A mechanism equivalent driving degradation stage identification and change point detection method

Abstract

The application discloses a mechanism-equivalent-driven degradation stage identification and change point detection method, belongs to the technical field of product performance degradation modeling and life prediction, and comprises the following steps: S1, product degradation data preprocessing and degradation interval division; S2, calculation of a mechanism-equivalent factor of each degradation interval; S3, construction of a hypothesis test sample, and normality test on the sample; S4, variance and mean equivalence test; and S5, determination of a failure mechanism change point and degradation stage identification. The mechanism-equivalent-driven degradation stage identification and change point detection method provided by the application is based on the mechanism-equivalent degradation modeling theory, a Tweedie exponential diffusion process (TEDP process) is used to model a product degradation process, and the accuracy and reliability of degradation stage identification and change point detection are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of product performance degradation modeling and life prediction, and in particular to a mechanism-equivalent-driven degradation phase identification and change point detection method. BACKGROUND

[0002] A product often has many failure modes, and for each failure mode, there is a specific failure mechanism corresponding to it. Because the product may be at different stress levels when working, if the failure mechanism of the product changes in the process, the failure process of the product will also change accordingly. When using the degradation amount of the product to carry out fault diagnosis and life prediction, in order to ensure that the inference is effective, it is necessary to ensure that the failure mechanism of the product is stable, otherwise, the conclusion obtained by extrapolation cannot accurately reflect the reliability performance of the product.

[0003] In recent years, product degradation modeling based on stochastic processes has been widely studied to deeply analyze the laws of mechanical components in performance degradation. Most of the research focuses on three processes: Wiener process, Gamma process and inverse Gaussian process. However, in some engineering applications, these three models may not be suitable and have certain limitations. In addition, if the true model is not among the above three candidate models, the reliability analysis results based on these models may be poor. Therefore, in order to more accurately describe the true degradation process, a more general degradation model is needed. The TEDP process contains the most commonly used Wiener process, Gamma process and inverse Gaussian process as its special cases, has superior universality, and has attracted widespread attention in the field of product performance degradation modeling. Compared with other models, TEDP can more flexibly describe the degradation process and improve the accuracy of reliability analysis.

[0004] Based on this, the present application proposes a mechanism-equivalent-driven degradation phase identification and change point detection method, which uses a highly universal degradation model to accurately model the degradation data of the product, and combines a mechanism-equivalent condition inspection process to give a degradation mechanism change point detection and degradation phase identification method of the product. SUMMARY

[0005] The purpose of the present application is to provide a mechanism-equivalent-driven degradation phase identification and change point detection method to solve the problems of unclear failure mechanism, weak model universality and low life prediction accuracy of the traditional product performance degradation modeling and life prediction method in the background art.

[0006] To achieve the above purpose, the present application provides a mechanism-equivalent-driven degradation phase identification and change point detection method based on the following basic settings:

[0007] Setting 1: the signal collected by the sensor can reflect the degradation amount of the product, and the degradation amount is affected by the degradation mechanism.

[0008] Setting 2: the products under each degradation interval belong to the same batch, and the elements in the mechanism equivalence factor vector sample of each degradation interval come from the same distribution population. And it is assumed that different elements are independent of each other, and there is no correlation between different distribution populations.

[0009] Comprising the following steps:

[0010] S1, product degradation data preprocessing and degradation interval division;

[0011] S2, calculating the mechanism equivalence factor of each degradation interval;

[0012] S3, constructing a hypothesis test sample and performing normality test on the sample;

[0013] S4, performing variance and mean equivalence test;

[0014] S5, determining the failure mechanism change point and degradation stage identification.

[0015] Preferably, step S1 specifically comprises:

[0016] Suppose n products are collected and divided into k degradation intervals according to time sequence, each degradation interval is measured c times, h = 1, 2, …, c; the degradation interval is denoted as i, i = 1, 2, …, k, the product serial number is denoted as j, j = 1, 2, …, n, the historical monitoring time and the corresponding degradation path are denoted as T 0→x ={t0,t1,…,t x} and Y 0→x ={y0,y1,…,y x}, wherein t xi represents the start or end time of each degradation interval, y xi =Y(t xi );

[0017] In order to ensure that the data used in subsequent modeling calculation can be effectively used, the data needs to be preprocessed to ensure that the data is monotonically increasing. Before data preprocessing, the data can also be extracted in time domain or frequency domain to more efficiently reflect the product degradation process. The present application adopts the order preserving regression and the first exponential smoothing method. The order preserving regression can obtain the dependent variable value satisfying the non-decreasing constraint relationship without changing the arrangement order of the independent variable. The statistical estimation formula of the order preserving regression is not explicitly expressed, but it can be solved by programming; the first exponential smoothing method gives the prediction value at t+1 time by calculating the weighted average of the actual observation value and the prediction value at t time, and the prediction formula is as follows:

[0018] Ft+1 = εY t + (1-ε)F t (1)

[0019] where Y t is the actual observation at time t; F t is the prediction at time t; and ε is a smoothing coefficient.

[0020] Preferably, the step S2 specifically comprises:

[0021] S21, performing degradation modeling based on TEDP process according to the degradation data;

[0022] S22, combining the acceleration factor invariance principle with the TEDP process to obtain a definition of a mechanism equivalence factor;

[0023] S23, considering that the sample data is more and the model form is more complex, a maximum likelihood estimation method is used to estimate parameters required for calculating the mechanism equivalence factor.

[0024] Preferably, the step S21 specifically comprises: setting {Y(t), t≥0} as an observed product degradation path, and letting Δt i = t i -t i-1 and Δy i =y i -y i-1 Due to the complexity of the TEDP model, there is no exact analytical expression for the distribution of the degradation increment f(Δy; μ, λ, r), however, by using the saddlepoint approximation method, an approximate expression for the degradation increment f(Δy; μ, λ, r) when λΔt→∞ can be given as:

[0025] f(Δy; μ, λ) = c(Δy; λ, Δt)·exp{λ[Δy·ω(μ)-Δt·κ(ω(μ))]} (2)

[0026] where μ represents a drift parameter, λ represents a diffusion parameter, c(·) and κ(·) are real functions, the mean and variance of Y(t) are μt and V(μ)t / λ, where μ = κ'(ω(μ)), V(μ) = κ''(ω(μ)) and ω'(μ) = 1 / V(μ); in particular, V(μ) = μ r , r∈(-∞, 0]∪[1, ∞), is defined as a variance function, and d(Δy; Δt, μ, r) is a unit deviation function, which is calculated by the following formula:

[0027]

[0028] Preferably, in step S22, the acceleration factor invariance principle is one of the most commonly used statistical principles in engineering applications, and the basic idea is that when the failure mechanism of the accelerated test does not change, the acceleration factor with engineering application is only determined by the stress level, and is irrelevant to the working time or reliability value of the product. By combining the acceleration factor invariance principle with the TEDP process, and through a series of derivations, the definition of the mechanism equivalence factor is obtained as follows:

[0029]

[0030] When the degradation mechanism remains unchanged, the mechanism equivalence factor should be a constant in theory during the degradation process. According to formula (4), as long as the parameters μ, r and λ are estimated, m can be obtained.

[0031] Preferably, in step S23, the log-likelihood function of the product degradation path is as follows:

[0032]

[0033] By taking the partial derivative of formula (5), the estimation formula of the parameters μ i and λ i is obtained as follows:

[0034]

[0035] Substitute and into formula (5), and solve the maximum extreme point to obtain

[0036] Preferably, step S3 specifically comprises:

[0037] In actual applications, the mechanism equivalence factor obtained from engineering data affected by random factors is a random variable. The parameters of each interval and each product are estimated respectively, and the vector sample of the mechanism equivalence factor is constructed as follows:

[0038]

[0039] Wherein, represents the mechanism equivalence factor of the i th degradation interval estimated based on the j th product, and is taken as the hypothesis test sample. Since the products under each degradation interval belong to the same batch, the elements in the vector can be considered to come from the same distribution population, and it is assumed that different elements are independent of each other, and different distribution populations have no correlation. Based on the above assumption, the mean and variance are used to test whether there is a significant difference between different distribution populations, so as to determine whether the degradation mechanism has changed;

[0040] There are many methods to test whether a sample follows a normal distribution. In this method, due to cost constraints, the number of elements in each degradation interval is small. Therefore, the Shapiro-Wilk (SW) test, which performs well with small sample sizes, is considered. The SW test in SPSS software can be used to test for this. Does it follow a normal distribution?

[0041] Preferably, step S4 specifically includes:

[0042] When the Shapiro-Wilk test is accepted, it is considered that... Following a normal distribution, degenerate intervals that fail the Shapiro-Wilk test are removed. Mechanism equivalence tests are then performed on the remaining samples. For the i-th normally distributed degenerate interval, unbiased estimates of the mean and variance are obtained using the following formula, where i = 1, 2, ..., k′:

[0043]

[0044] To further examine whether the sample distributions of the mechanistic equivalence factor vectors are identical across different degradation intervals, we first use the Bartlett test to assess the equivalence of variances. The Bartlett statistic has been proven effective in testing for significant differences in variances among populations with different normal distributions (a significant difference is indicated when the statistic falls into the rejection region). The null hypothesis of equal variances is stated as: H0: The Bartlett statistic is constructed as follows:

[0045]

[0046] in, ν i =n-1,

[0047] Given a significance level α, the rejection region is:

[0048]

[0049] While the Bartlett test is efficient at detecting significant differences across multiple intervals, it cannot provide information on the degradation interval corresponding to the change in degradation mechanism when the null hypothesis is rejected. In such cases, an F-test can be performed sequentially between adjacent degradation intervals until the specific location of the degradation mechanism change is determined.

[0050] Subsequently, analysis of variance (ANOVA) is used to test the equivalence of the means of samples within each degradation interval. However, it should be noted that one of the prerequisites for ANOVA is that the variances of all groups are equal, i.e., the homoscedasticity assumption. If the F-test reveals significant differences in variances among some intervals, directly using ANOVA for the mean test may affect the validity of the results. In this case, Welch ANOVA can be used to test the equivalence of the means. Welch ANOVA is an improved ANOVA method that does not require the variances of all groups to be consistent. By calculating the p-value of Welch ANOVA, it is determined whether there are significant differences in the means among the various degradation intervals.

[0051] Preferably, in step S5, the mean and variance of the mechanistic equivalent factor vector samples under different degradation intervals are compared in step S4. If there are significant differences between the overall mean or variance distributions, it is considered that the degradation mechanism of the product has changed in one or more degradation intervals; otherwise, it is considered that the degradation mechanism of the product has not changed. Based on this, the location of the mechanism change point is determined and the degradation stage under different degradation mechanisms is identified.

[0052] Therefore, the degradation stage identification and change point detection method driven by the above-mentioned mechanism equivalent has the following beneficial effects:

[0053] (1) Using the TEDP process to model the product degradation process enhances the versatility of the model, ensures the accuracy of the modeling, and makes the model more consistent with the degradation behavior in the real world.

[0054] (2) The mechanism equivalence test method based on degradation model parameters can accurately and quickly detect the change point of degradation mechanism by checking whether the model parameters meet the failure mechanism equivalence condition, and identify the degradation stage accordingly. This method does not require a complicated calculation process, and can make an accurate judgment based on the degradation data obtained in the experiment. It has high operability and convenience.

[0055] (3) This method has low requirements for the amount of degraded data, which shows its superiority in processing small sample data.

[0056] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0057] Figure 1 This is a flowchart of a degradation stage identification and change point detection method driven by mechanistic equivalence according to the present invention.

[0058] Figure 2This is a schematic diagram of the original vibration signal data of five wheels in an embodiment of the present invention, wherein (a) is wheel number one, (b) is wheel number two, (c) is wheel number three, (d) is wheel number four, and (e) is wheel number five;

[0059] Figure 3 This is a schematic diagram of the signal extraction of the mean feature of the first round in an embodiment of the present invention;

[0060] Figure 4 This is a schematic diagram of the preprocessed data of the first wheel in an embodiment of the present invention. Detailed Implementation

[0061] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0062] In this embodiment, wheel degradation data of a high-speed train operating in China was acquired. A condition monitoring system consisting of four sensors and a processor was installed on the wheels. Over time, due to material defects and workload, small cracks may appear beneath the wheel surface, leading to fatigue cracks. When the defective area of ​​the wheel comes into contact with the railway, vibration signals collected by the sensors can be used to track the wheel degradation process. Vibration values ​​of the wheels were measured every 20 kilometers over a distance of 200,000 kilometers. A total of five wheel vibration data points from the same train were collected, such as... Figure 2 As shown in this document, a TEDP degradation model of a wheel is established based on a degradation stage identification and change point detection method driven by equivalent mechanism, and the degradation mechanism change point and degradation stage are predicted.

[0063] like Figure 1 As shown, a degradation stage identification and change point detection method driven by equivalent mechanisms includes the following steps:

[0064] S1. Product degradation data preprocessing and degradation interval division

[0065] Due to the large number of data points and the presence of noise, feature extraction is performed on the data before preprocessing. Considering the sparse measurement frequency of the acquired data, this embodiment uses time-domain features to reflect the data state. Calculations show that the mean feature is better at presenting the monotonic trend of the data compared to other features. For each wheel, the mean of 10,000 data points is extracted in chronological order, with 100 original data points extracted at a time, resulting in 100 feature data points. Taking wheel number one as an example, the mean feature extraction result is as follows... Figure 3 As shown. The extracted feature signals of the other four wheels are similar.

[0066] Next, the data is preprocessed to ensure monotonically increasing data. First, ordinal regression is performed, which can be implemented using MATLAB. At this point, the data is not yet monotonically increasing, so exponential smoothing is applied. In this embodiment, the smoothing coefficient ε is set to 0.2 to ensure data smoothness. The preprocessed data for round one is as follows: Figure 4 As shown, the extracted feature signals of the other four wheels are similar.

[0067] For the processed data, the accuracy of the degradation interval division is determined according to the actual engineering requirements. This invention divides 100 feature data points for each wheel into 10 degradation intervals, equivalent to measuring ten times within each degradation interval, with the corresponding parameters: n=5, k=10, c=10.

[0068] S2. Calculate the mechanistic equivalence factor for each degradation interval.

[0069] Substitute the data of the five wheels into formulas (5), (6), and (7) in turn to solve for the parameters. and Then, the estimated value of the mechanism equivalence factor is obtained by using formula (4). The estimation results for all parameters are shown in Table 1.

[0070] Table 1 Parameter estimation results

[0071]

[0072]

[0073] S3. Construct a hypothesis testing sample and perform a normality test on the sample.

[0074] Based on Table 1 Based on the estimation results, construct a hypothesis test sample. as follows:

[0075]

[0076] This embodiment uses the SW test function in SPSS software to test... Does it follow a normal distribution? Perform a Swing test on each hypothesis test sample. If all samples pass, it indicates that the data set follows a normal distribution, satisfying the conditions for subsequent tests.

[0077] S4. Test for equivalence of variance and mean

[0078] First, Bartlett's test is used to examine the consistency of variance among these normal distributions. With a significance parameter α = 0.05, Bartlett's statistics are calculated for the ten intervals.

[0079]

[0080] The Bartlett statistic fell into the rejection region, indicating a significant difference in the variance of the MEF estimates across the ten degradation intervals. To determine the information of the degradation intervals corresponding to changes in the degradation mechanism, F-tests were performed one by one between adjacent degradation intervals. The test results are shown in Table 2.

[0081] Table 2 Test Results

[0082]

[0083]

[0084] Since the variances were unequal, Welch ANOVA was used to test the equivalence of the means. The test results are shown in Table 3.

[0085] Table 3. Results of Welch ANOVA test

[0086] Test interval Welch ANOVA test p-value Results k = 1 vs. k = 2 0.62657 Accept k = 2 vs. k = 3 0.36374 Accept k = 3 vs. k = 4 0.76126 Accept k = 4 vs. k = 5 0.98051 Accept k = 5 vs. k = 6 0.64154 Accept k = 6 vs. k = 7 0.88089 Accept k = 7 vs. k = 8 0.45154 Accept k = 8 vs. k = 9 0.40607 Accept k = 9 vs. k = 10 0.98596 Accept

[0087] S5. Identify failure mechanism change points and degradation stages.

[0088] Step four compares the mean and variance of the mechanistic isomorphism factor vector samples across different degradation intervals. Based on the F-test, and Between and and The null hypothesis was rejected, and the variances showed a significant difference, indicating a change in the degradation mechanism within the third degradation interval. Welch's ANOVA test found no significant differences in the mean compared to other intervals. Combining the tests of variance and mean, the mechanistic inflection point occurred in the third degradation interval. Therefore, we can identify the degradation stages: the degradation interval k = 1–2 belongs to the first degradation stage, and the degradation interval k = 4–10 belongs to the second degradation stage.

[0089] Therefore, this invention employs a mechanism-equivalence-driven degradation stage identification and change point detection method. It collects and preprocesses product degradation data, then divides the data into degradation intervals and models the degradation of each interval based on the TEDP process. Next, it uses normality tests, Bartlett's tests, and ANOVA to determine the mechanism equivalence of the degradation intervals. Finally, it identifies the timing of degradation mechanism changes and degradation stages. Compared with traditional methods, this invention, while ensuring the robustness of the degradation model, can more accurately identify the degradation stages of the product, has strong operability, and is applicable to various fields such as performance degradation modeling, life prediction, and failure analysis of products.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for identifying degradation stages and detecting change points driven by equivalent mechanisms, characterized in that, Includes the following steps: S1. Preprocessing of product degradation data and division of degradation intervals; S2. Calculate the mechanism equivalence factor for each degradation interval; S3. Construct a hypothesis testing sample and perform a normality test on the sample; S4. Perform tests for the equivalence of variance and mean; S5. Determine the failure mechanism change point and identify the degradation stage; Step S1 specifically includes: Suppose a total collection Degradation data for each product was categorized based on time series. There are several degradation intervals, and each degradation interval is... Second measurement, The degradation interval is represented as , The product serial number is represented as , The historical monitoring time and the corresponding degradation path are represented as follows: and ,in, Indicates the start or end time of each degradation interval. ; Data preprocessing was performed using ordinal-preserving regression and first-order exponential smoothing. The first-order exponential smoothing method calculates... The weighted average of the actual and predicted values ​​at time 1 is used to give The predicted value at time t is given by the following formula: （1） in, for The actual observed value at time; for The predicted value at any given time; For smoothing coefficients; Step S2 specifically includes: S21. Perform degradation modeling based on the TEDP process using degradation data; S22. Combining the principle of constant acceleration factor with the TEDP process, we obtain the definition of the mechanism equivalence factor; S23. Use the maximum likelihood estimation method to estimate the parameters required for the computer's theoretical equivalence factor; Step S21 specifically involves: Let... To observe the product degradation path, let and Using the saddle point approximation method, we give the following when... At that time, the degradation increment The approximate expression is: （2） in, Indicates the drift parameter, Indicates diffusion parameters, and It is a real function. The mean and variance are and ,in, , and In particular, , It is defined as the variance function. It is a unit deviation function, calculated using the following formula: （3）； The mechanism equivalence factor in step S22 is defined as follows: （4）； The log-likelihood function of the product degradation path in step S23 is: （5） By taking the partial derivative of formula (5), the parameters are obtained. and The estimation formula is: （6） （7） Will and Substituting into formula (5), we can find its maximum value and extreme points to obtain the result. ; Step S3 specifically includes: Parameters were estimated for each interval and each product, and the following sample of mechanistic isomorphic factor vectors was constructed: （8） in, Indicates based on the first The estimated product number Mechanism equivalence factor for each degradation interval, take As a sample for hypothesis testing, since the products in each degradation interval belong to the same batch, the vector... The elements in the model are assumed to come from the same distribution population, and it is assumed that the different elements are independent of each other and that there is no correlation between different distribution populations. Based on the above assumptions, the mean and variance tests are used to determine whether there are significant differences between different distribution populations, so as to determine whether the degradation mechanism has changed. Shapiro-Wilk test in SPSS software Does it follow a normal distribution? Step S4 specifically includes: When the Shapiro-Wilk test is accepted, it is considered that... Following a normal distribution, degradation intervals that failed the Shapiro-Wilk test were removed, and the remaining samples underwent a mechanistic equivalence test. For a normally distributed degenerate interval, unbiased estimates of the mean and variance are obtained using the following formula, where : （9） （10） To further examine whether the sample distributions of the mechanistic equivalence factor vectors are identical across different degradation intervals, the Bartlett test is first used to assess the equivalence of variances. The null hypothesis of equal variances is stated as follows: The Bartlett statistic is constructed as follows: （11） in, , , ; Given significance level The rejection domain is: （12） Perform F-tests one by one between adjacent degradation intervals until the specific location of the degradation mechanism change is determined; Subsequently, the equivalence of the means of samples within each degradation interval was tested using analysis of variance. If the F test found that there were significant differences in the variances of some intervals, the Welch ANOVA method was used to test the equivalence of the means. By calculating the p-value of Welch ANOVA, it was determined whether there were significant differences in the means of each degradation interval. In step S5, the mean and variance of the mechanistic equivalent factor vector samples under different degradation intervals are compared with those in step S4. If there are significant differences between the overall mean or variance distributions, it is considered that the degradation mechanism of the product has changed in one or several degradation intervals; otherwise, it is considered that the degradation mechanism of the product has not changed. Based on this, the location of the mechanism change point is determined and the degradation stage under different degradation mechanisms is identified.

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