Degradation variable fusion life prediction method and system under small sample condition

Abstract

The invention belongs to the technical field of equipment life prediction, and provides a degradation variable fusion life prediction method and system under a small sample condition, and the method is based on a Copula function and parameter resampling estimation, combines different selectable random process models to describe degradation variables with different characteristics, and then carries out the fusion of a plurality of degradation variables through the Copula function. Secondly, according to the characteristic that the degradation data of the equipment is sparse, a Bayesian bootstrap-maximum likelihood method is adopted to achieve estimation of the degradation model and Copula function parameters, and the model selection problem is described after the degradation data is obtained; a multivariate degradation variable description model based on degradation variable parameter test in interval time and a multivariate fusion function selection method are proposed, and the effectiveness of the proposed equipment multivariate fusion processing method is verified through life prediction under multivariate degradation variable fusion by examples.

Description

Technical Field

[0001] The present invention belongs to the technical field of equipment life prediction, and particularly relates to a method and system for fusing degradation variables to predict life under small sample conditions. Background Art

[0002] Generally, the degradation variable used for equipment degradation state estimation and remaining useful life (RUL) prediction modeling is one-dimensional, and the degradation process of the research object is measured through the change process of a typical signal. In some existing studies, two-dimensional or even multi-dimensional variables are also selected for research. However, such studies usually assume that two or more signals are independent, and their degradation process is to simply multiply the corresponding signal degradation probability densities to describe the degradation state of the research object. And in the research, a one-dimensional degradation model is often used to describe the research process under multiple degradation signals by assigning different parameters to it. But for complex systems, their daily tests often involve multiple signals, and there is a strong correlation between some signals. It is necessary to study a method for state evaluation and life prediction for the characteristics of multi-dimensional degradation variables with correlation in the equipment. In addition, due to the existence of various limitations, the samples of some applications show typical small sample characteristics. The small sample problem generally exists in the life estimation process of some complex equipment, and this condition brings challenges to the parameter estimation of the degradation model. Summary of the Invention

[0003] In order to solve the problems existing in the prior art, the present invention provides a method for fusing degradation variables to predict life under small sample conditions. By establishing a comprehensive health state description factor of the equipment, the above problems are solved through a degradation variable fusion and design parameter estimation method, enabling maintenance personnel to more accurately master the degradation situation of the equipment, and further providing decision support information for predicting the remaining useful life (RUL) of the equipment and formulating scientific and accurate maintenance strategies.

[0004] In order to achieve the above object, in the first aspect, the present invention provides a method for fusing degradation variables to predict life under small sample conditions, including the following steps:

[0005] S1, select the degradation test signals of key components based on the individual equipment test information, preprocess the test information to eliminate invalid values, delete the header to obtain the degradation variable vectors corresponding to X(t) and X(t) at different stages, and determine the degradation failure threshold value;

[0006] S2. Obtain the prior distribution of the parameters of the same-type products of the individual devices to be processed based on the historical degradation data or prior knowledge of the same-type products. Resample the small-sample individual data through the Bayesian bootstrap method to obtain the parameter estimates and their corresponding distributions of the selected degradation description models for each component. Calculate the parameters of the degradation description model through the corresponding relationship between the parameter estimates and the parameters of the stochastic process.

[0007] S3. Convert the parameters of the degradation description model obtained in S2 into the parameters corresponding to different degradation description models respectively. Based on the parameters corresponding to different stochastic processes, perform the AD test on the obtained degradation variable vectors of each component, and select the stochastic process closest to the distribution of the degradation variable vector to model the degradation processes of different components.

[0008] S4. Combine the newly obtained degradation data of each component, and update the parameters of each component based on the degradation parameter estimation method of the Bayesian bootstrap method.

[0009] S5. Based on the updated parameters, estimate the parameters of different multivariate degradation Copula functions through the maximum likelihood method, and select the joint distribution model based on the AIC criterion.

[0010] S6. When new test data is obtained, repeat S4 and S5 to complete the parameter update, and realize the life prediction under the condition of multivariate degradation variables based on the updated parameters and the degradation failure threshold value.

[0011] Furthermore, the degradation description model is the degradation state description based on the Wiener process, the degradation state description based on the Gamma process, or the degradation state description based on the inverse Gaussian process.

[0012] Furthermore, convert the parameters of the degradation description model obtained in S2 into the parameters corresponding to different degradation description models according to the following formula:

[0013]

[0014] where, ΔX is the increment of the degradation amount, N(μ,σ 2 ) represents the normal distribution, μ is the drift coefficient, σ > 0 represents the diffusion coefficient of the Wiener process; Ga(α,β) represents the Gamma distribution, α is the shape coefficient, β is the scale coefficient; IG(η,λ) represents the inverse Gaussian distribution, η,λ are the parameters of the inverse Gaussian distribution, respectively represent the expected value and variance value of the parameter values under different stochastic process conditions,

[0015] Furthermore, the resampling of the small-sample individual data through the Bayesian bootstrap method includes the following steps:

[0016] S11. Generate uniformly distributed random numbers in the interval (0, 1) and arrange them in order to obtain the sequence (ξ1, ξ2, …, ξ n-1 ).

[0017] S12. Let ξ0 = 0, ξ n = 1, the weight sequence be w b = (w1 b , w2 b , …, w n b ) and w i b = ξ i - ξ i-1 , (i = 1, 2, …, n), then holds;

[0018] S13. In the nth resampling process, the estimated sample mean and variance are calculated by the following formula:

[0019]

[0020] S14. Repeat the above resampling process l times to obtain the resampling parameter values Obtain the estimated values and confidence intervals of the parameters.

[0021] Further, when the system is described by multiple degradation variables, let X i,k represent the degradation signal value of the ith degradation variable of the system at the kth moment. The system degradation signal is:

[0022]

[0023] Set the marginal cumulative distribution function that a single variable follows as F i (ΔX i,k ). The increment of a single variable at the kth moment, ΔX i,k = ΔX i,k - ΔX i,k-1 . The distribution that the comprehensive degradation amount increment of the system follows is:

[0024] ΔX k (t) = (ΔX 1,k , ΔX 2,k , …, ΔX M,k ) ~ C(F1(ΔX 1,k ), F2(ΔX 2,k ), …, F M (ΔX M,k ); δ)

[0025] where δ is the hyperparameter of the Copula function, and ΔX i,k ~ M(X i , Θi ) and there is:

[0026]

[0027] where, ΔX i,k the k-th increment of the i-th signal, N(μ, σ 2 ) represents a normal distribution, μ is the drift coefficient, σ > 0 represents the diffusion coefficient of the Wiener process; Ga(α, β) represents a Gamma distribution, α is the shape coefficient, β is the scale coefficient; IG(η, λ) represents an inverse Gaussian distribution, η, λ are inverse Gaussian distribution parameters, and Λ(t) is a time function.

[0028] Furthermore, estimating the parameters of different multivariate degradation Copula functions by the maximum likelihood method includes:

[0029] The parameters estimated based on the first k degradation data of the j-th component are:

[0030]

[0031] The likelihood estimation based on all marginal probability density parameters The Copula function parameter estimation of the joint probability density is obtained as follows:

[0032]

[0033] The joint probability density distribution of multiple variables is:

[0034]

[0035] The degradation variable collected from on-site testing is denoted as the i-th degradation variable of the j-th component at the current moment, denoted as ΔXj(i). The collected degradation quantity change values are arranged in chronological order as (x1, x2,... x k ), let the cumulative function be F ad , and the empirical cumulative function be F adn , then the statistic is the distance between the two functions, denoted as:

[0036]

[0037] where, w(x) is the weight function, and the test for discretized degradation quantity increments is expressed as:

[0038]

[0039] Based on the A obtained from the AD test 2Determine the distribution type of the degradation quantity variable based on the value and p-value. According to the above formula, when the distance between the empirical cumulative function and the hypothesized cumulative function is smaller, the goodness of fit of the hypothesized distribution is better, and a single-variable degradation description model is determined.

[0040] Furthermore, the final joint distribution selected based on the AIC criterion includes:

[0041] Based on the results of parameter estimation, the calculation expression of the AIC criterion is:

[0042]

[0043]

[0044] where k represents the number of parameters, and the Copula function with the minimum AIC value is used as the function characterizing the correlation of different degradation variables.

[0045] In the second aspect, the present invention provides a degradation variable fusion life prediction system under small sample conditions, including an initialization module, a degradation description model parameter determination module, a parameter update module, a joint distribution determination module, and a life prediction module;

[0046] The initialization module selects the degradation test signals of key components based on the individual device test information, preprocesses the test information to eliminate invalid values, deletes the header to obtain the degradation variable vectors corresponding to X(t) and X(t) at different stages, and determines the degradation failure threshold value;

[0047] The degradation description model parameter determination module is used to obtain the prior distribution of the parameters of the same type of products of the processed individual devices according to the historical degradation data or prior knowledge of the same type of products, resample the small sample individual data by the Bayesian bootstrap method, obtain the parameter estimation and its corresponding distribution of the selected degradation description model for each component, calculate the degradation description model parameters through the corresponding relationship between the parameter estimation value and the parameters of the stochastic process; convert the obtained degradation description model parameters into the parameters corresponding to different degradation description models respectively, and perform an AD test on the degradation variable vectors of each component obtained based on the parameters corresponding to different stochastic processes, and select the stochastic process closest to the distribution of the degradation variable vector to model the degradation processes of different components;

[0048] The parameter update module is used to update the parameters of each component based on the degradation parameter estimation method of the Bayesian bootstrap method in combination with the newly obtained degradation data of each component;

[0049] The joint distribution determination module estimates the parameters of different multivariate degradation Copula functions by the maximum likelihood method based on the updated parameters, and selects the joint distribution based on the AIC criterion;

[0050] When new test data is added, the life prediction module updates the parameters based on the parameter update module and the joint distribution determination module, and combines the updated parameters and the degradation failure threshold to achieve life prediction under the condition of multiple degradation variables.

[0051] In a third aspect, the present invention can also provide a computer device, including a processor and a memory. The memory is used to store computer-executable programs. The processor reads the computer-executable programs from the memory and executes them. When the processor executes the computer-executable programs, it can implement the method for fusing degradation variable life prediction under small sample conditions of the present invention.

[0052] At the same time, a computer-readable storage medium is provided. A computer program is stored in the computer-readable storage medium. When the computer program is executed by a processor, it can implement the method for fusing degradation variable life prediction under small sample conditions of the present invention.

[0053] Compared with the prior art, the present invention has at least the following beneficial effects: For the problem of function degradation model selection, the present invention respectively conducts test selections on the degradation model and the Copula function selection based on hypothesis testing; the proposed method is verified by multi-variable instance data, and the results show that the multi-degradation variable fusion framework proposed by the present invention provides a more accurate life distribution estimation than a single variable; in view of the characteristics of small samples of complex equipment degradation data, the present invention proposes a degradation parameter estimation under small sample conditions based on Bayesian bootstrap-maximum likelihood. For the problem of description model selection after degradation data is obtained, a multivariate degradation variable description model and a multi-variable fusion function selection method based on the parameter test of degradation variables within the interval time are proposed. Through examples of life prediction under multi-degradation variable fusion, the effectiveness of the proposed multi-variable fusion processing method for equipment is verified.

[0054] Further combining the characteristics of the degradation process of equipment multi-dimensional degradation variable fusion, the description models of three degradation processes, namely Wiener process, Inverse Gaussian process and Gamma process, are analyzed. Based on the Copula function, the state description models under different system structures and multi-degradation variable conditions are analyzed respectively. Description of the Drawings

[0055] Figure 1 For the comparison of parameter estimation between the statistical method and the Bayesian bootstrap method.

[0056] Figure 2 For an implementable process of fusing degradation variable life prediction under small sample conditions.

[0057] Figure 3 For the comparison results of parameter estimation between Bayesian bootstrap and traditional bootstrap methods.

[0058] Figure 4It is the RUL distribution of multi-variable fusion at different working times.

[0059] Figure 5 It is the comparison between the RUL distributions of single variable and multi-variable fusion. Specific implementation mode

[0060] Degradation state description based on Wiener process

[0061] Let X(0) = 0, Λ(t) be a time function, and the Wiener process degradation model is shown in Equation (1):

[0062] X w (t) = μΛ(t) + σB(Λ(t)) (1)

[0063] Among them, μ is the drift coefficient, σ > 0 represents the diffusion coefficient of the Wiener process, B(·) is the standard Brownian motion. Based on the properties of the Wiener process, the degradation increment within the time interval Δt is independent and follows a normal distribution. Therefore, ΔX w (t) ~ N(μΔΛ(t), σ 2 ΔΛ(t)) holds, where the degradation increment ΔX w (t) = X(t + Δt) - X(t), the time increment transformation is expressed as ΔΛ(t) = Λ(t + Δt) - Λ(t). It can be found from the distribution of the degradation increment that the Wiener process model can be used to describe non-monotonic degradation processes. At this time, let the degradation amount failure threshold of the model be D, and the first hitting time (First Hitting Time

[0064] , FHT) is defined as T = inf{t: X(t) ≥ D | x0 < D}, then the cumulative probability distribution of FHT is:

[0065]

[0066] The corresponding marginal probability density function is:

[0067]

[0068] Then the marginal reliability function under the single variable condition is:

[0069]

[0070] Degradation state description based on Gamma process

[0071] The degradation description model based on the gamma (Gamma) process has the property of independent increments in non-overlapping time intervals. The difference from the Wiener process model is that the Gamma process model requires the increments to be non-negative, that is, for any pair of ΔΛ(t), there is ΔXga (t) ≥ 0, so the Gamma process model can only be used to model monotonic degradation processes. According to the properties of the Gamma process model, we have X ga (t) ~ Ga(αΔΛ(t), β), where α represents the shape coefficient, β represents the scale coefficient, and the variable X ga (t) follows a Gamma process, and its cumulative distribution function is shown in Equation (5):

[0072]

[0073] where x > 0, the Gamma function Due to the strictly monotonic property of the Gamma process, the corresponding FHT is defined as T = {t: X ga (t) D | x0 < D}, and based on the same threshold definition, the reliability function based on this process is expressed as:

[0074]

[0075] where:

[0076]

[0077] The corresponding probability density function (PDF) of the FHT is expressed as:

[0078]

[0079] Since it is difficult to solve the above equation, in calculations, an approximate solution of the distribution of the FHT in Equation (9) is generally used:

[0080]

[0081] Degradation state description based on the Inverse Gaussian process

[0082] The degradation description model based on the Inverse Gaussian process has the properties of independent increments and monotonicity, and is used to describe monotonic degradation processes. The degradation quantity described based on this process satisfies the following distribution: X ig (t) ~ IG(ηΛ(t), λΛ(t) 2 ), where IG(·) represents the Inverse Gaussian distribution, η and λ are the parameters of the Inverse Gaussian distribution, and Λ(t) is a time function. The marginal probability density of the Inverse Gaussian process is shown in Equation (10):

[0083]

[0084] Due to the same monotonic characteristics, the Inverse Gaussian process FHT and the Gamma process are defined the same, and the reliability function based on this process is expressed as:

[0085]

[0086] The corresponding PDF of FHT is shown in Equation (12):

[0087]

[0088] where φ(·) represents the probability density function of the standard normal distribution, and Φ(·) represents the cumulative function of the standard normal distribution.

[0089] Copula function

[0090] In existing research, it is usually assumed that the degradation of the system can be characterized by a single variable. When setting two-dimensional variables or multi-variable, it is usually assumed that the variables are independent of each other, or modeled and analyzed based on the degradation model of the same stochastic process. However, in actual situations, due to the highly consistent working hours of each component of the system equipment and the same operating environmental conditions, there is a certain correlation in their degradation processes. In order to evaluate the degradation state of the equipment based on multiple degradation signals and predict the remaining useful life (RUL), in real conditions, there are often multiple random variables with different marginal probability distributions and non-independent of each other in the system. It is difficult to establish a joint probability distribution model for the system. The present invention uses the Copula function to model the integrated degradation process of the equipment.

[0091] Let δ represent the parameter of the Copula function, which is used to measure the strength of the correlation between variables. The definition of the Copula function is as follows:

[0092] C(u1,u2,…,u n |δ)=Pr(U1≤u1,U2≤u2,…,U n ≤u n ) (13)

[0093] where Pr(·) represents the variable distribution probability function. Through the definition of the Copula function, the n-ary Copula function is a function that maps the n-dimensional space to [0,1], and can be used to establish a comprehensive health factor under the degradation of a multi-variable system. According to Sklar's theorem, let (X1,X2,…,X n ) represent the n-dimensional variable describing the system state. When not considering the correlation between variables, the marginal cumulative distribution functions corresponding to each variable are F1,F2,…,F n , then u i =F i (xi ),Let \(H\) be the joint distribution of \(n\)-dimensional variables and \(C\) be an \(n\)-ary Copula function. Then we have:

[0094] \(H(x_1,x_2,\cdots,x\) n ) = \(C(F_1(x_1),F_2(x_2),\cdots,F\) n (x\) n )\(\delta\) (14)

[0095] As can be seen from Equation (14), according to Sklar's theorem, under the condition of multiple variables, the marginal probability distribution of each variable alone and a Copula function can be combined into the joint distribution of the system, so as to realize the separation of the randomness of each variable and the coupling between variables. Let \(F\) i -1 \((i = 1,2,\cdots,n)\) be the inverse function of the marginal probability distribution of the \(i\)-th variable. Then we have \(x\) i = \(F\) i -1 (u\) i ) Based on this, the expression form of the Copula function can be obtained as:

[0096] \(C(u_1,u_2,\cdots,u\) n |\(\delta\)) = \(H(F_1\) -1 (u_1),F_2\) -1 (u_2),\cdots,F\) n -1 (u\) n )) (15)

[0097] The survival function corresponding to the Copula function \(C(u_1,u_2,\cdots,u\) n |\(\delta\)) is defined as follows: There is the following definition:

[0098]

[0099] Among them is the marginal Copula function related to \(i_1,i_2,\cdots,i\) k When the number of variables is 2, based on the above definition, we have Let \(f\) i (x\) i )(i = 1,2,\cdots,n) represent the marginal probability density of the \(i\)-th variable. Then the joint probability density of \(n\)-dimensional variables can be expressed as:

[0100]

[0101] The density of the \(n\)-ary Copula function is:

[0102]

[0103] Furthermore, it can be obtained that:

[0104]

[0105] Multivariate Degradation State Description Model

[0106] When the system is described by multiple degradation variables, let X i,k represent the degradation signal value of the i-th degradation variable of the system at the k-th moment. The system degradation signal can be expressed as:

[0107]

[0108] Set the marginal cumulative distribution function that a single variable follows as F i (ΔX i,k ). The increment ΔX i,k of a single variable at the k-th moment is ΔX i,k -ΔX i,k-1 . The distribution that the increment of the comprehensive degradation amount of the system follows is:

[0109] ΔX k (t) = (ΔX 1,k , ΔX 2,k , …, ΔX M,k ) ∼ C(F1(ΔX 1,k ), F2(ΔX 2,k ), …, F M (ΔX M,k ); δ)(21)

[0110] where δ is the hyperparameter of the Copula function, and ΔX i,k ∼ M(X i , Θ i ), and there is:

[0111]

[0112] Parameter Estimation Method under Small Sample Conditions

[0113] Two-step Parameter Estimation of Copula Function

[0114] In order to obtain the joint probability density function of the system in the present invention, four parts of content need to be determined: the degradation description model of each component, the parameters of the degradation description model, the selection of the Copula function, and the function parameter estimation. The parameters of the system joint probability distribution are represented by a vector. Let Θ = {Θ1, Θ2, …, Θ M , δ} be the parameters of the joint probability distribution. Then the marginal probability distributions of the remaining lifetimes of M components are respectively expressed as f1(ΔX1(t)|Θ1), f2(ΔX2(t)|Θ2), …, f M (ΔX M (t)|ΘM ), the distribution of the remaining useful life of the system is c(ΔX(t)|Θ). Assuming that k degradation data are collected for each degradation description variable at this time, then X(t) is as shown in Equation (20), and the likelihood function of the system RUL can be expressed as:

[0115]

[0116] Maximizing Equation (23) can obtain the maximum likelihood estimate of the hyperparameter Θ:

[0117]

[0118] Analyzing Equation (30), it can be seen that the likelihood function of the remaining useful life of the system consists of two parts: the Copula density function and the marginal probability cumulative distribution and PDF of each component. For a system composed of multiple components, each component has its corresponding marginal probability cumulative distribution and PDF parameters. When there are many components, it is necessary to solve the parameter vector Θ = {Θ1, Θ2, …, Θ M , δ} simultaneously, but it is difficult to solve when there are many components in the system. In addition, since the probability density of the Copula function is composed of the marginal density function and the coupling density function, except for the Copula function in the two parts of the likelihood function, the parameters of the remaining parts are the same, and there is no coupling characteristic in the parameter form of the likelihood function of each component. Therefore, to reduce the computational complexity of the model, the existing research in parameter estimation mainly adopts an approximate estimation method of two-step maximum likelihood. First, estimate the parameters of the marginal probability density of each component, and then based on the results estimated in the first step, regard the estimated parameters as known quantities and further estimate the parameters of the Copula function.

[0119] Degradation Parameter Estimation of Bayesian Bootstrap Method

[0120] First, assume that the prior distribution of the parameters of the jth component is p(Θ j ), and the likelihood function based on the existing data is:

[0121]

[0122] In Equation (25), the likelihood function of the parameters is established through the test data of individual components, and the prior part of the parameters is determined through the test data accumulation of the same components of similar equipment or the prior knowledge in the trial production stage. By transforming the form of the Bayesian posterior, the degradation parameter estimation can be converted into two parts: the prior and the likelihood function. The solution of the likelihood part has been analyzed in Equation (23), so the prior distribution of the corresponding parameters needs to be obtained to estimate the parameters. The parameters of the jth component are represented by Θ jIt is shown that in the present invention, corresponding to three common degradation random processes, the degradation quantity variables respectively follow Gaussian Distribution, Gamma distribution, and Inverse Gaussian distribution, and the expectations and variances of the corresponding degradation quantity variables of each distribution are as shown in Equation (26):

[0123]

[0124] Based on the accurate estimation of the expectations and methods of the degradation quantity variables from historical degradation data, the parameter estimation of the corresponding component random degradation marginal probability distribution can be obtained.

[0125] From a statistical perspective, the obtained degradation quantity monitoring data can be regarded as part of the samples of the overall degradation variables. However, all the degradation samples of the same type of equipment cannot be obtained, and there are cases where some degradation quantities are small samples. The basic idea of the bootstrap method is to use resampling with replacement of the observed values, and estimate the characteristics of the overall distribution through the recombination and information re - fusion of different subsamples. It is a simple and efficient parameter estimation method, which can estimate the parameters more accurately in the case of small samples. The idea of the bootstrap method has been promoted in the integration of weak learners into strong learners in machine learning. Suppose the sample size is n, and the sample observations are represented by x=(x1, x2, …, x n ). When the sample size is small, the probability density distribution of the parameters obtained by using the traditional bootstrap method is not smooth. The reason is the influence of the randomness interference of individual samples in the resampling process caused by the small sample size on the prior estimation of the parameters. The Bayesian bootstrap method can solve this problem. The steps of the Bayesian bootstrap method are as follows:

[0126] Step 1: Generate random numbers uniformly distributed in the interval (0, 1) and arrange them in order, and then the sequence (ξ1, ξ2, …, ξ n-1 ) can be obtained.

[0127] Step 2: Let ξ0 = 0, ξ n = 1, the weight sequence is w b = (w1 b , w2 b , …, w n b ) and there is w i b = ξ i - ξ i-1 , (i = 1, 2, …, n), so holds.

[0128] Step 3: In the n - th resampling process, the estimated sample expectation and variance Calculated by formula (27).

[0129]

[0130] Step 4: Repeat the above resampling process l times to obtain the resampling parameter values And based on this, obtain the estimated value and confidence interval of the parameter.

[0131] Comparison of parameter estimation by general statistical methods and Bayesian bootstrap method Figure 1 As shown, it can be seen that compared with the general statistical method, the Bayesian bootstrap method can obtain more sample parameter values through simulation resampling. When the sample size is small, different sample selection combinations can obtain relatively more parameter information, thus realizing more stable parameter estimation under small sample conditions.

[0132] Based on the estimation of the mean and variance of the sample, further calculate the expected value of the parameter values under different random processes, denoted as Then the parameter estimation of the random process can be obtained based on the moments corresponding to each degradation variable as follows:[[]]

[0133]

[0134] Copula function correlation parameter estimation

[0135] The parameters estimated based on the first k degradation data of the jth component can be expressed as:[[]]

[0136]

[0137] Likelihood estimation based on all marginal probability density parameters The Copula function parameter estimation of the joint probability density can be obtained as shown in formula (30).

[0138]

[0139] At this time, the joint probability density distribution of multiple variables can be updated as:[[]]

[0140]

[0141] Statistically analyze the degradation variable values collected from on-site tests. Denote the ith degradation variable of the jth component at the current moment as ΔX j (i). Arrange the collected degradation variable change values in chronological order. The sorted variables can be expressed as (x1, x2,... x k ), and let the cumulative function be F ad , and the empirical cumulative function be F adn , then the statistic is the distance A between the two functions 2Denoted as:

[0142]

[0143] Where w(x) is the weight function, which is generally taken as w(x)=[F(x)(1-F(x))] -1 , for the test of discretized degradation increment, the above distance is transformed into the form of summation, which can be expressed as:

[0144]

[0145] Based on the A obtained from AD test 2 The value and p-value can determine the distribution type of the degradation variable. From the above formula, it can be concluded that the smaller the distance between the empirical cumulative function and the hypothesized cumulative function, the better the fit of the hypothesized distribution.

[0146] After the single variable degradation description model is determined, based on the same binary degradation variable, the joint probability density distribution presented by selecting different Copula functions is quite different. It is necessary to use a targeted quantitative method to test the applicability of the Copula function for coupling the degradation data and compare them, and then select the optimal function coupling as the joint probability distribution. The present invention uses the Akaike information criterion (AIC) criterion to judge and select the optimal Copula function. Based on the results of parameter estimation, the calculation expression of the AIC criterion is:

[0147]

[0148]

[0149] Where k represents the number of parameters, and the Copula function with the smallest AIC value will be selected as the function that characterizes the correlation between different degradation variables.

[0150] Example 1, the degradation variable fusion life prediction under small sample conditions proposed by the present invention includes the following steps:

[0151] Step 1: Based on the test information of individual equipment, the degradation test signals of key components are selected, and the test information is preprocessed to remove invalid values, and the header is deleted to obtain X(t). The corresponding degradation variable vectors at different stages are expressed as ΔX(t) = (ΔX1, ΔX2, …, ΔX M ) Determine the relevant degradation failure threshold value and set it as D = (D1, D2, ..., D M );

[0152] Step 2: Obtain the prior distribution of the parameters of the same-type products of the individual devices to be processed from the historical degradation data or prior knowledge of the same-type products. Resample the small-sample individual data through the Bayesian bootstrap method to obtain the parameter estimates corresponding to the selected degradation description models of each component. And its corresponding distribution. Calculate the parameters of the degradation description model through the corresponding relationship between the parameter estimation values and the parameters of the stochastic process.

[0153] Step 3: Convert the parameters obtained in Step 2 into the parameters corresponding to different degradation description models according to Equation (28). Conduct an AD test on the degradation variable vectors of each component obtained based on the parameters corresponding to different stochastic processes, and select the stochastic process closest to the distribution of the degradation variable vectors to model the degradation processes of different components.

[0154] Step 4: For the newly obtained degradation data (X 1,k+1 , X 2,k+1 , …, X M,k+1 ) of each component, update the parameters of each component based on the parameter update strategy (2.2).

[0155] Step 5: Based on the updated parameters, estimate the parameters of different multivariate degradation Copula functions through the maximum likelihood method, and select the final joint distribution based on the AIC criterion (Akaike information criterion, AIC).

[0156] Step 6: When new test data is added, repeat Steps 4 - 5 to complete the parameter update, and realize the life prediction under the condition of multivariate degradation variables based on the obtained parameters.

[0157] The framework for joint life prediction of degradation variable fusion based on the multivariate Copula function is as Figure 2 shown.

[0158] Since the test data during the working process accumulates gradually, the estimation of the individual degradation parameters should also be carried out accordingly. Taking the DC voltage degradation rate parameter as an example, the performance of different parameter estimation methods is compared below. The number of resampling times set for the original bootstrap method and the Bayesian bootstrap method is 10,000 times. In the experiment, in order to verify the results of parameter estimation under small-sample conditions, the distribution of the estimated parameters obtained when the number of test data is set to N = 3, 6, 9, 12 respectively is obtained, and the statistical distribution results of the sampling means are as Figure 3As shown, the red intersection points on the horizontal axis in the figure are the degradation rates of the first N intervals calculated from the test data, and the histogram represents the mean frequency calculated after resampling. From the results calculated by resampling in the figure, it can be seen that compared with the traditional statistical method, both bootstrap methods can obtain the uncertainty distribution of parameter estimation. The posterior probability distribution of parameters obtained by the Bayesian bootstrap method under small sample conditions is better than that of the traditional bootstrap method. Especially when the data volume is greater than 6, the evaluation results based on the Bayesian bootstrap method can obtain a relatively smooth distribution, which is more conducive to subsequent parameter estimation. While the traditional bootstrap method can obtain a relatively smooth distribution when the data volume is 12. This is because the Bayesian bootstrap method uses Dirichlet distribution random numbers as weights in the resampling process, while the traditional bootstrap method uses multinomial distribution. For the practical application of the equipment working process, the former can achieve relatively stable parameter estimation in the initial stage of work.

[0159] The same method is used to process the remaining degradation parameters. The resampling expectations, variances of the degradation rates in the degradation description model are calculated, and the degradation model is selected. And the parameters corresponding to the degradation description model are calculated based on Equation (26). When all the test historical data are used, the results of each parameter are shown in Table 1.

[0160] Table 1 Degradation models and parameter estimations of key components for test intervals of individuals

[0161]

[0162] Multivariate degradation variable fusion life prediction

[0163] When predicting the life of the equipment under the condition of multivariate coupling, first, based on each variable and its corresponding failure threshold value, the reliability function and life distribution under the condition of a single variable are obtained. Then, based on the coupling parameter estimation value and Equation (31), the RUL distribution at each moment under the corresponding condition can be obtained. Starting from the data volume of 3 collected (that is, starting from the 12th working cycle of the equipment in this example), the degradation parameters and Copula function parameters are estimated step by step in chronological order, and the remaining life distributions under multivariate coupling at different moments and the corresponding RUL distribution expectations are obtained respectively as Figure 4As shown in the figure, the solid line of the red asterisk in the figure represents the real RUL change process, and the dashed line of the blue circle represents the expectation corresponding to the RUL distribution obtained based on the Copula function. It can be seen that from the beginning of the prediction to the 36th working cycle, there is a certain deviation between the predicted value of the life distribution and the real value. As time goes by, the difference between the predicted value and the real value gradually shrinks. With the accumulation of data, the parameter value estimation of each degradation variable under the multi-degradation variable RUL prediction framework gradually stabilizes, and the accumulation of data volume also makes the fusion parameter estimation between degradation variables more objective. At the 54th working cycle, the remaining life prediction based on a single variable and the remaining life distribution under the coupling condition are as Figure 5 shown. At the 54th working cycle, the times corresponding to the maximum values of the RUL prediction distribution probabilities based on the two degradation signals of the standard current distance and the closing error are 3 working cycles and 4.9 working cycles respectively, while the time corresponding to the RUL distribution based on the Copula function is 2.7 working cycles. Based on this result, it can be seen that the predicted life obtained by the coupling function is lower. In fact, since the test of the equipment is carried out at intervals, according to the historical data, the failure time can be determined to be between the 54th working cycle and the 58th working cycle after work. At this time, the estimation based on the Copula function is in line with the actual situation. It can be seen from the figure that the estimation uncertainty of the RUL distribution based on the framework proposed in the present invention is lower than that of the RUL estimation based on a single signal. Considering the actual situation, since there are multiple monitoring signals, it is difficult to evaluate and select each degradation variable. Using the RUL prediction framework of multi-degradation variable fusion to realize the fusion of multi-signal degradation information is more valuable for realizing the precise guarantee of equipment.

[0164] In summary, the present invention combines the characteristics of the multi-dimensional degradation variable fusion degradation process of the equipment, analyzes the three degradation process description models of the Wiener process, the Inverse Gaussian process, and the Gamma process according to the analysis, and based on the Copula function, analyzes the state description models under different system structures and multi-degradation variable conditions respectively. Aiming at the characteristic that only small samples can be obtained for the degradation data of complex equipment, a degradation parameter estimation under small sample conditions based on Bayesian bootstrap-maximum likelihood is proposed. Aiming at the problem of selecting a description model after obtaining degradation data, a multi-variable degradation variable description model based on the parameter test of degradation variables within the interval time and a multi-variable fusion function selection method are proposed. Finally, through an example of life prediction under the fusion of multi-variable degradation variables, the effectiveness of the proposed multi-variable fusion processing method for equipment is verified.

[0165] Embodiment 2. The present invention can also provide a degradation variable fusion life prediction system under small sample conditions, which is characterized in that it includes an initialization module, a degradation description model parameter determination module, a parameter update module, a joint distribution determination module, and a life prediction module;

[0166] The initialization module selects the degradation test signals of key components based on the individual device test information, preprocesses the test information to eliminate invalid values, deletes the header to obtain the degradation variable vectors corresponding to different stages of X(t) and X(t), and determines the degradation failure threshold value;

[0167] The degradation description model parameter determination module is used to obtain the prior distribution of the parameters of the same type of products of the individual devices to be processed based on the historical degradation data or prior knowledge of the same type of products, resample the small-sample individual data by the Bayesian bootstrap method, obtain the parameter estimates corresponding to the selected degradation description models of each component and their corresponding distributions, and calculate the degradation description model parameters through the corresponding relationship between the parameter estimation values and the parameters of the stochastic process; convert the obtained degradation description model parameters into the parameters corresponding to different degradation description models respectively, and perform the AD test on the degradation variable vectors of each component obtained based on the parameters corresponding to different stochastic processes, and select the stochastic process closest to the distribution of the degradation variable vectors to model the degradation processes of different components;

[0168] The parameter update module is used to update the parameters of each component based on the degradation parameter estimation method of the Bayesian bootstrap method by combining the newly obtained degradation data of each component;

[0169] The joint distribution determination module estimates the parameters of different multivariate degradation Copula functions by the maximum likelihood method based on the updated parameters, and selects the final joint distribution based on the AIC criterion;

[0170] When new test data is added, the remaining life prediction module completes the parameter update based on the parameter update module and the joint distribution determination module, and realizes the remaining life prediction under the condition of multivariate degradation variables based on the obtained parameters.

[0171] On the other hand, the present invention provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the remaining life prediction method for degradation variable fusion under small-sample conditions of the present invention can be realized.

[0172] The computer device may be a laptop computer, a desktop computer or a workstation.

[0173] The present invention can also provide a computer device, including a processor and a memory. The memory is used to store computer-executable programs. The processor reads the computer-executable programs from the memory and executes them. When the processor executes the computer-executable programs, the remaining life prediction method for degradation variable fusion under small-sample conditions of the present invention can be realized.

[0174] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), or a field programmable gate array (FPGA).

[0175] For the memory described in the present invention, it can be an internal storage unit of a laptop, a desktop computer or a workstation, such as a memory or a hard disk; or an external storage unit can also be adopted, such as a mobile hard disk or a flash card.

[0176] The computer-readable storage medium can include a computer storage medium and a communication medium. The computer storage medium includes volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. The computer-readable storage medium can include: read-only memory (ROM), random access memory (RAM), solid state drives (SSD), or optical discs, etc. Among them, the random access memory can include resistive random access memory (ReRAM) and dynamic random access memory (DRAM).

[0177] The above content is only for explaining the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A degradation variable fusion life prediction method under small sample conditions, characterized in that: The following steps are involved: S1, based on the individual equipment test information, select the degradation test signal of the key components, pre-process the test information to remove invalid values, delete the header to obtain X(t) and X(t) corresponding to the degradation variable vectors of different stages, and determine the degradation failure threshold value; S2, obtain the prior distribution of the parameters of similar products of the individual equipment being processed based on the historical degradation data of similar products or prior knowledge, resample the small sample individual data by Bayesian bootstrapping method, obtain the parameter estimation corresponding to the selected degradation description model of each component and its corresponding distribution, and calculate the degradation description model parameters through the corresponding relationship between the parameter estimation value and the random process parameter; S3, converting the degradation description model parameters obtained in S2 into parameters corresponding to different degradation description models, performing AD test on the obtained degradation variable vectors of each component based on the parameters corresponding to different random processes, and selecting the random process closest to the distribution of the degradation variable vector to model the degradation process of different components; S4, combining the newly acquired degradation data of each component, and updating the parameters of each component by using the degradation parameter estimation method based on the Bayesian bootstrap method; S5, based on the updated parameters, the parameters of different multivariate degenerate copula functions are estimated by the maximum likelihood method, and the joint distribution model is selected based on the AIC criterion; S6, when new test data is obtained, S4 and S5 are repeated to complete the parameter update, and life prediction under the condition of multiple degradation variables is realized based on the updated parameters and the degradation failure threshold value.

2. The degradation variable fusion life prediction method under small sample conditions according to claim 1 is characterized in that: The degradation description model is a degradation state description based on a Wiener process, a degradation state description based on a Gamma process, or a degradation state description based on an inverse Gaussian process.

3. The degradation variable fusion life prediction method under small sample conditions according to claim 2 is characterized in that: The degradation description model parameters obtained by S2 are converted into parameters corresponding to different degradation description models according to the following formula: Among them, ΔX is the degradation increment, N(μ,σ 2 ) represents normal distribution, μ is the drift coefficient, σ>0 represents the diffusion coefficient of the Wiener process; Ga(α,β) represents Gamma distribution, α is the shape coefficient, β is the scale coefficient; IG(η,λ) represents inverse Gaussian distribution, η,λ are the inverse Gaussian distribution parameters, They represent the expected parameter value and variance value under different random process conditions respectively.

4. The degradation variable fusion life prediction method under small sample conditions according to claim 1 is characterized in that: Resampling small sample individual data using the Bayesian bootstrap method includes the following steps: S11, generate uniformly distributed random numbers in the interval (0,1) and arrange them in order, thus obtaining the sequence (ξ1,ξ2,…ξ n-1 ). S12, let ξ0=0,ξ n =1, the weight sequence is w b =(w1 b ,w2 b ,…,w n b ) and there is w i b =ξ i -ξ i-1 ,(i=1,2,…,n), then Established; S13, during the nth resampling process, the estimated sample expectation and variance are calculated as follows: S14, repeat the above resampling process l times to obtain the resampling parameter value Obtain parameter estimates and confidence intervals.

5. The degradation variable fusion life prediction method under small sample conditions according to claim 1 is characterized in that: When the system is described by multiple degenerate variables, let X i,k represents the degradation signal value of the i-th degradation variable of the system at the k-th moment. The system degradation signal is: Assume that the marginal cumulative distribution function of a single variable is F i (ΔX i,k ), the increment ΔX of a single variable at the kth moment i,k =ΔX i,k -ΔX i,k-1 , the distribution of the system's comprehensive degradation increment is: ΔX k (t)=(ΔX 1,k ,ΔX 2,k ,…,ΔX M,k )~C(F1(ΔX 1,k ),F2(ΔX 2,k ),…,F M (ΔX M,k );δ) Among them, δ is the hyperparameter of the Copula function, ΔX ik ~M(X i ,Θ i ), and there is: Where ΔX i,k The kth increment of the ith signal, N(μ,σ 2 ) represents normal distribution, μ is the drift coefficient, σ>0 represents the diffusion coefficient of the Wiener process; Ga(α,β) represents Gamma distribution, α is the shape coefficient, β is the scale coefficient; IG(η,λ) represents inverse Gaussian distribution, η, λ are the inverse Gaussian distribution parameters, and Λ(t) is the time function.

6. The degradation variable fusion life prediction method under small sample conditions according to claim 1 is characterized in that: The parameters of different multivariate degenerate Copula functions estimated by maximum likelihood method include: The parameters estimated based on the first k degradation data of the jth component are: Likelihood estimates based on all marginal probability density parameters The Copula function parameter estimates for the joint probability density are as follows: The joint probability density distribution of multiple variables is: The degradation variable collected by the field test is recorded as the i-th degradation variable of the j-th component at the current moment is recorded as ΔX j (i) Arrange the collected degradation change values ​​in chronological order as (x1, x2, … x k ), let the cumulative function be F ad , the experience accumulation function is F adn , then the statistic is the distance between the two functions and is recorded as: Among them, w(x) is the weight function, and the test for the discretized degradation increment is expressed as: Based on the A obtained from AD test 2 The value and p-value determine the distribution type of the degradation variable. The above formula shows that the smaller the distance between the empirical cumulative function and the assumed cumulative function, the better the fit of the assumed distribution, and the single variable degradation description model is determined.

7. The degradation variable fusion life prediction method under small sample conditions according to claim 1 is characterized in that: The final joint distribution selected based on the AIC criterion includes: Based on the results of parameter estimation, the calculation expression of the AIC criterion is: Where k represents the number of parameters, and the Copula function with the smallest AIC value is used as the function to characterize the correlation between different degradation variables.

8. A degradation variable fusion life prediction system under small sample conditions, characterized in that: It includes an initialization module, a degradation description model parameter determination module, a parameter update module, a joint distribution determination module and a life prediction module; The initialization module selects the degradation test signals of key components based on the individual equipment test information, preprocesses the test information to remove invalid values, deletes the header to obtain the degradation variable vectors of X(t) and X(t) corresponding to different stages, and determines the degradation failure threshold value; The degradation description model parameter determination module is used to obtain the prior distribution of the parameters of similar products of the individual equipment being processed based on the historical degradation data of similar products or prior knowledge, resample the small sample individual data through the Bayesian bootstrap method, obtain the parameter estimation corresponding to the selected degradation description model of each component and its corresponding distribution, and calculate the degradation description model parameters through the correspondence between the parameter estimation value and the random process parameter; convert the obtained degradation description model parameters into parameters corresponding to different degradation description models, perform AD test on the obtained degradation variable vectors of each component based on the parameters corresponding to different random processes, and select the random process closest to the distribution of the degradation variable vector to model the degradation process of different components; The parameter updating module is used to update the parameters of each component based on the degradation parameter estimation method of the Bayesian bootstrap method in combination with the new degradation data of each component; The joint distribution determination module estimates the parameters of different multivariate degenerate copula functions based on the updated parameters by the maximum likelihood method, and selects the joint distribution based on the AIC criterion; When new test data is added to the life prediction module, the parameter update is completed based on the parameter update module and the joint distribution determination module, and the life prediction under the conditions of multiple degradation variables is realized by combining the updated parameters and the degradation failure threshold value.

9. A computer device, characterized in that: It includes a processor and a memory, the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and when the processor executes the computer executable program, it can implement the degradation variable fusion life prediction method under small sample conditions as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: A computer program is stored in a computer-readable storage medium. When the computer program is executed by a processor, the degradation variable fusion life prediction method under small sample conditions as described in any one of claims 1 to 7 can be implemented.

Images