Digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling

Abstract

The invention discloses a digital-analog linkage life prediction method based on nonlinear Wi engine process degradation modeling. The digital-analog linkage life prediction method comprises the following steps: selecting features with high association degree with a health state based on a Pearson's correlation coefficient; carrying out normalization and de-noising on the selected features; constructing a comprehensive health index based on multi-feature fusion; carrying out degradation modeling and life prediction on the evolution process of the constructed comprehensive health indexes by adopting a non-linear Wi-ener process; estimating values of degradation model parameters based on maximum likelihood estimation and a Bayesian parameter updating method; and optimizing model parameters, updating a weight coefficient of multi-feature fusion and a failure threshold value of degradation modeling, and obtaining a more accurate life prediction result. The invention provides a digital-analog linkage life prediction method based on nonlinear Wi-er process degradation modeling in order to solve the problems that an existing RUL prediction method based on statistical modeling does not consider the nonlinear degradation condition and feature extraction and degradation modeling links cannot form interactive linkage, so that residual life prediction is not accurate, and provides a digital-analog linkage life prediction method based on nonlinear Wi-er process degradation modeling. And high-precision life prediction and uncertainty quantification of a prediction result are realized.

Description

Technical Field

[0001] The present invention relates to the field of equipment failure prediction and health management in the aerospace and energy manufacturing industries, and in particular to a digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling. Background Art

[0002] Prognostics and Health Management (PHM) technology integrates fault monitoring, diagnosis, prediction, evaluation and maintenance decision-making functions, and can realize fault prediction and maintenance decision-making. Among them, remaining useful life (RUL) prediction, as the core task of PHM, is the link and key to connecting the perception of system operating status and realizing accurate health management based on the operating status.

[0003] Since the performance degradation of equipment is affected by multiple random factors such as the external environment, internal state changes, and working conditions, the RUL prediction results are inevitably uncertain. Therefore, the quantification of prediction uncertainty is the core of the transformation of life prediction from theoretical research to engineering application. Although the RUL prediction methods based on machine learning and deep learning have significant advantages in high-dimensional complex data processing and feature extraction, they have the nature of "black box", poor interpretability, and can only obtain deterministic prediction results. They have inherent deficiencies in uncertainty quantification, which greatly restricts the promotion and application of intelligent prediction algorithms. The RUL degradation model based on the Wiener process can derive its RUL probability distribution, quantify the uncertainty of the prediction results, and has a random non-monotonic independent incremental process. It is a hot topic of research at home and abroad. However, equipment degradation usually presents nonlinear characteristics, especially at the end of life, accelerated degradation often occurs. Therefore, it is necessary to introduce a nonlinear structure into the Wiener degradation model, and consider new degradation model parameter estimation and update methods to improve the RUL prediction effect.

[0004] In addition, the current RUL prediction method based on multi-source data fusion generally treats the two steps of comprehensive health index construction and random process modeling prediction separately, resulting in a poor match between the constructed health index and the degradation model, which seriously affects the accuracy of RUL life prediction. Therefore, studying how to realize the feedback loop of comprehensive health index construction and nonlinear Wiener process degradation modeling and promote the interaction and linkage between the two has become the research focus of achieving high-precision life prediction. Summary of the invention

[0005] The purpose of the present invention is to provide a digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling, so as to solve the above-mentioned problems existing in the prior art.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling includes the following steps:

[0008] S100, select features with high correlation with health status based on Pearson correlation coefficient;

[0009] S200, normalizing and denoising the selected features;

[0010] S300, construction of comprehensive health indicators based on multi-feature fusion;

[0011] S400, using a nonlinear Wiener process to carry out degradation modeling and life prediction for the evolution process of the above-constructed comprehensive health index;

[0012] S500, estimating values ​​of degradation model parameters based on maximum likelihood estimation and Bayesian parameter updating method;

[0013] S600, model parameter optimization, update the weight coefficient of multi-feature fusion and the failure threshold of degradation modeling to obtain more accurate life prediction results.

[0014] Furthermore, the specific method of step S100 is:

[0015] By calculating the Pearson correlation coefficient of each state monitoring parameter, S features are finally determined, namely: feature 1, feature 2, ..., feature S; each feature is represented by F j , where j = 1, 2, ..., S;

[0016] Assume there are N devices in total. For device i, i = 1, 2, ..., N, there are m i The measurement moments are:

[0017] Furthermore, the specific method of step S200 is:

[0018] For feature F of device i j , the characteristic F is measured j The original characteristic sequence of the degenerate state is:

[0019] right Perform minimum-maximum normalization processing to obtain the degradation state feature sequence normalized to [0,1]:

[0020] right The fully integrated empirical mode decomposition and adaptive noise algorithm are used for noise reduction to obtain the normalized and denoised characteristic data of the jth device of the i-th device.

[0021] Furthermore, the specific method of step S300 is:

[0022] Parameter initialization: For S features, set the feature fusion weight coefficient ω 1 ,ω 2 ,...,ω S The initial value of the device failure threshold v is set;

[0023] Feature weighted fusion: for S features Perform weighted fusion to obtain the degradation state of device i

[0024]

[0025] In which, let ω∈R S×1 is the weight coefficient vector, weight coefficient ω j ∈[0,1] represents the proportion of feature j in the data fusion process.

[0026] Furthermore, the specific method of step S400 is:

[0027] The degradation model based on nonlinear Wiener random process can be expressed as:

[0028]

[0029] Among them, x 0 Indicates that the device is at the initial time t 0 The starting point of the degradation; B(t) is the diffusion coefficient σ B Constant standard Brownian motion is used to characterize fluctuations in the time domain and obeys the standard normal distribution N(0,t) with a mean of 0 and a variance of t; μ(t;θ) represents the nonlinear drift coefficient, which reflects the degradation rate of the device. The power function abt is commonly used. b-1 Or it can be expressed as exponential function ab exp{bt}, where θ is the parameter vector of the function; a and b are unknown constant parameters;

[0030] Remaining life prediction:

[0031] The RUL of the equipment at time t is defined as the time when the comprehensive health index curve {X(t), t≥0} first crosses the preset failure threshold v, that is, the remaining life of the equipment T is defined as T=inf{t:X(t)≥v|X(0) <v};

[0032] Using the exponential function form of the drift coefficient μ(t;θ)=abexp(bt), the probability density function of the remaining life is expressed as:

[0033]

[0034] Considering the degradation differences of different devices, the degradation model is reflected by introducing parameters with random properties. The unknown nonlinear drift function parameter θ = (a, b) is used as a random parameter. It is assumed that a follows the normal distribution N (μ a ,σ a 2 ), N represents normal distribution, μ a is the expectation of a, σ a is the standard deviation; b is used to characterize the general characteristics of equipment degradation. Through the following total probability formula, f can be derived T (T) expression.

[0035] For {X(t), t≥0}, if a~N(μ a ,σ a 2 ), b is a fixed value. According to Lemma 1, the PDF of the first arrival time of the degradation model is expressed as:

[0036]

[0037] Among them, f T (T) represents the PDF of the first arrival time at time t, γ(t) and β(t) are intermediate variables, expressed as γ(t)=exp(bt)-1, β(t)=exp(bt)-btexp(bt)-1 respectively.

[0038] Furthermore, the specific method of step S500 is:

[0039] Degradation model parameter estimation based on maximum likelihood estimation:

[0040] When analyzing the nonlinear degradation model, a set of unknown parameter vectors must be determined, denoted as Θ = (μ a ,σ a 2 ,σ B 2 ,b)'; Assume that there are N monitoring data of equipment for degradation modeling, and the i-th equipment is i,1 , t i,2 ,…,t i,mi The degradation data collected at these different measurement time points can be expressed as Rush among them irepresents the number of monitoring data of the i-th device, and the value range of i is 1 to N. Based on the property of the stationary independent increment of the Wiener process, the distribution of degradation data conforms to the multidimensional normal distribution, and its mean and covariance matrix can be determined respectively:

[0041] Mean: μ i =μ a T i , covariance:

[0042] Among them, T i is the first intermediate variable, expressed as T i,j is the second intermediate variable, denoted as T i,j =t b i,j ;Ω i is the third intermediate variable, expressed as Ω i =σ B 2 K i ; K i is the fourth intermediate variable, expressed as

[0043] It is known that the degradation data of N devices is X=(X 1 ,X 2 ,...,X N )', the degradation of different devices is independent of each other, so the unknown parameter of the nonlinear degradation model Θ=(μ a ,σ a 2 ,σ B 2 ,b)''s log-likelihood function is expressed as:

[0044]

[0045] Where l represents the log-likelihood function,

[0046] Find the unknown parameter μ of its log-likelihood function a and σ a The first-order partial derivative of

[0047]

[0048] Let μ a The first-order partial derivative of is 0, and its maximum likelihood estimate is obtained Substituting it into the log-likelihood function expression, we get σ a , σ b and b about The profile likelihood function of is:

[0049]

[0050] Find the σ that maximizes the profile likelihood function a , σ b and b, bring in The expression is: a The maximum likelihood estimate of

[0051] According to the above parameter estimation results, the predicted value of the life of the i-th randomly degraded equipment can be expressed as

[0052]

[0053] Furthermore, the specific method of step S500 also includes:

[0054] Parameter update based on Bayesian formula:

[0055] In nonlinear models, the random variable μ a The value of is often used to update the drift parameter using the Bayesian formula; let the current measurement time be tm, then the corresponding measurement time t 1:m ={t 1 ,t 2 ,...,t m The degenerate data of} is X 1:m ={x 1 ,x 2 ,...,x m}, the Bayesian formula can be used to deduce the drift parameter at a specific monitoring time with known historical measurement data X 1：m Under the condition of μ a The posterior distribution P(μ a ∣X 1:m )for:

[0056]

[0057] Among them, P(μ a ), P(X 1:m ) respectively represent the drift parameter μ a and historical monitoring data X 1:m The probability distribution of P(X 1:m ∣μ a ) indicates that μ is known a Conditions about X 1:m The probability distribution of

[0058] According to the Bayesian formula:

[0059] P(μ a ∣X 1:m )∝P(X 1:m ∣μ a)P(μ a ) (9)

[0060] It can be deduced that:

[0061]

[0062] in, P(x m ∣X 1:m-1 ,μ a ) indicates that when the historical measurement data X is known 1：m-1 and drift parameter μ a Conditions about x m The distribution function of the known historical degradation data is expressed as P(μ a ∣X 1:m-1 );

[0063] The properties of the Wiener process show that given the historical data and the drift parameter, the current degradation data x m The probability distribution of is normal, then P(x m ∣X 1:m-1 ,μ a ) can be expressed as:

[0064]

[0065] in, Δ represents the increment, Δu m represents u(t m ;θ) and u(t m-1 ;θ), namely Δu m =u(t m ;θ)-u(t m-1 ; θ); Δx m Represents x m With x m-1 The difference, Δx m =x m -x m-1 ; Δt m Indicates t m With t m-1 The difference, Δt m =t m -t m-1 ; then the drift parameter μ a In t m The posterior estimate of is expressed as:

[0066]

[0067] It is deduced that:

[0068]

[0069] Furthermore, the specific method of step S600 is:

[0070] Calculate life expectancy By using formula (14), we can solve the optimal weight coefficient ω: 1 ,ω 2 ,...,ω S and failure threshold v

[0071] based on Point estimates of the prediction results obtained for each randomly degraded device Construct the following optimization objective function to represent the prediction results

[0072]

[0073] Where W = {ω 1 ,ω 2 ,…,ω S} is the fusion coefficient vector corresponding to S sensors, and (i) are the predicted life value and the corresponding actual life value respectively; Based on formula (14), the optimal solution can be obtained by minimizing J(W,v)

[0074]

[0075] Through the above solution, the weight coefficients of multi-feature fusion and the failure threshold of degradation modeling are iteratively optimized to achieve digital-analog linkage.

[0076] The beneficial effects of the present invention are as follows: the present invention discloses a digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling, comprising the following steps: selecting features with high correlation with monitoring parameters based on the Pearson correlation coefficient; normalizing and denoising the selected features; constructing indicators with multi-feature fusion; using nonlinear Wiener process to carry out degradation modeling and life prediction on the evolution process of the above-constructed comprehensive health indicators; estimating the values ​​of the degradation model parameters based on maximum likelihood estimation and Bayesian parameter updating method; optimizing model parameters to obtain more accurate life prediction results. In response to the urgent need for accurate remaining life prediction and quantification of its uncertainty, the present invention proposes a remaining life prediction method based on digital-analog linkage, realizes the interactive linkage and feedback loop between the construction of comprehensive health indicators and nonlinear random degradation modeling, and guides predictive maintenance, optimization of task planning, and resource allocation decisions. The main contributions are as follows:

[0077] (1) Aiming at the problem that machine learning / deep learning methods are difficult to quantify the uncertainty of life prediction, a degradation modeling and RUL prediction method based on nonlinear Wiener process is proposed, and the MLE and Bayesian methods are used to dynamically update the model parameters to achieve the uncertainty quantification of the prediction results.

[0078] (2) In order to address the current problems of isolated construction of comprehensive health indicators based on multi-source data fusion and nonlinear Wiener process degradation modeling, a digital-analog coupled RUL prediction method is proposed to achieve highly accurate remaining life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flow chart of a digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling of the present invention;

[0080] Figure 2 It is the overall technical line diagram of the present invention;

[0081] Figure 3 It is a curve diagram showing the time taken for the voltage to drop to the cut-off voltage during the discharge process of the present invention as a function of the number of charge and discharge cycles;

[0082] Figure 4 It is a curve diagram showing the change of the discharge time of the current in the discharge process of the present invention at a constant current of 2A with the number of charge and discharge cycles;

[0083] Figure 5 It is a curve showing the time of reaching the highest temperature during the discharge process of the present invention as a function of the number of charge and discharge cycles;

[0084] Figure 6 is a minimum-maximum normalized characteristic curve diagram of the present invention;

[0085] Figure 7 It is a normalized constant current discharge time curve noise reduction diagram of the present invention;

[0086] Figure 8 It is a noise reduction graph of the normalized discharge time curve to the cut-off discharge time of the present invention;

[0087] Fig. 9 It is a normalized maximum temperature time curve noise reduction graph of the present invention;

[0088] Fig.10 It is the updated value of each parameter at each stage of the present invention;

[0089] Fig.11 This is a life prediction result diagram based on the nonlinear Wiener process of the present invention. DETAILED DESCRIPTION

[0090] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation methods described herein are only used to explain the present invention and are not used to limit the present invention.

[0091] Reference Figures 1 to 11 A digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling is shown, comprising the following steps:

[0092] S100, select features with high correlation with health status based on Pearson correlation coefficient;

[0093] S200, normalizing and denoising the selected features;

[0094] S300, construction of comprehensive health indicators based on multi-feature fusion;

[0095] S400, using a nonlinear Wiener process to carry out degradation modeling and life prediction for the evolution process of the above-constructed comprehensive health index;

[0096] S500, estimating values ​​of degradation model parameters based on maximum likelihood estimation and Bayesian parameter updating method;

[0097] S600, model parameter optimization, update the weight coefficient of multi-feature fusion and the failure threshold of degradation modeling to obtain more accurate life prediction results.

[0098] In this embodiment, the "number" in the digital-model linkage refers to the comprehensive health index constructed by multi-source data fusion based on the weight coefficient, the "model" refers to the random degradation modeling of the time-varying evolution process of the constructed comprehensive health index, and the "linkage" refers to the construction of an objective function with minimizing the difference between the actual value and the predicted value as the core. By reversely optimizing the adjustment of the fusion coefficient in the comprehensive health index construction stage and the model parameters in the degradation modeling stage, the interactive linkage between the comprehensive health index construction and the degradation modeling is realized.

[0099] The overall technical solution is as follows Figure 2 As shown in the figure. First, the degradation characteristics are extracted based on the multidimensional condition monitoring data, and a one-dimensional comprehensive health index is constructed using a weighted strategy. Subsequently, the time-varying evolution trend of the comprehensive health index is modeled using a nonlinear Wiener process, and the model parameters are estimated using maximum likelihood estimation and Bayesian updating to achieve a preliminary prediction of RUL. Finally, based on the idea of ​​digital-analog linkage, an optimization objective function is constructed to minimize the deviation between the predicted life span and the actual life span, so as to reversely adjust the fusion weight of the comprehensive index construction link and the model parameters of the degradation modeling and prediction link to achieve the final prediction of RUL.

[0100] Furthermore, the specific method of step S100 is:

[0101] By calculating the Pearson correlation coefficient of each state monitoring parameter, S features are finally determined, namely: feature 1, feature 2, ..., feature S; each feature is represented by F j , where j = 1, 2, ..., S;

[0102] Assume there are N devices in total. For device i, i = 1, 2, ..., N, there are m i The measurement moments are: The Pearson correlation coefficient method is selected as the feature selection strategy, which aims to select features with high correlation by evaluating the correlation between individual features and key parameters O such as performance and lifespan.

[0103] Furthermore, the specific method of step S200 is:

[0104] For feature F of device i j , the characteristic F is measured j The original characteristic sequence of the degenerate state is:

[0105] Considering the differences in the dimensions and magnitudes of the parameters monitored by different sensors, Perform minimum-maximum normalization processing to obtain the degradation state feature sequence normalized to [0,1]:

[0106] right The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm is used for noise reduction to obtain the normalized and denoised feature data of the jth device of the i-th device.

[0107] Furthermore, the specific method of step S300 is:

[0108] Parameter initialization: For S features, set the feature fusion weight coefficient ω 1 ,ω 2 ,...,ω S The initial value of the device failure threshold v is set;

[0109] Feature weighted fusion: for S features By performing weighted fusion, we can obtain a one-dimensional comprehensive health indicator sequence that represents the time-varying trend of the degradation state of equipment i: in

[0110]

[0111] In the formula, let ω∈R S×1 is the weight coefficient vector, weight coefficient ω j ∈[0,1] represents the proportion of feature j in the data fusion process.

[0112] To simplify the derivation process, the following degradation modeling method is applicable to all devices, so the parameter i representing the device number is omitted, and the comprehensive health index constructed above is rewritten as X(t) = {x 1 ,x 2 ,...,x m}, the next step is to explain the establishment of a certain equipment degradation model.

[0113] Considering that the degradation mechanism of equipment in practical applications is relatively complex and often exhibits nonlinear characteristics, the nonlinear Wiener process is used to carry out degradation modeling and life prediction for the evolution process of the comprehensive health index constructed above.

[0114] Furthermore, the specific method of step S400 is:

[0115] For the above comprehensive health indicator sequence of a certain equipment, the degradation model based on nonlinear Wiener random process can be expressed as:

[0116]

[0117] Among them, x 0 Indicates that the device is at the initial time t 0 The starting point of the degradation; B(t) is the diffusion coefficient σ B Constant standard Brownian motion is used to characterize fluctuations in the time domain and obeys the standard normal distribution N(0,t) with a mean of 0 and a variance of t; μ(t;θ) represents the nonlinear drift coefficient, which reflects the degradation rate of the device. The power function abt is commonly used. b-1 Or it can be represented by the exponential function abexp{bt}, where θ is the parameter vector of the function; a and b are unknown constant parameters.

[0118] Remaining life prediction:

[0119] The RUL of the equipment at time t is defined as the time when the comprehensive health index curve {X(t), t≥0} first crosses the preset failure threshold v (first arrival time), that is, the remaining life of the equipment T is defined as T=inf{t:X(t)≥v|X(0) <v};

[0120] Using the exponential function form of the drift coefficient μ(t;θ) = abexp(bt), the probability density function (PDF) of the remaining life is expressed as:

[0121]

[0122] Considering the degradation differences of different devices, the degradation model is reflected by introducing parameters with random properties. The unknown nonlinear drift function parameter θ = (a, b) is used as a random parameter. It is assumed that a follows the normal distribution N (μ a ,σ a 2 ), N represents normal distribution, μ a is the expectation of a, σ a is the standard deviation; b is used to characterize the general characteristics of equipment degradation. Through the following total probability formula, f can be derived T (T) expression.

[0123] Lemma 1: If X~N(μ,σ 2 ), and v,A,B∈R,C∈R + , R is the set of real numbers, R+ is the set of positive real numbers, v, A, B, C represent any algebraic expression that meets the conditions, then

[0124]

[0125] For {X(t), t≥0}, if a~N(μ a ,σ a 2 ), b is a fixed value. According to Lemma 1, the PDF of the first arrival time of the degradation model is expressed as:

[0126]

[0127] Among them, f T (T) represents the PDF of the first arrival time at time t, γ(t) and β(t) are intermediate variables, expressed as γ(t)=exp(bt)-1, β(t)=exp(bt)-btexp(bt)-1 respectively.

[0128] Degradation model parameter estimation: Based on maximum likelihood estimation and Bayesian parameter updating method, μ is estimated a ,σ a 2 ,σ B 2 , the value of b;

[0129] Furthermore, the specific method of step S500 is:

[0130] Degradation model parameter estimation based on maximum likelihood estimation:

[0131] When analyzing the nonlinear degradation model, a set of unknown parameter vectors must be determined, denoted as Θ = (μ a ,σ a 2 ,σ B2 ,b)'; Assume that there are N monitoring data of equipment for degradation modeling, and the i-th equipment is i ,1,t i The degradation data collected at these different measurement time points can be expressed as Where mi represents the number of monitoring data of the i-th device, and the value range of i is 1 to N; based on the property of stable independent increments of the Wiener process, the distribution of degradation data conforms to the multidimensional normal distribution, and its mean and covariance matrix can be determined respectively:

[0132] Mean: μ i =μ a T i , covariance: ∑ i =Ω i +σ a 2 T i T i '

[0133] Among them, T i is the first intermediate variable, expressed as T i,j is the second intermediate variable, denoted as T i,j =t b i,j ;Ω i is the third intermediate variable, expressed as Ω i =σ B 2 K i ; K i is the fourth intermediate variable, expressed as

[0134] It is known that the degradation data of N devices is X=(X 1 ,X 2 ,...,X N )', the degradation of different devices is independent of each other, so the unknown parameter of the nonlinear degradation model Θ=(μ a ,σ a 2 ,σ B 2 ,b)''s log-likelihood function is expressed as:

[0135]

[0136] Where l represents the log-likelihood function,

[0137] Find the unknown parameter μ of its log-likelihood function a and σ a The first-order partial derivative of

[0138]

[0139] Let μ a The first-order partial derivative of is 0, and its maximum likelihood estimate is obtained Substituting it into the log-likelihood function expression, we get σ a , σ b and b about The profile likelihood function of is:

[0140]

[0141] Find the σ that maximizes the profile likelihood function a , σ b and b, bring in The expression is: a The maximum likelihood estimate of

[0142] According to the above parameter estimation results, the predicted value (point estimate) of the life of the i-th randomly degraded equipment can be expressed as

[0143]

[0144] Furthermore, the specific method of step S500 also includes:

[0145] Parameter update based on Bayesian formula:

[0146] In nonlinear models, the random variable μ a The value of is often used to update the drift parameter using the Bayesian formula; let the current measurement time be tm, then the corresponding measurement time t 1:m ={t 1 ,t 2 ,...,t m The degenerate data of} is X 1:m ={x 1 ,x 2 ,...,x m}, the Bayesian formula can be used to deduce the drift parameter at a specific monitoring time with known historical measurement data X 1：m Under the condition of μ a The posterior distribution P(μ a ∣X 1:m )for:

[0147]

[0148] Among them, P(μ a ), P(X 1:m ) respectively represent the drift parameter μ a and historical monitoring data X1:m The probability distribution of P(X 1:m ∣μ a ) indicates that μ is known a Conditions about X 1:m The probability distribution of .

[0149] According to the Bayesian formula:

[0150] P(μ a ∣X 1:m )∝P(X 1:m ∣μ a )P(μ a ) (10)

[0151] It can be deduced that:

[0152]

[0153] in, P(x m ∣X 1:m-1 ,μ a ) indicates that when the historical measurement data X is known 1：m-1 and drift parameter μ a Conditions about x m The distribution function of the known historical degradation data is expressed as P(μ a ∣X 1:m-1 );

[0154] The properties of the Wiener process show that given the historical data and the drift parameter, the current degradation data x m The probability distribution of is normal, then P(x m ∣X 1:m-1 ,μ a ) can be expressed as:

[0155]

[0156] in, Δ represents the increment, Δu m represents u(t m ;θ) and u(t m-1 ;θ), namely Δu m =u(t m ;θ)-u(t m-1 ; θ); Δx m Represents x m With x m-1 The difference, Δx m =x m -x m-1 ; Δt m Indicates t m With tm-1 The difference, Δt m =t m -t m-1 ; then the drift parameter μ a In t m The posterior estimate of is expressed as:

[0157]

[0158] It is deduced that:

[0159]

[0160] Furthermore, the specific method of step S600 is:

[0161] Calculate life expectancy By using formula (14), we can solve the optimal weight coefficient ω: 1 ,ω 2 ,...,ω S and failure threshold v

[0162] based on Point estimates of the prediction results obtained for each randomly degraded device Construct the following optimization objective function to represent the prediction results

[0163]

[0164] Where W = {ω 1 ,ω 2 ,…,ω S} is the fusion coefficient vector corresponding to S sensors, and (i) are the predicted life value and the corresponding actual life value respectively; Based on formula (15), the optimal solution can be obtained by minimizing J(W,v)

[0165]

[0166] Through the above solution, the weights of multi-feature fusion and the failure threshold of degradation modeling are iteratively optimized to achieve digital-analog linkage.

[0167] Example

[0168] The method of the present invention is verified using the lithium battery data set of NASA Prognostic Center of Excellence (PCoE). Taking B0005 battery as an example, relevant parameters are extracted from the battery discharge cycle process as health features.

[0169] (1) Health characteristics based on voltage

[0170] Through data visualization analysis, it is found that as the charge and discharge cycles increase, the battery discharge voltage versus time curve moves to the left, the discharge time is shortened, and the battery degrades. The time for the voltage to drop to the cut-off voltage in the discharge cycle is defined as t cv , t cv ={t cv0 ,t cv1 ,...t cvm}. Among them, m is the number of charge and discharge cycles, and the time it takes for the voltage to drop to the cut-off voltage in the i-th charge and discharge cycle is t cvi The curve of this characteristic changing with the number of charge and discharge cycles is as follows Figure 3 shown.

[0171] (2) Health characteristics based on current

[0172] The time for the battery to discharge at a constant current of 2A becomes shorter as the number of charge and discharge cycles increases. During the discharge process, the time for the battery to discharge at a constant current of 2A is defined as t cc , t cc ={t cc0 ,t cc1 ,...t ccm}, where m is the number of charge and discharge cycles, and during the i-th discharge process, the current is discharged at a constant current of 2A for a time t cci The curve of this characteristic changing with the number of charge and discharge cycles is as follows Figure 4 shown.

[0173] (3) Health characteristics based on temperature

[0174] The discharge temperature curve moves to the left as the charge and discharge cycles increase, and the time to reach the highest temperature during the discharge process becomes shorter, indicating that the internal resistance of the lithium battery continues to increase as it degrades. During the discharge process, the time to reach the highest temperature is defined as t mt , t mt ={t mt0 ,t mt1 ,...t mtm}, where m is the number of charge and discharge cycles, and the time to reach the highest temperature during the i-th discharge process is t mti The curve of this characteristic changing with the number of charge and discharge cycles is as follows Figure 5 shown.

[0175] Based on the above health characteristics, correlation coefficient analysis was used for feature selection, and Pearson correlation coefficient was calculated for exploration.

[0176] like Figure 6 Three health characteristics cvi ,t cc , and t mt Pearson correlation coefficient analysis results between tcvi ,t cc , and t mt The correlation coefficient values ​​with capacity are 0.9924, 0.9999, and 0.9998, respectively, all close to 1, indicating that there is a strong positive correlation between these three characteristics and capacity.

[0177] All three features are used for subsequent predictions. Max-MinNormalization is performed on the three features and capacity. The results after processing are as follows: Figure 6 shown.

[0178] Since the battery degradation experiment involves static operation and capacity self-recovery, there are points where the capacity degradation trajectory and the characteristic trajectory jump upward. Therefore, the CEEMDAN algorithm is used to reduce the noise of the characteristic trajectory. The results after processing are as follows: Figure 7 , Figure 8 and Fig. 9 shown.

[0179] By analyzing the degradation data of four lithium batteries B0005, B0006, B0007, and B0018, it can be inferred that there are significant differences between the degraded individuals, so this individual difference is represented by setting random parameters. The unknown nonlinear drift function parameter θ=(a,b) a is used as a random parameter, the above nonlinear model is used to model and solve the parameters, the maximum likelihood estimation method is used to estimate the parameters, and the Bayesian method is used to implement the parameter update. Matllab is used to implement the above process. The parameter values ​​at each stage are as follows Fig.10 As shown, the horizontal axis is the Bayesian update stage.

[0180] Use the required parameters to predict RUL, and the prediction results are as follows: Fig.11 As shown in the figure, a monitoring point is set every 5 cycles, the pink box represents the actual life, and the red cross represents the predicted life. It can be seen from the figure that the cross is close to the box, and the predicted probability density curve can well cover the real life, indicating the effectiveness of nonlinear Wiener process degradation modeling for RUL prediction.

[0181] Taking the B0005 battery as an example, the optimal weight is obtained after digital-analog linkage: i =[0.49873, 0.25114, 0.25013], i = 1, 2, 3. As shown in Table 1, the mean square error MSE of RUL prediction after digital-analog linkage solution is 109.411, which indicates the average difference between the predicted Wiener process curve and the validation data set in the original data. The mean square error is low, indicating that the model performs well on the validation set, and the estimated Wiener process curve is consistent with the change trend of the actual data.

[0182] Table 1 Wiener process life prediction results and errors under digital-analog linkage

[0183]

[0184] Compared with the RUL prediction of comprehensive health indicators with equal weight fusion, as shown in Table 2, the MSE and MAE of the RUL prediction method under digital-analog linkage are smaller, indicating that the prediction error under the digital-analog linkage method is smaller, which is better than the RUL prediction of comprehensive health indicators with equal weight fusion.

[0185] Table 2 Comparison of prediction results errors under equal weight fusion and digital-analog linkage

[0186]

[0187] By adopting the above technical solution disclosed in the present invention, the following beneficial effects are obtained:

[0188] In response to the urgent need for accurate remaining life prediction and uncertainty quantification, this paper proposes a remaining life prediction method based on digital-analog linkage, realizes the interactive linkage and feedback loop of comprehensive health index construction and nonlinear random degradation modeling, and guides predictive maintenance, optimization task planning and resource allocation decision-making. The main contributions are as follows:

[0189] (1) Aiming at the problem that intelligent life prediction methods based on machine learning and deep learning are difficult to quantify uncertainty, a nonlinear Wiener process degradation modeling and RUL prediction method is proposed, and the MLE and Bayesian methods are used to dynamically update the model parameters to achieve uncertainty quantification of the prediction results.

[0190] (2) In order to address the current problems of isolated construction of comprehensive health indicators based on multi-source data fusion and random process degradation modeling, a RUL prediction method combining digital and analog linkage is proposed to achieve highly accurate remaining life prediction.

[0191] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be considered as the scope of protection of the present invention.

Claims

1. A digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling, characterized in that: The following steps are involved: S100, select features with high correlation with health status based on Pearson correlation coefficient; S200, normalizing and denoising the selected features; S300, construction of comprehensive health indicators based on multi-feature fusion; S400, using a nonlinear Wiener process to carry out degradation modeling and life prediction for the evolution process of the above-constructed comprehensive health index; S500, estimating values ​​of degradation model parameters based on maximum likelihood estimation and Bayesian parameter updating method; S600, model parameter optimization, update the weight coefficient of multi-feature fusion and the failure threshold of degradation modeling to obtain more accurate life prediction results.

2. The digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling according to claim 1 is characterized in that: The specific method of step S100 is: By calculating the Pearson correlation coefficient of each state monitoring parameter, S features are finally determined, namely: feature 1, feature 2, ..., feature S; each feature is represented by F j , where j = 1, 2, ..., S; Assume there are N devices in total. For device i, i = 1, 2, ..., N, there are m i The measurement moments are:

3. The digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling according to claim 2 is characterized in that: The specific method of step S200 is: For feature F of device i j , the characteristic F is measured j The original characteristic sequence of the degenerate state is: right Perform minimum-maximum normalization processing to obtain the degradation state feature sequence normalized to [0,1]: right The fully integrated empirical mode decomposition and adaptive noise algorithm are used for noise reduction to obtain the normalized and denoised characteristic data of the jth device of the i-th device.

4. The digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling according to claim 3 is characterized in that: The specific method of step S300 is: Parameter initialization: For S features, set the feature fusion weight coefficients ω1, ω2, ..., ω S The initial value of the device failure threshold v is set; Feature weighted fusion: for S features By performing weighted fusion, we can obtain a one-dimensional comprehensive health indicator sequence that represents the time-varying trend of the degradation state of equipment i: In which, let ω∈R S×1 is the weight coefficient vector, weight coefficient ω j ∈[0,1] represents the proportion of feature j in the data fusion process.

5. The digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling according to claim 4 is characterized in that: The specific method of step S400 is: The degradation model based on nonlinear Wiener random process can be expressed as: Where x0 represents the starting point of the degradation of the device at the initial time t0; B(t) is the diffusion coefficient σ B Constant standard Brownian motion is used to characterize fluctuations in the time domain and obeys the standard normal distribution N(0,t) with a mean of 0 and a variance of t; μ(t;θ) represents the nonlinear drift coefficient, which reflects the degradation rate of the device. The power function abt is commonly used. b-1 Or it can be expressed as an exponential function abexp{bt}, where θ is the parameter vector of the function; a and b are unknown constant parameters; Life expectancy prediction: The RUL of the equipment at time t is defined as the time when the comprehensive health index curve {X(t), t≥0} first crosses the preset failure threshold v, that is, the remaining life of the equipment T is defined as T=inf{t:X(t)≥v|X(0) <v}; Using the exponential function form of the drift coefficient μ(t;θ)=abexp(bt), the probability density function of the remaining life is expressed as: Considering the degradation differences of different devices, the degradation model is reflected by introducing parameters with random properties. The unknown nonlinear drift function parameter θ = (a, b) is used as a random parameter. It is assumed that a follows the normal distribution N (μ a ,σ a 2 ), N represents normal distribution, μ a is the expectation of a, σ a is the standard deviation; b is used to characterize the general characteristics of equipment degradation. Through the following total probability formula, f can be derived T (T) expression; For {X(t), t≥0}, if a~N(μ a ,σ a 2 ), b is a fixed value. According to Lemma 1, the PDF of the first arrival time of the degradation model is expressed as: Among them, f T (T) represents the PDF of the first arrival time at time t, γ(t) and β(t) are intermediate variables, expressed as γ(t)=exp(bt)-1, β(t)=exp(bt)-btexp(bt)-1 respectively.

6. The digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling according to claim 5 is characterized in that: The specific method of step S500 is: Degradation model parameter estimation based on maximum likelihood estimation: When analyzing the nonlinear degradation model, a set of unknown parameter vectors must be determined, denoted as Θ = (μ a ,σ a 2 ,σ B 2 ,b)'; Assume that there are N monitoring data of equipment for degradation modeling, and the i-th equipment is i,1 , t i,2 ,…,t i,mi The degradation data collected at these different measurement time points can be expressed as Where m i represents the number of monitoring data of the i-th device, and the value range of i is 1 to N. Based on the property of the stationary independent increment of the Wiener process, the distribution of degradation data conforms to the multidimensional normal distribution, and its mean and covariance matrix can be determined respectively: Mean: μ i =μ a T i , covariance: ∑ i =Ω i +σ a 2 T i T i ' Among them, T i is the first intermediate variable, expressed as T i,j is the second intermediate variable, denoted as T i,j =t b i,j ;Ω i is the third intermediate variable, expressed as Ω i =σ B 2 K i ; K i is the fourth intermediate variable, expressed as It is known that the degradation data of N devices is X=(X1,X2,...,X N )', the degradation of different devices is independent of each other, so the unknown parameter of the nonlinear degradation model Θ=(μ a ,σ a 2 ,σ B 2 ,b)''s log-likelihood function is expressed as: Where l represents the log-likelihood function, Find the unknown parameter μ of its log-likelihood function a and σ a The first-order partial derivative of Let μ a The first-order partial derivative of is 0, and its maximum likelihood estimate is obtained Substituting it into the log-likelihood function expression, we get σ a , σ b and b about The profile likelihood function of is: Find the σ that maximizes the profile likelihood function a , σ b and b, bring in The expression is: a The maximum likelihood estimate of According to the above parameter estimation results, the predicted value of the life of the i-th randomly degraded equipment can be expressed as:

7. The digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling according to claim 6 is characterized in that: The specific method of step S500 also includes: Parameter update based on Bayesian formula: In nonlinear models, the random variable μ a The value of is often used to update the drift parameter using the Bayesian formula; let the current measurement time be tm, then the corresponding measurement time t 1:m ={t1,t2,...,t m The degenerate data of} is X 1:m ={x1,x2,...,x m }, the Bayesian formula can be used to deduce the drift parameter at a specific monitoring time with known historical measurement data X 1：m Under the condition of μ a The posterior distribution P(μ a ∣X 1:m )for: Among them, P(μ a ), P(X 1:m ) respectively represent the drift parameter μ a and historical monitoring data X 1:m The probability distribution of P(X 1:m ∣μ a ) indicates that μ is known a Conditions about X 1:m The probability distribution of According to the Bayesian formula: P(μ a ∣X 1:m )∝P(X 1:m ∣μ a )P(μ a ) (10) It can be deduced that: in, P(x m ∣X 1:m-1 ,μ a ) indicates that when the historical measurement data X is known 1：m-1 and drift parameter μ a Conditions about x m The distribution function of the known historical degradation data is expressed as P(μ a ∣X 1:m-1 ); The properties of the Wiener process show that given the historical data and the drift parameter, the current degradation data x m The probability distribution of is normal, then P(x m ∣X 1:m-1 ,μ a ) can be expressed as: in, Δ represents the increment, Δu m represents u(t m ;θ) and u(t m-1 ;θ), namely Δu m =u(t m ;θ)-u(t m-1 ;θ);Δx m Represents x m With x m-1 The difference, Δx m =x m -x m-1 ; Δt m Indicates t m With t m-1 The difference, Δt m =t m -t m-1 ; then the drift parameter μ a In t m The posterior estimate of is expressed as: It is deduced that:

8. The digital-analog linkage life prediction method based on nonlinear Wiener process degradation modeling according to claim 7 is characterized in that: The specific method of step S600 is: Calculate life expectancy By using formula (15), we can solve the optimal weight coefficients ω1, ω2, ..., ω S and the failure threshold v is based on Point estimates of the prediction results obtained for each randomly degraded device Construct the following optimization objective function to represent the prediction results Where W = {ω1,ω2,…,ω S } is the fusion coefficient vector corresponding to S sensors, and (i) are the predicted life value and the corresponding actual life value respectively; Based on formula (15), the optimal solution can be obtained by minimizing J(W,v) Through the above solution, the weight coefficients of multi-feature fusion and the failure threshold of degradation modeling are iteratively optimized to achieve digital-analog linkage.

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