Product residual life prediction method considering multi-parameter time sequence correlation modeling

Abstract

The invention provides a product residual life prediction method considering multi-parameter time sequence correlation modeling, and the method comprises the steps: firstly, carrying out the standardization processing of multi-performance parameter degradation data of a mechanical electronic product, and carrying out the function type principal component analysis based on the adaptive selection of a mixed basis function, screening out key performance parameters representing the degradation state of the product; secondly, aiming at the screened key performance parameters, a parameter estimation method based on a nonlinear Wiener process of Markov Monte Carlo is adopted, and a degradation model and a life prediction model of each performance parameter are established; and finally, on the basis of edge distribution of each parameter, modeling multi-parameter dynamic time sequence correlation through a Copula function, and forming a joint residual life prediction model. The method has an adaptive degradation feature extraction capability, and can effectively fuse multi-parameter time sequence information so as to predict the residual life of the product more comprehensively and more accurately.

Description

Technical Field

[0001] This invention relates to the field of lifespan prediction technology, and more specifically to a method for predicting the remaining lifespan of a product that considers multi-parameter time-series correlation modeling. Background Technology

[0002] In real-world operating conditions, the failure of electromechanical products is not the result of a single parameter degradation, but rather a macroscopic manifestation of the interaction and competition of multiple performance parameters driven by various degradation mechanisms. Therefore, a single degradation parameter is insufficient to comprehensively characterize the product's health status. Comprehensively utilizing multi-parameter information and characterizing their correlations is crucial for constructing a highly accurate and generalizable lifespan prediction model. Currently, in the field of product remaining life prediction based on performance degradation data, existing methods mostly focus on a single degradation parameter or independently model multiple parameters, failing to fully characterize the dynamic temporal correlations of multiple performance parameters during the degradation process. This limits the ability to represent the degradation state of electromechanical products, leading to potential prediction biases. Furthermore, existing technologies often rely on fixed and singular function forms for feature extraction of degradation information, lacking the ability to adaptively model complex degradation patterns, which affects the accuracy of key performance parameter selection and the reliability of lifespan prediction. Therefore, there is an urgent need for a remaining life prediction method that can effectively integrate the temporal correlations of multiple parameters and possess adaptive degradation feature extraction capabilities to improve prediction accuracy and engineering value. Summary of the Invention

[0003] This invention addresses the technical problems existing in the prior art by providing a product remaining life prediction method that considers multi-parameter time-series correlation modeling, comprising:

[0004] Step 1: Standardize the degradation data of multiple performance parameters of the electromechanical products to form a standardized matrix of performance parameter degradation data;

[0005] Step 2: Construct hybrid basis functions based on B-spline basis functions and Daubechies wavelet basis functions, and evaluate the fitting effect of basis functions through least squares reconstruction error to achieve adaptive selection of basis functions;

[0006] Step 3: Using the functional principal component analysis method, extract eigenvalues ​​and eigenvectors from the degradation functions corresponding to the selected basis functions, and screen out the key performance parameters that can characterize the degradation state of the product.

[0007] Step 4: For each selected performance parameter, establish a degradation model based on the nonlinear Wiener process, as shown in Equation (1):

[0008] X(t) = X(t0) + a(1-e -bt )+σ B B(t) (1)

[0009] Where X(t0) is the initial value of the degradation parameter; a(1-e -bt Let be a nonlinear degradation trajectory function describing the degradation trend, and let 'a' represent the uncertainty of degradation among different samples, following a normal distribution a ~ N(μ a ,σ a ), b represents the model parameter that produces a fixed effect between samples; σ B The diffusion coefficient reflects the intensity of random fluctuations during degradation; B(t) is a standard Wiener process, B(t)-B(s)~N(0,ts). Based on the degradation model and observation data, a system containing the population parameter (μ) is constructed. a ,σ a ,b,σ B and individual parameter a i Hierarchical Bayesian posterior probability model;

[0010] Step 5, establish the random effects parameter a in the nonlinear Wiener process model. i Decentralization is performed, and log-exponential smoothing is applied to the positive constraint parameters in the model;

[0011] Step 6: Based on the reparameterized and mapped model, the Markov chain Monte Carlo method is used to sample the posterior distributions of the population parameters and individual parameters through an adaptive sampling framework that includes an initial coarse estimation stage and a NUTS sampling stage, so as to obtain parameter estimates.

[0012] Step 7: Based on the lifetime prediction model for each performance parameter and the actual lifetime data, determine the marginal probability distribution of each performance parameter at each predetermined time point.

[0013] Step 8: Calculate Kendall's rank using the moving window method at different degradation time points, select the optimal Copula function type and estimate its parameters using the AIC information criterion, and establish a time-series correlation model for multi-performance parameter lifetime prediction.

[0014] Step 9: Based on the time-series correlation model and the marginal distribution of each performance parameter, establish a product remaining life prediction model that considers multi-parameter time-series correlation modeling.

[0015] To address the shortcomings of existing technologies, this invention proposes a product remaining life prediction method that considers multi-parameter time-series correlation modeling by screening key performance parameters, accurate single-parameter degradation modeling, and multi-parameter time-series correlation modeling. This provides a solution for life prediction under complex performance degradation of electromechanical products. Attached Figure Description

[0016] Figure 1A flowchart of a product remaining life prediction method considering multi-parameter time-series correlation modeling provided by the present invention;

[0017] Figure 2 The degradation curves of the aero-engine performance parameters S7 and S12 are shown.

[0018] Figure 3 The probability density curve for remaining lifetime prediction based on multi-parameter time-series correlation modeling of aero-engines. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Figure 1 A flowchart of a product remaining life prediction method considering multi-parameter time-series correlation modeling provided by the present invention is shown. The method mainly includes:

[0021] Step 1: Standardize the degradation data of multiple performance parameters of the electromechanical product to form a standardized matrix of performance parameter degradation data, specifically including:

[0022] Define matrix X to represent the degradation data of multiple performance parameters of the product:

[0023]

[0024] Where n is the number of time points; p is the number of performance parameters; x ij This represents the degradation value of the j-th (j∈[1,p]) performance parameter at the i-th (i∈[1,n]) time point.

[0025] Considering the differences in numerical range and units among the various performance parameters, the degradation data needs to be standardized:

[0026]

[0027] in, Let be the mean of the j-th performance parameter; Let x' be the standard deviation of the j-th performance parameter; ij This is the standardized data; the standardized matrix is ​​denoted as X′.

[0028] Step 2 involves constructing a hybrid basis function based on B-spline basis functions and Daubechies wavelet basis functions, and evaluating the basis function fitting effect through least-squares reconstruction error to achieve adaptive basis function selection. Specifically, this includes:

[0029] Step 2.1: Construct a hybrid basis function based on B-spline basis functions and Daubechies wavelet basis functions. The construction process of the B-spline basis functions is as follows:

[0030] Define the time domain t∈Γ=[t min ,t max The node sequence is constructed using a uniform distribution:

[0031]

[0032] Where K is the number of basis functions; d is the spline order; t min =τ0=…=τ d , t max =τ K =…=τ K+d .

[0033] The expression for the B-spline basis function is:

[0034]

[0035] in, Let N be the value of the k-th (k∈[1,K]) d-th order B-spline basis function at time point t; k,r (t) represents the value of the r-th order B-spline basis function on the k-th node interval at time point t; β kr This is the control factor.

[0036] N k,r (t) has the following recursive relation:

[0037]

[0038] Therefore, the expression for the B-spline basis function matrix is:

[0039]

[0040] The construction process of Daubechies wavelet basis functions is as follows:

[0041] Set the time domain t∈Γ=[t min ,t max Given the number of decomposition levels F, based on multiresolution analysis (MRA), the scaling function φ(t) and wavelet number ψ(t) satisfy:

[0042]

[0043] Among them, h v and g v These are the coefficients of the low-pass and high-pass filters, respectively, satisfying g v =(-1) v h 1-v .

[0044] The expression for the Daubechies wavelet basis functions is:

[0045] ψ f,v (t)=2 -f / 2 ψ(2 -f (11)

[0046] Where, ψ f,v (t) represents the Daubechies wavelet basis function with scale f and translation v; f∈{0,1,…,F-1} is the scale parameter; v∈{0,1,…,2} f -1} is the translation parameter.

[0047] The basis functions at each scale are reconstructed using the inverse discrete wavelet transform (IDWT) and combined to form the initial Daubechies wavelet basis function matrix B. ini-wavelet :

[0048]

[0049] Then for B ini-wavelet After orthogonalization, the expression for the Daubechies wavelet basis function matrix is ​​obtained:

[0050]

[0051] Where qr(·) is the QR decomposition; (I is the identity matrix).

[0052] Step 2.2: Construct the least squares reconstruction error and adaptively select the basis function, the expression of which is:

[0053]

[0054] Where ω is the regularization coefficient (ω∈(0,1)), X′ is the degenerate data normalization matrix, and B is the basis function matrix (including B). spline and B wavelet ), where Θ is the coefficient matrix, and its expression is:

[0055]

[0056] Then, adaptive basis function selection is performed based on RSE:

[0057]

[0058] Among them, RSE spline and RSE wavelet The basis function matrix is ​​B. spline and B wavelet The least squares reconstruction error at that time.

[0059] Step 3: Using functional principal component analysis, extract eigenvalues ​​and eigenvectors from the degradation functions corresponding to the selected basis functions, and screen out key performance parameters that can characterize the product degradation state, specifically including:

[0060] Step 3.1: After determining the basis functions, project the degenerate data normalization matrix X′ onto the selected basis function space to obtain the projection coefficient matrix:

[0061] Y = (B 'T B ' ) -1 B 'T X ' (17)

[0062] Calculate the covariance matrix of Y:

[0063]

[0064] Wherein, Σ is the p×p covariance matrix, which describes the correlation between the p performance parameters.

[0065] Perform eigenvalue decomposition on the covariance matrix Σ:

[0066] Σ=UΛU T (19)

[0067] Among them, Λ=diag(δ1,δ2,…,δ p ) is an eigenvalue diagonal matrix, δ j Let U be the j-th eigenvalue; U = [U1, U2, ..., Uj] p ] is the eigenvector matrix, U j For the corresponding δ j The eigenvectors represent the directions of the j-th principal component. The magnitudes of the eigenvalues ​​reflect the contribution of the corresponding principal component to the data variance, and the components of the eigenvectors represent the weights of the principal components on various performance parameters.

[0068] Arrange in descending order of eigenvalues: δ1≥δ2≥···≥δ p And select the eigenvectors corresponding to the first m largest eigenvalues ​​to form the projection matrix V. m :

[0069] V m =[U1,U2,...,U m (20)

[0070] Where m is the number of selected principal components, such that the cumulative contribution rate When a certain threshold is reached, the contribution rate of the j-th principal component is...

[0071] Finally, by analyzing the eigenvector U j The magnitude of each component quantifies the contribution of each performance parameter to the principal component. For example, the eigenvector U1 of the first principal component is [U... 11 U 12 ,…,U 1p ] T Middle,U 1k This represents the contribution weight of the k-th performance parameter to the first principal component. The performance parameter with the largest absolute value indicates that its influence in the direction of that principal component is significant and can be used as a key parameter to characterize product degradation.

[0072] Step 3.2 involves analyzing the degradation data of 20 performance parameters (S1-S20) from 10 aero-engines (numbered 1-10). First, steps 1-3.1 were performed on the degradation data of engine 1. The results showed that the contribution rates of the first principal component (con1) and the second principal component (con2) were 98.43% and 0.63%, respectively, with a cumulative contribution rate (Con) of 99%, reaching the set threshold. Steps 1-3.1 were then repeated for the remaining engines, recording the performance parameter with the largest contribution weight in the first and second principal components for each engine. The frequency of each performance parameter being identified as a key parameter across all engines was then statistically analyzed, and the results are shown in Table 1.

[0073] Table 1. Frequency Statistics of Key Performance Parameters of 10 Aero Engines

[0074]

[0075] According to the statistical results in Table 1, in the first principal component dimension, performance parameter S12 was selected as the key performance parameter most frequently (5 times, accounting for 50%); in the second principal component dimension, S7 was significantly more frequent than other parameters (3 times, accounting for 30%). This indicates that among the 10 engines, S12 and S7 play a dominant role in the first and second principal components reflecting the degradation state mode, respectively. Based on this statistical analysis, S12 and S7 were selected as the key performance parameter combination characterizing the engine degradation state.

[0076] Step 4: For the selected S12 and S7 performance parameters, construct nonlinear Wiener process models respectively, and their degradation curves are shown in the figure. Figure 2 As shown, a model containing the total parameters (μ) is constructed based on the degradation model and observation data. a ,σa ,b,σ B and individual parameter a i Hierarchical Bayesian posterior probability model:

[0077] p(Θ|X)∝p(X|Θ)p(Θ), Θ={μ a ,σ a ,b,σ B ,a 1:N} (twenty one)

[0078] Step 5: For the random effects parameter a i We perform decentralization and express it as the population parameter μ. a ,σ a With a standard normal auxiliary variable η i The combination of is shown in formula (22).

[0079] a i ′=μ a +σ a η i ,(η i ~N(0,1)) (22)

[0080] For the diffusion coefficient σ with positive constraint B And the model parameter b, perform log-exponential smoothing mapping. The parameter is converted into an unconstrained space. The reparameterized model is shown in Equation (23).

[0081]

[0082] Step 6: Based on the reparameterized and mapped model, the Markov chain Monte Carlo method is used to sample the posterior distributions of the population parameters and individual parameters through an adaptive sampling framework that includes an initial coarse estimation stage and a NUTS sampling stage, and the parameter estimates are shown in Table 2.

[0083] Table 2 Parameters of the nonlinear Wiener process model for aero-engines

[0084] parameter S7 S12 <![CDATA[μ a ]]> <![CDATA[9.37×10 -3 ]]> <![CDATA[8.88×10 -3 ]]> <![CDATA[σ A ]]> <![CDATA[1.21×10 -8 ]]> <![CDATA[1.65×10 -8 ]]> <![CDATA[σ B ]]> 0.115 0.0848 b 0.391 0.414

[0085] Step 7: Passing through time t k Lifetime prediction models for performance parameters S7 and S12 and actual remaining lifetime of each sample Obtain the time t for each sample k The marginal distributions of performance parameters S7 and S12, and the relationship between their corresponding sampling points, at time t. k The distribution value of sample j in performance parameter i is calculated as shown in formula (24).

[0086]

[0087] Among them, f RULi-j (s|t k (t) represents time t k The life prediction model for sample j based on performance parameter i, actual j u represents the actual lifespan value. j For time t k The distribution value of sample j in the marginal distribution of performance parameter i.

[0088] Step 8: Use the moving window method to calculate at different stages of degradation, capture the correlation parameter values ​​at different times, and calculate Kendall's rank τ according to formula (25).

[0089]

[0090] Where sign[*] is the sign function, which takes the value 1 when the input parameter is greater than 0, -1 when it is less than 0, and 0 when it is equal to 0.

[0091] Based on the Kendall rank and Copula parameter transformation relationship, parameter estimation of different types of Copula functions is performed. The Kendall rank and Copula parameter transformation relationship is shown in Table 3.

[0092] Table 3. Relationship between various Copula function parameters and Kendall's rank.

[0093]

[0094] For each type of Copula function, calculate the parameter estimate θ. C (t) and the maximum likelihood function, and the Copula function with the smallest information value is selected as the correlation structure model between performance parameters S7 and S12 by using the AIC criterion.

[0095] Step 9: Based on the optimally selected Copula function type and parameters, establish a lifetime prediction model considering time-series correlation at each time point, t. k The lifetime prediction model is shown in formula (26).

[0096]

[0097] in, For performance parameter S7 at time point t k The following is the CDF result for predicting RUL as l, F RUL2 (l|t k () represents the performance parameter S12 at time point t k The following are the CDF results for predicting RUL as l. For time point t k Based on the Copula function correlation model established by two performance degradation parameters, the variation of the remaining life prediction probability density function of the aero-engine with the number of cycles is obtained as follows: Figure 3 As shown.

[0098] Using the above method, the remaining life of 10 sets of aero-engine degradation data was predicted, with an average percentage error of 7.69%. Through performance parameter screening and time-series correlation modeling, the proposed method can more comprehensively and accurately predict the remaining life of products considering multi-parameter time-series correlation.

[0099] This invention effectively identifies key performance parameters characterizing product degradation by integrating degradation data from multiple performance parameters and employing functional principal component analysis with adaptive selection of mixed basis functions. Based on these key performance parameters, a single-parameter nonlinear Wiener process model is established, and data processing, including decentralization of uncertain parameters, is performed. The model parameters are then accurately estimated using the Markov Monte Carlo method. Based on the remaining lifetime predictions for each single parameter, multi-parameter time-series correlation modeling is conducted to obtain joint lifetime prediction results. This method overcomes the shortcomings of traditional remaining lifetime prediction methods, such as insufficient characterization capability of single parameters and neglect of time-series correlations between parameters, representing a significant improvement over traditional remaining lifetime prediction methods.

[0100] It should be noted that in the above embodiments, the descriptions of each embodiment have different focuses. If a part is not described in detail in a certain embodiment, it can be supplemented and understood by referring to the relevant content of other embodiments.

[0101] Although preferred embodiments of the invention have been described in detail herein, those skilled in the art, upon understanding the core inventive concept, can make further changes and modifications based on this. Therefore, the appended claims should be interpreted as covering the preferred embodiments and all changes and modifications within the scope of the invention.

[0102] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Any such modifications and variations that fall within the scope of the claims of this invention and their equivalents should be considered part of this invention.

Claims

1. A method for predicting the remaining useful life of a product considering multi-parameter time-series correlation modeling, characterized in that, include: Step 1: Standardize the degradation data of multiple performance parameters of the electromechanical products to form a standardized matrix of performance parameter degradation data; Step 2: Construct hybrid basis functions based on B-spline basis functions and Daubechies wavelet basis functions, and evaluate the fitting effect of basis functions through least squares reconstruction error to achieve adaptive selection of basis functions; Step 3: Using the functional principal component analysis method, extract eigenvalues ​​and eigenvectors from the degradation functions corresponding to the selected basis functions, and screen out the key performance parameters that can characterize the degradation state of the product. Step 4: For each selected performance parameter, establish a degradation model based on the nonlinear Wiener process, as shown in Equation (1): X(t)=X(t0)+a(1-e -bt )+σ B B(t) (1) Where X(t0) is the initial value of the degradation parameter; a(1-e -bt Let be a nonlinear degradation trajectory function describing the degradation trend, and let 'a' represent the uncertainty of degradation among different samples, following a normal distribution a ~ N(μ a ,σ a ), b represents the model parameter that produces a fixed effect between samples; σ B The diffusion coefficient reflects the intensity of random fluctuations during degradation; B(t) is a standard Wiener process, B(t)-B(s)~N(0,ts). Based on the degradation model and observation data, a system containing the population parameter (μ) is constructed. a ,σ a ,b,σ B and individual parameter a i Hierarchical Bayesian posterior probability model; Step 5, establish the random effects parameter a in the nonlinear Wiener process model. i Decentralization is performed, and log-exponential smoothing is applied to the positive constraint parameters in the model; Step 6: Based on the reparameterized and mapped model, the Markov chain Monte Carlo method is used to sample the posterior distributions of the population parameters and individual parameters through an adaptive sampling framework that includes an initial coarse estimation stage and a NUTS sampling stage, so as to obtain parameter estimates. Step 7: Based on the lifetime prediction model for each performance parameter and the actual lifetime data, determine the marginal probability distribution of each performance parameter at each predetermined time point. Step 8: Calculate Kendall's rank using the moving window method at different degradation time points, select the optimal Copula function type and estimate its parameters using the AIC information criterion, and establish a time-series correlation model for multi-performance parameter lifetime prediction. Step 9: Based on the time-series correlation model and the marginal distribution of each performance parameter, establish a product remaining life prediction model that considers multi-parameter time-series correlation modeling.

2. The product remaining life prediction method considering multi-parameter time-series correlation modeling according to claim 1, characterized in that, Hybrid basis functions are constructed based on B-spline basis functions and Daubechies wavelet basis functions. The fitting effect of the basis functions is evaluated by least-squares reconstruction error, achieving adaptive selection of basis functions, including: Step 2.1: Construct a hybrid basis function based on B-spline basis functions and Daubechies wavelet basis functions. The expression for the B-spline basis function matrix is: in, Let N be the value of the k-th (k∈[1,K]) d-th order B-spline basis function at time point t. k,r (t) represents the value of the r-th order B-spline basis function at time point t on the k-th node interval, β kr For control coefficients; The expression for the Daubechies wavelet basis function matrix is: Where, ψ f,v (t) represents the Daubechies wavelet basis function with scale f and shift v, where f∈{0,1,…,F-1} is the scale parameter, and v∈{0,1,…,2} is the scale parameter. f -1} represents the translation parameter, and qr(·) represents the QR decomposition. I is the identity matrix; Step 2.2, construct the least squares reconstruction error, its expression is: Where ω is the regularization coefficient (ω∈(0,1)), X′ is the degenerate data normalization matrix, and B is the basis function matrix, including B spline and B wavelet Θ is the coefficient matrix, and its expression is: Then, adaptive basis function selection is performed based on RSE: Among them, RSE spline and RSE wavelet The basis function matrix is ​​B. spline and B wavelet The least squares reconstruction error at that time.

3. The product remaining life prediction method considering multi-parameter time-series correlation modeling according to claim 1, characterized in that, The random effects parameter a in the establishment of the nonlinear Wiener process model i Decentralization is performed by applying a log-exponential smoothing mapping to the positive constraint parameters in the model, including: The random effects parameter a i Represented as the population parameter μ a ,σ a With a standard normal auxiliary variable η i The combination of these is given by the formula shown in (7): a i ′=μ a +s a or i ,(or i ~N(0,1)) (7) For the diffusion coefficient σ with positive constraint B And the model parameter b, perform log-exponential smoothing mapping. Converting it to parameters in an unconstrained space, the reparameterized model is shown in Equation (8): X′(t)=(μ a ′+σ a 'or i (e) b′t′ -1)+σ′ B B(t) (8) 4. The product remaining life prediction method considering multi-parameter time-series correlation modeling according to claim 1, characterized in that, Kendall's rank is calculated using the moving window method at different degradation time points. The optimal Copula function type is selected and its parameters are estimated using the AIC information criterion. A time-series correlation model for multi-performance parameter lifetime prediction is established, including: The different stages of degradation were calculated using the moving window method to capture the correlation parameter values ​​at different times, and the Kendall rank τ was calculated according to formula (9): Where sign[*] is the sign function, which takes the value 1 when the input parameter is greater than 0, -1 when it is less than 0, and 0 when it is equal to 0; Based on the Kendall correlation rank and Copula parameter transformation relationship, parameter estimation is performed for different types of Copula functions, and the parameter estimates θ are calculated. C (t) and the maximum likelihood function are used to select the Copula function with the smallest information value as the correlation structure model between the degradation parameters by using the AIC criterion.

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