power-law model and the exponential model are both suitable as the main effect function of electrical stress. Without loss of generality, the following will take the above four typical model forms as examples to illustrate how to further determine the specific form of the main effect function using the statistical correlation discrimination criterion. The above four model forms in Table 1 can be respectively transformed into logarithmic linear models, as shown in Equations (1) to (4):

[0075] For the Arrhenius model:

[0076]

[0077] where a = lnA,

[0078] For the Eyring model:

[0079]

[0080] where a = lnA,

[0081] For the power-law model:

[0082] lnμ(E) = a + blnE (3)

[0083] where a = lnA, b = B.

[0084] For the exponential model:

[0085] lnμ(E) = a + bE (4)

[0086] where a = lnA, b = B.

[0087] Based on Equations (1) to (4), the statistical correlation discrimination criterion is defined as shown in Equation (5):

[0088]

[0089] where E(·) — the expectation function; D(·) — the variance function; ψ(S) — the function form related to the component degradation rate on the left side of Equations (1) to (4), such as lnμ(S) and ln(μ(S) / S); ω(S) — the function form related to the stress variable on the right side of Equations (1) to (4), such as 1 / S, ln(S), and S, where S represents the stress, representing the temperature stress T and the electrical stress E.

[0090] When calculating the correlation coefficient ρ in Equation (5), the component degradation rate μ(S) can be obtained by fitting the data of the single-stress preliminary test. The closer |ρ| is to 1, the more accurate the form of the main effect function is indicated.

[0091] S102. Construction of an adaptive coupling function based on maximum likelihood optimization:

[0092] Suppose there are N D acceleration stress variables in the multi-stress accelerated degradation test, which can be expressed as element S k as the k-th acceleration stress variable. The main effect functions of each acceleration stress variable are determined by the failure physics and statistical correlation discrimination criteria. For the convenience of subsequent expression, the main effect functions of each acceleration stress variable are uniformly expressed here as:

[0093] μ k (S k ) = α k h k (S k , β k ) (6)

[0094] In the formula, μ k (S k ) —— the main effect function of the k-th acceleration stress variable; h k (·) —— the form of the main effect function of the k-th acceleration stress variable determined by the failure physics and statistical correlation discrimination criteria; β k —— a constant related to the component failure activation energy; α k —— a parameter related to factors such as product characteristics and test design.

[0095] When each acceleration stress variable is independent, its influence on characteristic parameters such as the component degradation rate is multiplicative. Therefore, on the premise of not considering the coupling effect, the influence of the multi-stress condition on characteristic parameters such as the component degradation rate can be expressed as:

[0096]

[0097] In engineering practice, the influence of the multi-stress condition on characteristic parameters such as the degradation rate usually has a coupling effect. In order to fully quantify and characterize such a coupling effect, it is defined as the influence of other existing stress variables on the main effect function. Therefore, some specific parameters in the main effect function shown in Equation (7) can be further expressed as functions of other existing stress variables.

[0098] Since β k in Equation (7) is related to the failure activation energy, under the premise assumption that the degradation mechanism remains unchanged in the accelerated degradation test, β kshould always be a fixed constant. Based on this, parameter α k is further expressed as a function of other stress variables except the stress variable S k , as shown in Equation (8):

[0099] α k (S\{S k ) = λ k g k ((S\{S k}), γ k ) (8)

[0100] where α k (S\{S k ) —— the coupling function term corresponding to the k-th acceleration stress variable; S\{S k} —— other stress variables except stress S k ; g k (·) —— the coupling function form corresponding to the k-th acceleration stress variable; λ k , γ k —— unknown parameters to be estimated in the coupling function term corresponding to the k-th acceleration stress variable.

[0101] During the actual service process of components, there are many types of environmental stresses and workloads, and their coupling mechanisms are also different. It is difficult to define a definite function form g k (·) to quantitatively characterize the coupling effect of multi-stress conditions. Therefore, the present invention constructs a more flexible quantitative characterization method applicable to the coupling effect of various multi-stress conditions by introducing alternative function forms.

[0102] Exponential functions and power functions are two types of models for describing the law of accelerating stress action. When their model parameters vary within a certain range, they usually have good fitting ability and can be used to describe and characterize various linear or non-linear effects. Therefore, exponential functions and power functions are used as alternative forms of the coupling function to quantitatively characterize the coupling mechanism of multi-stress conditions, as shown in Equation (9):

[0103]

[0104] Based on Equations (7) to (9), by combining relevant constant terms, the preliminary form of the acceleration model considering the coupling effect of multi-stress conditions can be obtained as shown in Equation (10):

[0105]

[0106] where λ, β k , γ k (k = 1,..., N D) represents the unknown parameters to be estimated in the acceleration model. Here, λ is the unknown parameter to be estimated, and λ is represented as a whole. k is represented.

[0107] Acceleration models usually need to be combined with performance parameter degradation models to obtain acceleration degradation models for quantitatively analyzing acceleration degradation test data under different stress conditions. When obtaining the log-likelihood function lnL(Ω) of the acceleration degradation model, the optimal functional form of g k (·) and the set of unknown parameters Ω = {λ, β k , γ k}(k = 1,..., N D ) can be adaptively determined by maximizing the log-likelihood function lnL(Ω). In summary, the process of establishing an acceleration model considering the coupling effect of multiple stress conditions is as follows Figure 1 shown.

[0108] First, analyze the mission environment profile of the component, clarify the sensitive stress types with acceleration effects, and then determine the N D acceleration stress variables in the acceleration degradation test. On this basis, design and conduct a multi-stress acceleration degradation test for the component and collect degradation data.

[0109] Then, construct a preliminary form of the multi-stress acceleration model as shown in Equation (10), and determine the form of the main effect function in the acceleration model based on the failure physics and statistical correlation discrimination criteria.

[0110] Finally, construct a multi-stress acceleration degradation model and its log-likelihood function. Based on the swarm intelligence optimization algorithm, with the maximum log-likelihood function as the goal, adaptively determine the optimal form of each coupling function in the acceleration model and the model parameter estimation results through iterative optimization.

[0111] The established acceleration model considering the coupling effect of multiple stress conditions quantifies and characterizes the coupling mechanism of multiple stress conditions by simultaneously constructing the main effect functions and coupling functions of each acceleration stress variable, and has the following advantages compared with the existing multi-stress acceleration models:

[0112] A. The main effect functions of each acceleration stress variable are jointly determined by two criteria, which can give sufficient and reasonable explanatory bases from the perspectives of failure physics laws and statistical correlations respectively;

[0113] B. Starting from the coupling mechanism of multiple stress conditions, the definition of the coupling function is given, and at the same time, the optimal form of the coupling function can be determined through an adaptive optimization method, enhancing the flexibility, accuracy, and applicability of the model matching different stress conditions.

[0114] S2. Establishment of a multi-stress acceleration degradation model for components considering the consistency of degradation mechanisms:

[0115] It is a basic assumption of accelerated degradation tests and accelerated degradation modeling that the degradation mechanisms of products under different accelerated stress levels are consistent. Therefore, from the perspective of analyzing the consistency of degradation mechanisms, based on the random effect Wiener process model, the quantitative influence relationship of the coupling effect of multi-stress conditions on the degradation process of component performance parameters is derived through the invariant criterion of the acceleration factor, the multi-stress accelerated degradation modeling method is studied, the failure distribution function and log-likelihood function corresponding to the multi-stress accelerated degradation model are derived, and the model parameter estimation algorithm is given.

[0116] Random effect Wiener process model:

[0117] Y(t) = X(t) + ε = X0 + υΛ(t) + σ B B(Λ(t)) + ε

[0118] In the formula, Y(t) — the measured degradation amount of the component performance parameter at time t; X(t) — the true degradation amount of the component performance parameter at time t; ε — measurement error; X0 — the true degradation amount of the component performance parameter at the initial time, generally considered that X0 = X(0) = 0; υ — drift coefficient, characterizing the degradation rate of the component; σ B — diffusion coefficient, characterizing the degradation fluctuation degree of the component; B(·) — standard Brownian motion; Λ(t) — time scale function, characterizing the linear or nonlinear effect of the component degradation process; when the component undergoes linear degradation, Λ(t) = t; when the component undergoes nonlinear degradation, Λ(t) = t b , b is the time scale parameter.

[0119] S201. Multi-stress accelerated degradation modeling based on the invariant criterion of the acceleration factor:

[0120] In accelerated degradation tests, the acceleration factor is an important index used to calculate and extrapolate parameters such as the degradation rate of products under different stress conditions. Based on the random effect Wiener process model, when the component performance parameter first reaches the given failure threshold D, failure occurs, and its life is defined as in the formula

[0121] T = inf{t|X(t) ≥ D} = inf{t|υΛ(t) + σ B B(Λ(t)) ≥ D, t > 0}

[0122] Among them, inf' represents the infimum.

[0123] Assume that the failure distribution functions of the component under multi-stress conditions and are F p (t p ) and F q (tq ) where p and q represent different operating conditions, represents the k-th acceleration stress variable under operating conditions p and q; t p and t q represent the failure times under operating conditions p and q.

[0124] If F p (t p ) = F q (t q ), then the acceleration factor is:

[0125] AF p,q = t q / t p (11)

[0126] According to the constant acceleration factor criterion in the accelerated degradation test, when the degradation mechanism of the product remains unchanged, the acceleration factor is only related to the acceleration stress level and is independent of other variables such as time. Therefore, for any failure time t p , the following relationship should be satisfied:

[0127] F p (t p ) = F q (AF p,q · t p ) (12)

[0128] Further differentiating t p in Equation (12) gives:

[0129]

[0130] In the equation, f p (·) and f q (·) respectively represent the probability density function forms, and F p (·) and F q (·) represent the failure distribution functions.

[0131] Let Λ(t) = t b , then there is:

[0132]

[0133]

[0134] where b p , b q represent the time scale parameters of different operating conditions; the drift coefficient under operating condition p the drift coefficient under operating condition q is the diffusion coefficient under operating condition p, is the diffusion coefficient under condition q; D is the given failure threshold.

[0135] Based on the invariant criterion of the acceleration factor, eliminate the failure time t in Equation (16) p and t q on the acceleration factor AF p,q The influence is as follows:

[0136] b p = b q (17)

[0137] Substitute Equation (17) into Equation (16) and simplify to obtain:

[0138]

[0139] Similarly, further eliminate the failure time t in Equation (18) p and t q on the acceleration factor AF p,q The influence:

[0140]

[0141]

[0142] Combining Equation (17), Equation (19) and Equation (20), the derivation gives:

[0143]

[0144] It can be seen that when the degradation mechanism of the component does not change, the time-scale parameter b is a fixed constant, that is, it is not affected by the acceleration stress. In addition, the mean value of the degradation rate standard deviation and the square of the diffusion coefficient are all affected by the acceleration stress, and there is a correlation among the three.

[0145] Based on Equation (21), for the convenience of constructing and subsequent derivation of the multi-stress accelerated degradation model, the quantitative influence relationship of the acceleration stress on the performance degradation process can be characterized as follows:

[0146]

[0147] Among them, ξ1 and ξ2 represent the correlation coefficients,

[0148] Because is correlated with the rate mean and standard deviation, the difference in their values can be linearly adjusted by the correlation coefficient. Since what is intuitively reflected in Equation (23) is σ BTherefore, it can replace the mean value of the rate, and the actual difference lies in the value of λ. What is directly reflected in Equation (23) is σ B , while the mean value and standard deviation of the degradation rate are both implicit in υ(S) and not convenient to directly represent. Therefore, this transformation is made to reduce variables, reduce the calculation cost, and facilitate representation.

[0149] Based on Equation (22), the multi-stress accelerated degradation model is established as shown in Equation (23):

[0150] Y(t,S) = X(t,S) + ε = X0 + υ(S)Λ(t) + σ B (S)B(Λ(t)) + ε (23)

[0151] In the formula, Y(t,S) —— the measured value of the performance parameter degradation amount of the component at time t under the multi-stress condition S; X(t,S) —— the true value of the performance parameter degradation amount of the component at time t under the multi-stress condition S; υ(S) —— the drift coefficient under the multi-stress condition S, representing the degradation rate of the component under this stress condition, and σ B (S) —— the diffusion coefficient under the multi-stress condition S, representing the fluctuation degree of the component degradation process under this stress condition. ε is the measurement error; it is assumed that ε independently follows a normal distribution with a mean of 0 and a standard deviation of σ ε at each test time, that is to describe the measurement error of the component performance parameter.

[0152] Based on Equation (22), the failure probability density function and failure distribution function corresponding to the multi-stress accelerated degradation model are obtained as:

[0153]

[0154] Among them, Φ represents the standard normal distribution function;

[0155] In the multi-stress accelerated degradation test, if the component has a total of U performance parameters and their degradation processes are correlated, the marginal accelerated degradation model Y u (t,S) of the u (u = 1,..., U)th performance parameter can be characterized by Equation (23), and its marginal failure probability density function f u (t,S) and marginal failure distribution function F u (t,S) can be represented by Equations (24) and (25) respectively. According to the multi-performance parameter degradation correlation model based on the Copula function, the joint failure distribution function and probability density function of the multi-stress accelerated degradation model considering the degradation correlation of U performance parameters can be expressed as:

[0156] F joint (t,S) = C(F1(t,S),..., Fu (t, S),..., F U (t, S); θ1) (26)

[0157]

[0158] Wherein, C(·) and c(·) respectively represent the Copula function and its probability density function, and θ1 is the correlation parameter in the Copula function.

[0159] S202. Parameter estimation of the multi-stress accelerated degradation model:

[0160] Suppose there are N D accelerated stress variables in the multi-stress accelerated degradation test of components, and there are L different combinations of multi-stress working conditions in the test. Under each test stress working condition, n samples are put in, and each sample is tested m times in the test. t i1l , t i2l ,..., t iml represents the test time of the i-th sample under the l-th stress working condition, and Y il =(Y i1l , Y i2l ,..., Y iml )' represents the degradation amount of the performance parameter measured at the corresponding moment. The time scale function matrix is defined as T il =(T i1l , T i2l ,..., T iml )', where According to the properties of the Wiener process, Y il obeys a multivariate normal distribution, as shown in Equation (28):

[0161]

[0162] Wherein, the variance of the represented multivariate normal distribution is the covariance matrix, T' il represents the transpose of T il , S l is the accelerated stress variable S under the l-th stress working condition; I m represents the m-order identity matrix,

[0163] Substituting Equation (22) into Equation (28), the log-likelihood function of the multi-stress accelerated degradation model can be obtained.

[0164] Through the coupling function g in the multi-stress accelerated degradation model kThe optimal form of (·) and the estimated values of the model parameters can be adaptively obtained by maximizing the log-likelihood function shown in Equation (29), and the process is as shown in Algorithm 1.

[0165]

[0166] When considering the degradation correlation of U performance parameters of the component, the parameters to be estimated in its multi-stress accelerated degradation model include U marginal accelerated degradation model parameters Ω u (u = 1,..., U) and the correlation parameter θ1 of the Copula function. Based on the parameter estimation idea and related assumptions, further considering the accelerated stress variable, the joint distribution function of the degradation increments of the U performance parameters of the i-th sample under the l-th stress condition during the interval between the (j - 1)-th test and the j-th test can be expressed as:

[0167]

[0168] Its likelihood function can be expressed as:

[0169]

[0170] In the formula, the marginal distribution function F ΔY (·) of the degradation increment of the u-th performance parameter and its probability density function f ΔY (·):

[0171]

[0172] Among them, the subscript u in the parameter represents the parameter corresponding to the u-th performance parameter, represents σ corresponding to the u-th performance parameter B ; ΔΛ u represents ΔΛ corresponding to the u-th performance parameter, and ΔΛ represents the change amount of the time scale Λ; represents the degradation increments of the U performance parameters of the i-th sample under the l-th stress condition during the interval between the (j - 1)-th test and the j-th test; t ij represents the test time of the i-th sample under the l-th stress condition, represents the variance of the measurement errors of the U performance parameters of the sample; ξ 1u and ξ 2u are the correlation coefficients among the U performance parameters of the sample

[0173] Then the log-likelihood function can be expressed as:

[0174]

[0175] Among them, θ1 is the parameter to be solved in the copula;

[0176] On this basis, the optimization idea of Algorithm 1 can be used to adaptively obtain the optimal form of the coupling function (determined in Formula (9)) and the parameters Ω of U marginal accelerated degradation models with the maximization of Formula (33) as the objective function. u (u = 1, ..., U) and the estimated value of the correlation parameter θ1 of the Copula function. When there are too many model parameters, the parameter estimation idea of the "two-step method" can also be adopted, that is, in the first step, the optimal form of the coupling function and the corresponding parameter estimation results in the marginal accelerated degradation model of each performance parameter of the component are obtained by using Algorithm 1 respectively. In the second step, the above results are directly substituted into Formula (33), and the estimation of the correlation parameter θ1 is completed by maximizing Formula (33).

[0177] Example: Verification of the effectiveness of the multi-stress accelerated degradation model.

[0178] Numerical simulation verification: Through numerical simulation examples, in the single performance parameter degradation dimension, the effectiveness of the accelerated degradation model considering the coupling effect of multi-stress conditions is emphasized. First, define A0 * 、A1 * and A2 * three types of multi-stress accelerated degradation models, which are respectively constructed by different forms of multi-stress acceleration models and random effect Wiener process models, as shown in Figure 2 Model A0 * uses the accelerated model considering the coupling effect of multi-stress conditions constructed in Section 3.2; Model A1 * uses the generalized multi-stress acceleration model proposed by Liu et al.; Model A2 * ignores the coupling function term on the basis of A1 * .

[0179] To enhance the rationality of stress type selection and model parameter setting in numerical simulation, this example fully simulates the actual stress conditions and capacitance value degradation process of a certain filter capacitor. Three types of acceleration stress, temperature (T), voltage (E), and random vibration (G), are set in the multi-stress conditions. The stress level combination forms in the accelerated degradation test are as shown in Table 6 in Section 3.4.2, and 100 test samples are placed under each stress level combination. Each sample is tested 30 times during the test cycle. The multi-stress accelerated degradation test data is generated by Model A0 * , and its specific model form and parameter setting method are shown in Table 2. The failure threshold is set to 0.45, and the simulation process is repeated 1000 times. In addition to the models A0 Figure 2 defined in * 、A1 * and A2 * , a new type of model A3 * is added here, which is defined as Model A0 * when γ3 = 0.sub - models

[0180] Table 2 Simulation Model Forms and Parameter Settings

[0181]

[0182] Then, use model A0 * 、A1 * 、A2 * and A3 * to model the accelerated degradation data. When using model A0 * for modeling, it is necessary to accurately identify the optimal form of the coupling function in Equation (23). In 1000 simulations, the identification frequencies of 8 alternative coupling function combinations are shown in Table 3. It can be seen that the identification accuracy of the pre - set optimal coupling function reaches 99.1%, which fully demonstrates that the proposed accelerated degradation model can accurately identify and characterize the coupling mechanism of multi - stress conditions.

[0183] Table 3 Identification Frequencies of the Optimal Coupling Function of Model A0 * in 1000 Simulations

[0184]

[0185]

[0186] Based on the identified optimal coupling function form, the mean, mean deviation, and mean square error of the parameter estimation results of model A0 * are shown in Table 4. It can be seen from the table that the mean of the parameter estimation results of model A0 * is very close to the parameter setting value in Table 2, and the mean deviation and mean square error of the parameter estimation results are small enough, indicating the accuracy of the proposed model parameter estimation method. Then, with the help of the AIC shown in Equation (36) and the mean square error of the average life of components under 3 groups of verification stress conditions (Group 1 in Table 6: 333K, 8Grms, 175V; Group 6: 353K, 12Grms, 300V; and Group 12: 373K, 20Grms, 100V), two indicators are used to quantitatively illustrate the effectiveness and accuracy of model A0 * compared with A1 * 、A2 * 、A3 * The comparison results are shown in Table 5.

[0187] Table 4 Mean, Mean Deviation, and Mean Square Error of the Parameter Estimation Results of Model A0 * in 1000 Simulations

[0188]

[0189] Table 5 Model A0 in 1000 simulations * , A1 * , A2 * and A3 * Calculation results of AIC and mean square error of average life

[0190]

[0191]

[0192] As can be seen from Table 5, in 1000 simulations, model A0 * has the smallest AIC value, and compared with models A1 * , A2 * , A3 * , the obtained mean square error value of average life is the smallest, which fully demonstrates the effectiveness of the proposed model A0 * , and also illustrates the necessity of accurately establishing the main effect function and coupling function in the multi-stress accelerated degradation modeling process. At the same time, it can be further seen that in engineering practice, if the coupling action mechanism of multi-stress conditions is not accurately characterized and the model is misused, the accuracy of accelerated degradation modeling will be significantly reduced.

[0193] Taking the accelerated degradation test data of a filter capacitor in a spaceborne switching power supply under the coupling action of temperature, voltage and random vibration stress as an example, the effectiveness of the proposed model is verified. In the multi-stress accelerated degradation test of the capacitor, the random vibration stress is only applied in the initial stage (simulating the random vibration during the satellite launch), while the temperature and voltage stresses are continuously applied during the test period. The test device is as Figures 3 - 4 shown Figure 3 , which is the random vibration stress loading platform Figure 4 , and is the voltage, temperature stress loading and parameter automatic test platform, which can realize the loading of the above stress conditions and the automatic test of the capacitor capacitance value and equivalent series resistance respectively.

[0194] Based on the above multi-stress accelerated degradation test and test platform of the capacitor, a total of 12 groups of accelerated degradation tests under different stress conditions are designed, and the stress conditions are shown in Table 6.

[0195] Table 6 Stress conditions table of multi-stress accelerated degradation test of capacitor

[0196]

[0197] 10 test samples are placed under each stress condition shown in Table 6, and the capacitance value and equivalent series resistance of the capacitor are tested every three days (72 hours). The test period is 42 days (1008 hours). The degradation trajectories of the capacitance value and equivalent series resistance of the capacitor under different stress conditions obtained in the test are asFigures 5 - 6 as shown

[0198] For Figures 5 - 6 the original degradation data shown, first perform multi-factor analysis of variance separately to qualitatively test whether there is a coupling effect between voltage, temperature, and random vibration stress. The interaction graph of the multi-factor analysis of variance is as shown Figures 7 - 8 below. Among them, the X-axis represents different stress levels of temperature, voltage, and random vibration, Figures 7 - 8 and the Y-axis respectively represents the average degradation rates of the calculated capacitance value and equivalent series resistance of the capacitor. It can be seen from the figure that the average degradation rate curves under different stress conditions are significantly non-parallel, indicating that the coupling effect between stresses is relatively significant, thus demonstrating the necessity of considering the coupling effect of multi-stress conditions when performing accelerated degradation modeling.

[0199] Then, use the multi-stress accelerated degradation model A0 * proposed by the present invention and its comparison models A1 * , A2 * and A3 * to further quantitatively analyze the accelerated degradation test data of the capacitance value and equivalent series resistance of the capacitor. As can be seen Figures 5 - 6 from, the degradation trajectories of the capacitance value and equivalent series resistance are approximately linear. Therefore, uniformly set Λ(t)=t in Equation (23). Based on the failure physics and statistical correlation discrimination criteria proposed in Section 3.2.1, the main effect functions of temperature, voltage, and random vibration stress for the capacitance value and equivalent series resistance are respectively determined as the Arrhenius model and the power-law model, that is and According to the process shown in Algorithm 1, the optimal coupling function combinations in the multi-stress accelerated degradation models of the capacitance value and equivalent series resistance are respectively and It can be seen that for different accelerated degradation test data, the power-law model and the exponential model each have advantages in characterizing the coupling effect of multi-stress conditions, and also demonstrate the necessity of introducing an adaptively optimized coupling function when establishing a multi-stress accelerated degradation model. For the capacitance value and equivalent series resistance, the parameter estimation results and AIC values of models A0 * , A1 * , A2 * and A3 * are shown in Tables 7 and 8 respectively.

[0200] Table 7 Capacitance value degradation data: Parameter estimation results and AIC values of models A0 * , A1 * , A2 * and A3 *

[0201]

[0202]

[0203] Table 8 Equivalent series resistance degradation data: Model A0 * , A1 * , A2 * and A3 * Parameter estimation results and AIC values

[0204]

[0205] As can be seen from Table 7 and Table 8, for both the capacitance value and the equivalent series resistance of the capacitor, the multi-stress accelerated degradation model A0 * proposed by the present invention has the smallest AIC value, indicating that it has the highest modeling accuracy. This is mainly attributed to the accurate characterization of the acceleration effect of the main effect function and the adaptive coupling function in A0 * on each stress variable. Although model A1 * has more coupling function terms and more parameters, its modeling accuracy is still lower than that of A0 * , which also shows that it is inappropriate to use only the exponential model to describe the main effects and coupling effects of all stresses. In addition, by comparing models A2 * and A3 * it can be seen that whether all or part of the stress condition coupling effect is ignored, it will lead to a significant reduction in modeling accuracy. In summary, the accelerated degradation model A0 * established by the present invention considering the coupling effect of multi-stress conditions can significantly improve the accuracy of accelerated degradation modeling.

[0206] Based on the parameter estimation values of the marginal accelerated degradation models A0 * for the capacitance value and equivalent series resistance of the capacitor, the degradation correlation parameter θ1 can be further estimated according to Equation (33). The correlation parameter estimation results and AIC values of different Copula functions are shown in Table 9. Among them, the Frank Copula function has the smallest AIC value, so it can more accurately quantify the correlation between the capacitance value and the equivalent series resistance during the accelerated degradation process.

[0207] Table 9 Correlation parameter estimation results of different Copula functions

[0208]

[0209] By further comparing A0 * , A1 * , A2 * and A3 *As the reliability evaluation results of the edge acceleration degradation model under 3 groups of verification stress conditions (Group 1 in Table 6: 333K, 8Grms, 175V; Group 6: 353K, 12Grms, 300V; and Group 12: 373K, 20Grms, 100V) are used to further illustrate the effectiveness of the proposed model, as Figures 9 - 11 shown, the scatter points in the figure represent the empirical reliability function obtained based on the pseudo-failure life of the capacitor, which is used as the verification benchmark. It can be seen that based on the edge acceleration degradation model A0 * the obtained reliability curve is closest to the empirical reliability based on the pseudo-failure life, thus verifying the edge acceleration degradation model A0 * effectiveness and accuracy.

[0210] On this basis, the effectiveness of the proposed model is further illustrated by quantitatively comparing the mean square error between the reliability curves based on each edge acceleration degradation model and the empirical reliability based on the pseudo-failure life, as shown in Table 10. It can be seen from the table that under 3 groups of different verification stress conditions, based on the proposed edge acceleration degradation model A0 * the obtained mean square error of reliability is reduced by at least 46.67%, indicating that accurately characterizing the coupling mechanism of multi-stress conditions can significantly improve the accuracy of multi-stress accelerated degradation modeling.

[0211] Table 10 Mean square error of reliability based on edge degradation models A0 * 、A1 * 、A2 * and A3 *

[0212]

[0213] To accurately characterize the coupling mechanism of multi-stress conditions, the present invention proposes a method for accelerating the degradation modeling of components considering the coupling of multi-stress conditions, and constructs a quantitative relationship between the performance parameters of components, time, and multi-stress conditions.

[0214] In this embodiment, the main effect function of the acceleration model is constructed based on the physics of failure and the statistical correlation discrimination criterion, and the adaptive coupling function is constructed based on the maximum likelihood optimization criterion, accurately characterizing the coupling mechanism of multi-stress conditions. Compared with the existing models, this model has both interpretability and flexibility and applicability matching different stress conditions. Based on the random effect Wiener process model, the quantitative influence relationship of the coupling of multi-stress conditions on the component performance degradation process is derived through the analysis of the consistency of degradation mechanisms and the acceleration factor invariance criterion, a multi-stress accelerated degradation model of components is established, the failure distribution function and logarithmic likelihood function corresponding to the multi-stress accelerated degradation model are derived, and the model parameter estimation algorithm is given.

[0215] Based on numerical simulation examples, the accuracy of the optimal coupling function form adaptive identification and parameter estimation in the proposed model is verified. In 1000 simulations, the identification accuracy of the optimal coupling function reaches 99.1%, fully demonstrating that the proposed accelerated degradation model can accurately characterize the coupling action mechanism under multi-stress conditions. Multifactor variance analysis is carried out on the degradation data of capacitance value and equivalent series resistance of a certain filter capacitor under voltage, temperature, and random vibration stress conditions, clarifying that the coupling effect between stresses is relatively significant, indicating the necessity of considering the coupling action of multi-stress conditions when conducting accelerated degradation modeling. The verification results show that compared with the existing model, the multi-stress accelerated degradation model proposed in the present invention has the smallest AIC value, and under 3 groups of different verification stress conditions, the mean square error of the reliability evaluation results obtained based on the model proposed in the present invention is reduced by at least 46.67%, indicating that accurately characterizing the coupling action mechanism of multi-stress conditions can significantly improve the accuracy of multi-stress accelerated degradation modeling. Specific Embodiment 2:

[0217] This embodiment is a computer storage medium, and at least one instruction is stored in the storage medium. The at least one instruction is loaded and executed by a processor to implement the method for accelerated degradation modeling of components considering the coupling action of multi-stress conditions.

[0218] It should be understood that the instruction includes a computer program product, software, or computerized method corresponding to any method described in the present invention; the instruction can be used to program a computer system or other electronic devices. The computer storage medium may include a readable medium on which the instruction is stored, which may include but is not limited to a magnetic storage medium and an optical storage medium; the magneto-optical storage medium includes a read-only memory ROM, a random access memory RAM, an erasable programmable memory (such as EPROM and EEPROM), and a flash memory layer, or other types of media suitable for storing electronic instructions. Specific Embodiment 3:

[0220] This embodiment is a device for accelerated degradation modeling of components considering the coupling action of multi-stress conditions. The device includes a processor and a memory. It should be understood that the device includes any device including a processor and a memory described in the present invention. The device may further include other units and modules for display, interaction, processing, control, etc. through signals or instructions, as well as other functions.

[0221] At least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to implement the method for accelerated degradation modeling of components considering the coupling action of multi-stress conditions.

[0222] Those skilled in the art should understand that at least one stored instruction is a computer program product corresponding to a method or system. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present application can be implemented in various computer languages. For example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0223] The present application is described with reference to the flowcharts and / or block diagrams of methods, systems, and computer program products according to the embodiments of the present application, and can also be used for corresponding devices. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a machine for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0224] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0225] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0226] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concepts. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0227] Obviously, those skilled in the art can make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalent technologies, this application is also intended to include these modifications and variations.

[0228] The above numerical examples of the present invention are only for illustrating in detail the calculation model and calculation process of the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is impossible to enumerate all the implementation manners here. Any obvious changes or variations derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. A component accelerated degradation modeling method considering the coupling of multiple stress conditions, characterized in that: include: S1. Assume that there are N components in the multi-stress accelerated degradation test. D An accelerated stress variable, expressed as Element S k is the kth accelerating stress variable; the main effect function of each accelerating stress variable is expressed as μ k (S k )=α k h k (S k ,β k );where μ k (S k ) is the main effect function of the kth accelerated stress variable. The main effect function refers to the relationship between the quantitative influence of each stress variable on the degradation characteristic parameters of the component when it acts alone; α k is the parameter, h k (·) is the main effect function form of the kth accelerating stress variable determined based on the failure physics and statistical correlation criteria; β k is a constant related to the activation energy of component failure; Then the acceleration model considering the coupling of multiple stress conditions is obtained: Where μ(S) is the influence of multiple stress conditions on the degradation characteristic parameters of components; λ, β k represents the unknown parameters to be estimated in the acceleration model, and λ corresponds to the adjustment parameter; γ k g represents the unknown parameters to be estimated in the acceleration model, corresponding to the parameters in the coupling function corresponding to the acceleration stress variable; k (·) is the coupling function form corresponding to the kth accelerating stress variable, which has multiple alternative forms; S2. Establish a multi-stress accelerated degradation model: Y(t,S)=X(t,S)+ε=X0+υ(S)Λ(t)+σ B (S)B(Λ(t))+ε Where Y(t,S) is the measured value of the performance parameter degradation of the component at time t under the multi-stress condition S; X(t,S) is the true value of the performance parameter degradation of the component at time t under the multi-stress condition S; υ(S) is the degradation rate under the multi-stress condition S, and That is, the mean is μ υ (S), variance is The normal distribution of B (S) is the diffusion coefficient under the multi-stress condition S, which indicates the degree of fluctuation of the component degradation process under this stress condition; ξ1 and ξ2 represent the correlation coefficients, Λ(t)=t b Time scale function, b is the time scale parameter; ε is the measurement error, which is independent and has a mean of 0 and a standard deviation of σ ε Normal distribution of S202. Parameter estimation of multi-stress accelerated degradation model: The component multi-stress accelerated degradation test includes L groups of different multi-stress conditions. Under each group of test stress conditions, n samples are put in, and each sample is tested m times in the test. i1l ,t i2l ,...,t iml represents the test time of the i-th sample under the l-th group of stress conditions, Y il =(Y i1l ,Y i2l ,...,Y iml )' represents the performance parameter degradation measured at the corresponding time, and the time scale function matrix is ​​defined as T il =(T i1l ,T i2l ,...,T iml )',in According to the properties of the Wiener process, Y il It follows a multivariate normal distribution; Considering the degradation correlation of U performance parameters of components, the estimated parameters of the multi-stress accelerated degradation model include U edge accelerated degradation model parameters Ω u and the correlation parameters of the Copula function θ1, u=1,...,U, Among them b u , is the λ corresponding to the parameter corresponding to the u-th performance parameter σ , β k , γ k , b, ξ1, ξ2, σ ε ; Based on the degradation increment of the U performance parameters of the ith sample under the lth group of stress conditions between the j-1th test and the jth test The joint distribution function of gets the likelihood function: In the formula, F ΔY (·) and f ΔY (·) is the marginal distribution function and probability density function of the degradation increment of the uth performance parameter; c(·) represents the probability density function; Its log-likelihood function is expressed as: Among them, θ1 is the parameter to be determined in copula; Taking the maximization of the log-likelihood function as the objective function, the optimal form of the coupling function and the U edge acceleration degradation model parameters Ω are determined. u And the estimated value of the correlation parameter θ1 of the Copula function; thereby realizing the accelerated degradation modeling of components considering the coupling effect of multiple stress conditions.

2. The component accelerated degradation modeling method considering the coupling of multiple stress conditions according to claim 1 is characterized in that: Determine the main effect function form h of the kth accelerating stress variable by using the failure physics and statistical correlation criteria k (·), firstly, multiple single stress acceleration models determined based on the physical law of failure are used as alternative forms of the main effect function in the multi-stress acceleration model, and then the main effect function form is determined based on the correlation coefficient ρ, where the correlation coefficient ρ refers to a coefficient determined based on the statistical correlation discrimination criterion; The statistical correlation criteria are as follows: Where E(·) is the expected function; D(·) is the variance function; ψ(S) is the function form related to the degradation rate of components in the single stress acceleration model, S represents stress, which represents temperature stress T and electrical stress E; ω(S) is the function form related to the stress variable in the single stress acceleration model.

3. The component accelerated degradation modeling method considering the coupling of multiple stress conditions according to claim 2 is characterized in that: In the process of determining the form of the main effect function based on the correlation coefficient ρ, the single stress acceleration model with |ρ| closest to 1 is selected as the main effect function.

4. The component accelerated degradation modeling method considering the coupling of multiple stress conditions according to any one of claims 1 to 3, characterized in that: The process of obtaining the acceleration model considering the coupling of multiple stress conditions includes the following steps: Without considering the coupling effect, the influence of multiple stress conditions on the degradation characteristic parameters of components is expressed as: The parameter α k Further expressed as stress-removing variable S k In addition, the functions of other stress variables are as follows: a k (S\{S k })=λ k g k ((S\{S k }),c k ) In the formula, α k (S\{S k }) is the coupling function term corresponding to the kth accelerating stress variable; S\{S k } is the stress relief S k Other stress variables besides g k (·) is the coupling function form corresponding to the kth accelerating stress variable; λ k ,γ k is the unknown parameter to be estimated in the coupling function term corresponding to the kth accelerated stress variable; Combined with the alternative form of the coupling function corresponding to the kth accelerating stress variable, the form of the acceleration model considering the coupling effect of multiple stress conditions is obtained: In the formula, λ,β k ,γ k represents the unknown parameters to be estimated in the acceleration model; g k (·) is the coupling function form corresponding to the kth accelerating stress variable, which has multiple alternative forms.

5. The component accelerated degradation modeling method considering the coupling of multiple stress conditions according to claim 4 is characterized in that: Alternative forms of the coupling function corresponding to the kth accelerating stress variable include the following functional forms: In the formula, γ k It is the parameter in the coupling function corresponding to the accelerated stress variable, and is an unknown parameter to be estimated when reflected in the accelerated model.

6. The component accelerated degradation modeling method considering the coupling of multiple stress conditions according to claim 5 is characterized in that: Y il The multivariate normal distribution is as follows: In the formula, The variance of the multivariate normal distribution represented by is the covariance matrix, T i ' l Indicates T il The transpose of S l is the accelerated stress variable S under the first group of stress conditions; I m represents the m-order identity matrix, 7. The component accelerated degradation modeling method considering the coupling of multiple stress conditions according to claim 6 is characterized in that: The degradation increment of the U performance parameters of the i-th sample under the l-th group of stress conditions between the j-1th test and the jth test The joint distribution function of is: Where C(·) represents the Copula function.

8. The component accelerated degradation modeling method considering the coupling of multiple stress conditions according to claim 6 is characterized in that: The marginal distribution function F of the degradation increment of the uth performance parameter ΔY (·) and its probability density function f ΔY (·)as follows: in, represents the degradation increment of the U performance parameters of the i-th sample under the l-th stress condition between the j-1-th test and the j-th test; the u in the parameter subscript represents the parameter corresponding to the u-th performance parameter, σ Bu represents the σ corresponding to the u-th performance parameter B ; ΔΛ u represents the ΔΛ corresponding to the u-th performance parameter, ΔΛ represents the change in the time scale Λ; Φ represents the standard normal distribution function.

9. A computer storage medium, characterized in that The storage medium stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the component accelerated degradation modeling method considering the coupling effect of multiple stress conditions as described in any one of claims 1 to 8.

10. A component accelerated degradation modeling device considering the coupling of multiple stress conditions, characterized in that: The device includes a processor and a memory, wherein the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the component accelerated degradation modeling method considering the coupling effect of multiple stress conditions as described in any one of claims 1 to 8.

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