A complex equipment residual life prediction method based on sparse variational bayes

Abstract

The application provides a complex equipment residual life prediction method based on sparse variational Bayesian, and the steps are as follows: collecting health state monitoring variables and equipment degradation index data of complex equipment in a database; taking the health state monitoring variables as input and the equipment degradation index as output, a residual service life prediction linear regression model with noise data is constructed; the regression model is parameter estimated by using a variational Bayesian method, the weight coefficients of the model are output, and the weight coefficients of the regression model are sparsified to remove the weight coefficients with small proportion and the state monitoring variables, so that the linear regression model under different working conditions is obtained; the health state monitoring variables of the equipment to be predicted are collected, and the residual service life is predicted according to the linear regression model under different working conditions. The application considers the influence of measurement noise and parameter uncertainty, selects fewer health state monitoring variables by using the sparse variational Bayesian method, and realizes more accurate residual service life prediction.

Description

A method for predicting the remaining life of complex equipment based on sparse variational Bayes. Technical Field

[0001] This invention relates to the field of equipment remaining service life prediction, and in particular to a method for predicting the remaining service life of complex equipment based on sparse variational Bayes. Background Technology

[0002] Spacecraft operate in harsh environments (high radiation, high temperature, high pressure, etc.), inevitably experiencing performance degradation and malfunctions. Performance degradation or malfunctions can range from affecting mission completion to causing safety accidents. Remaining Useful Life (RUL) prediction not only assesses the health status of equipment but also supports maintenance decisions, playing a crucial role in ensuring safe and reliable operation. It is an important component of equipment prediction and health management. The health status of such complex equipment is often influenced by multiple factors, and due to unclear mechanisms and measurement uncertainties, identifying key variables characterizing equipment degradation from multiple measurement variables and establishing accurate prediction models presents significant challenges. Therefore, RUL prediction for complex equipment remains an open problem.

[0003] Such equipment typically has multiple variables reflecting the system's health status. When the underlying mechanisms are unclear, selecting and modeling key variables reflecting the overall degradation trend of the equipment is the main task in predicting remaining service life. Considering the current multi-condition and uncertain data conditions in system equipment, a sparse variational Bayesian method is used to select key variables for the equipment's remaining service life and establish a remaining service life prediction model. Taking into account the impact of uncertainty, measurement noise and parameters are probabilistically described, and the variational Bayesian method is used for posterior estimation of the parameters. Combined with the variance of the model parameters, monitoring variables related to the equipment's health status are removed in real time, and key variables are selected to achieve accurate prediction of the equipment's remaining service life. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the remaining service life of complex equipment based on sparse variational Bayes. This invention selects and predicts the remaining service life of equipment by processing the monitored variables.

[0005] The objective of this invention is achieved through the following technical solution, the specific steps of which are as follows:

[0006] 1) Data Acquisition: Collect health status monitoring variables and equipment degradation index data for complex equipment from the database;

[0007] 2) Model building: Using the health status monitoring variables in the dataset obtained in step 1) as input variables and the equipment degradation index as output variables, a linear regression model for predicting the remaining service life of the data with noise is built.

[0008] 3) Model training: The variational Bayes method is used to estimate the parameters of the regression model, output the weight coefficients of the model, and perform sparsification on the weight coefficients in the regression model, removing the weight coefficients with small proportions and their state monitoring variables, to obtain the linear regression model under different working conditions.

[0009] 4) Remaining service life prediction: Collect the status monitoring variables of the equipment to be predicted, and predict the remaining service life according to the linear regression model under different working conditions in step 3).

[0010] Furthermore, the specific method for constructing the model in step 2) is as follows:

[0011] Y=UΘ+ω (1)

[0012] In formula (1), Y=[y1,y2,...,y N ] T To equip N health state sequences within different periods, U = [U1, U2, ..., U...] M ] T For a matrix consisting of M monitored variable sequences, for each U i (1≤i≤M), we have U i =[u i,1 ,u i,2 ,...,u i,N ] T The parameter vector Θ = [θ1, θ2, ..., θ M ] T The noise vector ω = [ω1, ω2, ..., ω] is measured. N ] T .

[0013] Furthermore, the specific steps for model training in step 3) are as follows:

[0014] 3-1) Set time K-1 as the initial time and initialize the distribution of each parameter in the model;

[0015] 3-2) Construct the objective function for parameter estimation. Based on the prior distribution of each parameter at time K-1, use the variational Bayesian method to approximate the posterior distribution of each parameter in the objective function at time K.

[0016] 3-3) Select the solution that optimizes the objective function at time K according to the VB maximization step of the variational Bayesian inference method and apply it to time K+1; let time K = K+1, return to step 3-2), repeat steps 3-2)-3-3) until the lower bound function of the objective function converges, and output the model coefficients and likelihood function values.

[0017] 3-4) Remove the model coefficients with a small proportion obtained in step 3-3) and their corresponding health status monitoring variables, return to step 3-1), and repeat steps 3-1)-3-4) until the ARD variable reaches its maximum, output the optimal parameters of the model, and obtain the optimized linear regression model.

[0018] Furthermore, the specific steps for initializing the distribution of each parameter in the model in step 3-1) are as follows:

[0019] 3-1-1) Suppose that the parameter vector Θ follows a Gaussian-Gamma distribution:

[0020]

[0021] In equation (2), α -1 Let be the variance of the Gaussian distribution, and a0 and b0 be the hyperparameters of the gamma distribution, respectively.

[0022] 3-1-2) Assume the measurement noise vector ω follows a Gaussian distribution:

[0023]

[0024] In equation (3), τ -1 Let be the variance of a Gaussian distribution, and let be a gamma distribution, i.e.:

[0025]

[0026] In equation (4), c0 and d0 are the hyperparameters of the gamma distribution, respectively;

[0027] 3-1-3) Assuming the parameters are independent of each other, their joint prior distribution can be expressed as:

[0028]

[0029] In formula (5), α=[α1,α2,...,α M ] T .

[0030] Furthermore, the specific steps in step 3-2) to approximate the posterior distribution of each parameter in the objective function at time K using the variational Bayesian method are as follows:

[0031] 3-2-1) Construct the objective function for parameter estimation, and perform mathematical transformations on the objective function based on the relevant ideas of variational Bayes;

[0032] 3-2-2) Combining the prior distributions of each parameter at time K-1, the posterior distributions of each parameter variable at time K are updated progressively, including the posterior distribution q. k (Θ), q k (α), q k (τ).

[0033] Furthermore, the specific steps in 3-2-1) for constructing the objective function for parameter estimation and performing mathematical transformations on the objective function based on the relevant ideas of variational Bayes are as follows:

[0034] 3-2-1-1) Constructing the objective function: Let y 1:N =[y1,y2,...,y N ] T Therefore, according to the Maximum Likelihood Estimation (MLE) algorithm, the identification of model parameters can be transformed into the following optimization problem:

[0035]

[0036] 3-2-1-2) For the output y 1:N Maximizing the probability density function is equivalent to maximizing its log-likelihood function, and the output function y 1:N The log-likelihood function can be written as:

[0037]

[0038] In equation (7), q(Θ,α,τ) is an arbitrary probability density function, which, according to Bayes' criterion, is:

[0039]

[0040] Then we have:

[0041] lnp(y 1:N )=J+KL (9)

[0042] In equation (9),

[0043]

[0044] Among them, KL is q(Θ,α,τ) and p(Θ,α,τ|y 1:N The KL divergence between q(Θ,α,τ) and p(Θ,α,τ|y) is greater than or equal to 0 if and only if q(Θ,α,τ) = p(Θ,α,τ|y). 1:NWhen y = y, the equality holds, therefore lnp(y) = y. 1:N )≥J, J is lnp(y 1:N The lower bound function of ).

[0045] 3-2-1-3) Based on the ideas of variational Bayes, the log-likelihood function is mathematically transformed. The variational Bayes (VB) method uses the variational method to continuously maximize the lower bound function J by solving the posterior distribution q(Θ,α,τ), thereby realizing the likelihood function p(y). 1:N Maximizing ). Assuming that the parameters of each model are independent, and that they follow mean-field theory:

[0046] q(Θ,α,τ)=q(Θ)q(α)q(τ) (11)

[0047] Therefore, during the maximization of the lower bound function J, the posterior distributions of each parameter can be updated sequentially while keeping other parameters fixed.

[0048] Furthermore, in step 3-2-2), the specific steps for progressively updating the posterior distribution of each parameter variable within time K, based on the prior distribution of each parameter at time K-1, are as follows:

[0049] 3-2-2-1) Inferring the lower bound function J:

[0050] Let ξ∈Φ=[Θ,α,τ] and Φ -ξ ={Φ\ξ}, in the k-th iteration, the variational Bayesian method fixes the posterior distribution q. k (Φ -ξ ), update q k (ξ), the lower bound function J with respect to q k (ξ) can be represented as:

[0051]

[0052] In equation (12), C is a constant, and Q*(Θ,α,τ) can be expressed as:

[0053]

[0054] but,:

[0055] q k (ξ)∝Q*(Θ,α,τ)(14)

[0056] For the constructed linear regression model, its total probability density function p(y) 1:N ,Θ,α,τ), we have:

[0057]

[0058] 3-2-2-2) Update q(Θ):

[0059] The posterior distribution q(Θ) can be expressed as:

[0060]

[0061] In equation (16), C is a constant, then,

[0062]

[0063] In formula (17), Λ=diag(α1,α2,...,α M Let be a diagonal matrix, and the posterior distribution q(Θ) can be viewed as a Gaussian distribution:

[0064]

[0065] In equation (18),

[0066]

[0067] In equation (19), · is defined as the desired operation;

[0068] 3-2-2-3) Update q(α), q(τ):

[0069] The posterior distribution q(α) can be expressed as:

[0070]

[0071] The posterior distribution q(α) can be viewed as a gamma distribution:

[0072]

[0073] Based on the properties of gamma distribution, we have:

[0074]

[0075] Similarly, the posterior distribution q(τ) is obtained:

[0076]

[0077] The expected value and variance of the parameter τ are:

[0078]

[0079] Furthermore, the specific steps for outputting the model coefficients and likelihood function values ​​in step 3-3) are as follows:

[0080] 3-3-1) Maximize the log-likelihood function lnp at time K. k (y 1:N ):

[0081]

[0082] (Fixed step 3-2) Update the obtained q k-1 (Θ,α,τ), update the parameters using the maximum value of the lower bound function J at time K, and apply the optimal solution of the parameters to time K+1:

[0083] q k (Θ,α,τ)=argmaxJ k (26)

[0084] 3-3-2) Solving for the lower bound function J k The value of J, if k -J k-1 <ε, where: ε is the designed threshold, then the output model parameters Θ, α, τ are values;

[0085] If J k -J k-1 If ≥ε, then return to step 3-2), and repeat steps 3-2)-3-3) until the lower bound function J satisfies the condition.

[0086] Furthermore, the specific steps for outputting the optimal parameters of the model in steps 3-4) to obtain the optimized linear regression model are as follows:

[0087] 3-4-1) For model parameters θ i Assume it follows a normal distribution with a mean of 0, α i -1 It is its variance; using the variance value to characterize the importance of a parameter in the model is called automatic correlation determination of ARD variables. In sparse Bayesian analysis, the parameter α is used as the basis for variable selection. In the number of iterations s, let the set of variables in the model be M. s , where: M 0 ={1,2,...,M}, the model to be estimated is expressed as:

[0088] Y = U(M) s )Θ(M s )+ω (27)

[0089] Obtain the model parameters Θ(M) s ) and the ARD variable set, denoted as α(Ms Based on the ARD variables and their meanings, after each iteration, in α(M) s Find the largest ARD value in the model and remove the corresponding variable to obtain a new model.

[0090] Let exID represent the variable index corresponding to the maximum ARD value, and let the new variable set be M. s+1 ={M s \exID}, rebuild the model based on the new set of variables and solve for the model parameters;

[0091] 3-4-2) The VB method, while obtaining the model parameters, also provides the corresponding likelihood function value of the model, i.e., the maximum lower bound function, denoted as J(M s If the key variable is determined based on the largest lower bound function, then the selection of the key variable is transformed into the following optimization problem:

[0092] M * =arg max J(M s (28).

[0093] Because of the adoption of the above technical solution, the present invention has the following advantages:

[0094] 1. This application describes the relationship between monitoring variables of the health status of complex equipment and equipment degradation indicators by constructing a linear regression model with unknown noise information, which has a wide range of applications.

[0095] 2. This application proposes to use the variational Bayesian method for inference of linear regression models. This method provides state parameter estimation and noise estimation, thereby improving the model recognition accuracy.

[0096] 3. This application proposes to use the sparse variational Bayesian method to select monitoring variables for the health status of complex equipment, identify key variables, and improve the accuracy of remaining service life prediction.

[0097] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained from the following description and claims. Attached Figure Description

[0098] The accompanying drawings of this invention are described below.

[0099] Figure 1 is a schematic diagram of the method flow of the present invention.

[0100] Figure 2 shows the degradation trend of 70% of the data fitted using the sparse variational Bayesian method of the present invention.

[0101] Figure 3 shows the remaining lifetime estimation results obtained by the proposed sparse variational Bayesian method, the traditional method, and the Lasso method. Detailed Implementation

[0102] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0103] Example 1:

[0104] A method for predicting the remaining life of complex equipment based on sparse variational Bayesian methods, the specific steps of which are as follows:

[0105] 1) Data Acquisition: Download the remaining service life prediction dataset provided by NASA to obtain health status monitoring variables and equipment degradation index data for complex equipment; the method is as follows:

[0106] Let t i Let be the number of cycles for the engine in the i-th iteration, and Δt be the total number of cycles for the engine divided by the number of cycles t at the current moment. i The difference between them:

[0107] △t=max{t1,t2,...,t k}-t i (29)

[0108] In equation (29): t k This represents the total number of cycles the engine undergoes from its initial state to its complete failure state. The engine health status index y is defined. i for:

[0109]

[0110] In equation (30): 0 indicates that the engine is in a state of complete failure at that moment, and 1 indicates that the engine is in the initial state.

[0111] 2) Model Construction: Using the health status monitoring variables in the dataset obtained in step 1) as input variables and equipment degradation indicators as output variables, a linear regression model for predicting remaining service life with noisy data is constructed; the specific method is as follows:

[0112] Y=UΘ+ω (31)

[0113] In formula (31), Y=[y1,y2,...,y N ] T To equip N health state sequences within different periods, U = [U1, U2, ..., U...] M ] T For a matrix consisting of M monitored variable sequences, for each Ui (1≤i≤M), we have U i =[u i,1 ,u i,2 ,...,u i,N ] T The parameter vector Θ = [θ1, θ2, ..., θ M ] T The noise vector ω = [ω1, ω2, ..., ω] is measured. N ] T .

[0114] 3) Model training: The variational Bayes method is used to estimate the parameters of the regression model, output the weight coefficients of the model, and perform sparsification on the weight coefficients in the regression model, removing the weight coefficients with small proportions and their state monitoring variables, to obtain the linear regression model under different working conditions.

[0115] 3-1) Set time K-1 as the initial time and initialize the distribution of each parameter in the model; the specific steps are as follows:

[0116] 3-1-1) Suppose that the parameter vector Θ follows a Gaussian-Gamma distribution:

[0117]

[0118] In equation (32), α -1 Let be the variance of the Gaussian distribution, and a0 and b0 be the hyperparameters of the gamma distribution, respectively.

[0119] 3-1-2) Assume the measurement noise vector ω follows a Gaussian distribution:

[0120]

[0121] In equation (33), τ -1 Let be the variance of a Gaussian distribution, and let be a gamma distribution, i.e.:

[0122]

[0123] In equation (34), c0 and d0 are the hyperparameters of the gamma distribution, respectively;

[0124] 3-1-3) Assuming the parameters are independent of each other, their joint prior distribution can be expressed as:

[0125]

[0126] In formula (35), α=[α1,α2,...,α M ] T .

[0127] 3-2) Construct the objective function for parameter estimation. Based on the prior distribution of each parameter at time K-1, use the variational Bayesian method to approximate the posterior distribution of each parameter in the objective function at time K. The specific steps are as follows:

[0128] 3-2-1) Construct the objective function for parameter estimation, and perform mathematical transformations on the objective function based on the relevant ideas of variational Bayes; the specific steps are as follows:

[0129] 3-2-1-1) Constructing the objective function: Let y 1:N =[y1,y2,...,y N ] T Therefore, according to the Maximum Likelihood Estimation (MLE) algorithm, the identification of model parameters can be transformed into the following optimization problem:

[0130]

[0131] 3-2-1-2) For the output y 1:N Maximizing the probability density function is equivalent to maximizing its log-likelihood function, and the output function y 1:N The log-likelihood function can be written as:

[0132]

[0133] In equation (37), q(Θ,α,τ) is an arbitrary probability density function, which, according to Bayes' criterion, is:

[0134]

[0135] Then we have:

[0136] lnp(y 1:N )=J+KL (39)

[0137] In equation (39),

[0138]

[0139] In equation (40), KL represents q(Θ,α,τ) and p(Θ,α,τ|y 1:N The KL divergence between q(Θ,α,τ) and p(Θ,α,τ|y) is greater than or equal to 0 if and only if q(Θ,α,τ) = p(Θ,α,τ|y). 1:N When y = y, the equality holds, therefore lnp(y) = y. 1:N )≥J, J is lnp(y 1:N The lower bound function of ).

[0140] 3-3-1-3) Based on the ideas of variational Bayes, the log-likelihood function is mathematically transformed. The variational Bayes (VB) method uses the variational method to continuously maximize the lower bound function J by solving the posterior distribution q(Θ,α,τ), thereby realizing the likelihood function p(y). 1:N Maximizing ). Assuming that the parameters of each model are independent, and that they follow mean-field theory:

[0141] q(Θ,α,τ)=q(Θ)q(α)q(τ) (41)

[0142] Therefore, during the maximization of the lower bound function J, the posterior distributions of each parameter can be updated sequentially while keeping other parameters fixed.

[0143] 3-2-2) Combining the prior distributions of each parameter at time K-1, the posterior distributions of each parameter variable at time K are updated progressively, including the posterior distribution q. k (Θ), q k (α), q k (τ); The specific steps are as follows:

[0144] 3-2-2-1) Inferring the lower bound function J:

[0145] Let ξ∈Φ=[Θ,α,τ] and Φ -ξ ={Φ\ξ}, in the k-th iteration, the variational Bayesian method fixes the posterior distribution q. k (Φ -ξ ), update q k (ξ), the lower bound function J with respect to q k (ξ) can be represented as:

[0146]

[0147] In equation (42), C is a constant, and Q*(Θ,α,τ) can be expressed as:

[0148]

[0149] but,:

[0150] q k (ξ)∝Q*(Θ,α,τ)(44)

[0151] For the constructed linear regression model, its total probability density function p(y) 1:N ,Θ,α,τ), we have:

[0152]

[0153] 3-2-2-2) Update q(Θ):

[0154] The posterior distribution q(Θ) can be expressed as:

[0155]

[0156] In equation (46), C is a constant, then,

[0157]

[0158] In formula (47), Λ=diag(α1,α2,...,α M Let be a diagonal matrix, and the posterior distribution q(Θ) can be viewed as a Gaussian distribution:

[0159]

[0160] In equation (48),

[0161]

[0162] In equation (19), <·> is defined as the expected operation;

[0163] 3-2-2-3) Update q(α), q(τ):

[0164] The posterior distribution q(α) can be expressed as:

[0165]

[0166] The posterior distribution q(α) can be viewed as a gamma distribution:

[0167]

[0168] Based on the properties of gamma distribution, we have:

[0169]

[0170] Similarly, the posterior distribution q(τ) is obtained:

[0171]

[0172] The expected value and variance of the parameter τ are:

[0173]

[0174] 3-3) According to the VB maximization step of the variational Bayesian inference method, select the solution that optimizes the objective function at time K and apply it to time K+1; let time K = K+1, return to step 3-2), and repeat steps 3-2)-3-3) until the lower bound function of the objective function converges, and output the model coefficients and likelihood function values; the specific steps are as follows:

[0175] 3-3-1) Maximize the log-likelihood function lnp at time K. k (y 1:N ):

[0176]

[0177] (Fixed step 3-2) Update the obtained q k-1 (Θ,α,τ), update the parameters using the maximum value of the lower bound function J at time K, and apply the optimal solution of the parameters to time K+1:

[0178] q k (Θ,α,τ)=argmaxJ k (56)

[0179] 3-3-2) Solving for the lower bound function J k The value of J, if k -J k-1 <ε, where: ε is the designed threshold, then the output model parameters Θ, α, τ are values;

[0180] If J k -J k-1 If ≥ε, then return to step 3-2), and repeat steps 3-2)-3-3) until the lower bound function J satisfies the condition.

[0181] 3-4) Remove the model coefficients with smaller proportions obtained in step 3-3) and their corresponding health status monitoring variables, return to step 3-1), and repeat steps 3-1) to 3-4) until the ARD variable reaches its maximum. Output the optimal model parameters to obtain the optimized linear regression model. The specific steps are as follows:

[0182] 3-4-1) For model parameters θ i Assume it follows a normal distribution with a mean of 0, α i -1 It is its variance; using the variance value to characterize the importance of a parameter in the model is called automatic correlation determination of ARD variables. In sparse Bayesian analysis, the parameter α is used as the basis for variable selection. In the number of iterations s, let the set of variables in the model be M. s , where: M 0 ={1,2,...,M}, the model to be estimated is expressed as:

[0183] Y = U(M) s )Θ(M s )+ω (57)

[0184] Obtain the model parameters Θ(M) s ) and the ARD variable set, denoted as α(M s Based on the ARD variables and their meanings, after each iteration, in α(M) s Find the largest ARD value in the model and remove the corresponding variable to obtain a new model.

[0185] Let exID represent the variable index corresponding to the maximum ARD value, and let the new variable set be M. s+1 ={M s \exID}, rebuild the model based on the new set of variables and solve for the model parameters;

[0186] 3-4-2) The VB method, while obtaining the model parameters, also provides the corresponding likelihood function value of the model, i.e., the maximum lower bound function, denoted as J(M s If the key variable is determined based on the largest lower bound function, then the selection of the key variable is transformed into the following optimization problem:

[0187] M * =argmaxJ(M s (58).

[0188] 4) Remaining service life prediction: Collect the condition monitoring variables of the equipment to be predicted, and predict the remaining service life based on the linear regression model under different operating conditions in step 3). The specific steps are as follows:

[0189] 4-1) First, establish a similarity lifetime prediction model based on residuals.

[0190] Step 2) A health status model of the equipment under multiple monitoring variables was established. In order to accurately predict the RUL, the remaining service life of the equipment needs to be obtained through the equipment health status.

[0191] This embodiment uses a quadratic function to construct the degradation model, that is, it uses a quadratic function to fit the degradation trend of the equipment's historical health status data. Secondly, it uses the 1-norm to define the distance function d(i,j) and the score (i,j) between the historical data and the prediction model data, namely:

[0192]

[0193] In equation (59), y j Let j be the health status index of the j-th engine. To estimate the health status index of the j-th engine using a quadratic function model on the i-th engine, the following steps are taken: For each predicted health status sequence, the closest health status sequence data are obtained from the training dataset. A statistical measure of the data sample is constructed, and its probability distribution value is fitted. The median of the distribution is used as the predicted estimate of the RUL of the equipment component.

[0194] 4-2) Next, a validation set for lifetime prediction is selected, and the key variables for predicting the remaining service life of the equipment are selected using the sparse variational Bayesian method. Table 1 shows a comparison of the key variable selection between the method proposed in this application and existing methods.

[0195] Table 1 compares the selection of key variables on the aero-engine dataset using existing methods and the method proposed in this application.

[0196]

[0197]

[0198] Table 2 shows the variances of the prediction errors generated by the proposed method, Lasso's method, and traditional methods when the data volume is 50%, 70%, and 90%, respectively.

[0199] Table 2 compares the variance of prediction errors generated by the proposed method, Lasso's method, and traditional methods.

[0200]

[0201] As shown in Figures 2 and 3, when the engine operating cycle is 70%, the sparse Bayesian method proposed in this invention can fit the downward trend of the remaining service life prediction well, and the estimated value of the remaining service life prediction is closer to the true value. This method provides an effective method for selecting equipment health status monitoring variables, demonstrating the effectiveness of using the sparse variational Bayesian method for selecting monitoring variables in the case of multiple monitoring variables.

[0202] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0203] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more flowchart illustrations and / or one or more block diagrams.

[0204] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more block diagrams.

[0205] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.

[0206] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the remaining life of complex equipment based on sparse variational Bayes, characterized in that, The specific steps are as follows: 1) Data acquisition: Collect health status monitoring variables and equipment degradation index data of complex equipment from the database; 2) Model construction: Use the health status monitoring variables obtained in step 1) as input variables and equipment degradation index as output variables to construct a linear regression model for predicting the remaining service life of noisy data; 3) Model training: Use variational Bayesian method to estimate the parameters of the regression model, output the weight coefficients of the model, and perform sparsification on the weight coefficients in the regression model, removing the weight coefficients with small proportions and their status monitoring variables to obtain linear regression models under different operating conditions; 4) Remaining service life prediction: Collect the status monitoring variables of the equipment to be predicted, and predict the remaining service life according to the linear regression models under different operating conditions in step 3); The specific method for constructing the model in step 2) is as follows: In equation (1), For equipment A sequence of health statuses over different periods. for A matrix consisting of sequences of monitored variables, for each ,have parameter vector Measure noise vector The specific steps for model training in step 3) are as follows: 3-1) Setting up 3-2) Initialize the distribution of model parameters at the initial time; construct the objective function for parameter estimation based on... The prior distributions of each parameter at time step are analyzed using the variational Bayesian method. Approximate estimation of the posterior distribution of each parameter in the objective function at time step 3-3) Selecting the parameter that maximizes the VB based on the variational Bayesian inference method. The optimal solution of the objective function at time t is applied to Time; making time Return to step 3-2), repeat steps 3-2) to 3-3) until the lower bound of the objective function converges, and output the model coefficients and likelihood function values; 3-4) remove the model coefficients and their corresponding health status monitoring variables obtained in step 3-3), return to step 3-1), repeat steps 3-1) to 3-4) until the ARD variable reaches its maximum, output the optimal parameters of the model, and obtain the optimized linear regression model.

2. The method for predicting the remaining life of complex equipment based on sparse variational Bayes as described in claim 1, characterized in that, The specific steps for initializing the distribution of model parameters in step 3-1) are as follows: 3-1-1) Set the parameter vector Follows a Gaussian-Gamma distribution: In equation (2), Let V be the variance of the Gaussian distribution. Let be the hyperparameters of the gamma distribution; 3-1-2) Let the measurement noise vector be... Follows a Gaussian distribution: In equation (3), Let be the variance of a Gaussian distribution, and let be a gamma distribution, i.e.: In equation (4), Let be the hyperparameters of the gamma distribution; 3-1-3) Assume the parameters are independent of each other, and their joint prior distribution can be expressed as: In equation (5), 。 3. The method for predicting the remaining life of complex equipment based on sparse variational Bayes as described in claim 1, characterized in that, In step 3-2), the variational Bayes method is used to... The specific steps for approximating the posterior distributions of the parameters in the objective function at each time step are as follows: 3-2-1) Construct the objective function for parameter estimation, and perform mathematical transformations on the objective function based on the relevant ideas of variational Bayes; 3-2-2) Combine... The prior distribution of each parameter at each time stepwise is updated. The posterior distribution of each parameter variable at time t, including the posterior distribution. 、 、 。 4. The method for predicting the remaining life of complex equipment based on sparse variational Bayes as described in claim 3, characterized in that, The specific steps in 3-2-1) for constructing the objective function for parameter estimation and mathematically transforming the objective function according to the relevant ideas of variational Bayes are as follows: 3-2-1-1) Constructing the objective function: Let Then, according to the maximum likelihood estimation (MLE) algorithm, the identification of model parameters can be transformed into the following optimization problem: (6) 3-2-1-2) For the output Maximizing the probability density function is equivalent to maximizing its log-likelihood function, and the output function is... The log-likelihood function can be written as: In equation (7), For any probability density function, according to Bayes' criterion, we have: (8) Then we have: In equation (9), (10) Among them, for and The KL divergence between them, and If and only if When the equality holds, therefore, ， for The lower bound function; 3-2-1-3) Based on the relevant ideas of variational Bayes, its log-likelihood function is mathematically transformed. The variational Bayes (VB) method uses the variational method to solve the posterior distribution. continuously maximize the lower bound function Thus, the likelihood function is realized. To maximize; assuming that the parameters of each model are independent, and that each parameter follows mean-field theory: (11) Therefore, in the lower bound function During the maximization process, the posterior distributions of each parameter can be updated sequentially while keeping other parameters constant.

5. The method for predicting the remaining life of complex equipment based on sparse variational Bayes as described in claim 3, characterized in that, Step 3-2-2) combined The prior distribution of each parameter at each time stepwise is updated. The specific steps for determining the posterior distribution of each parameter variable within a given time step are as follows: 3-2-2-1) Inferring the lower bound function. :make and In the In the next iteration, the variational Bayes method fixes the posterior distribution. ,renew lower bound function about It can be represented as: In equation (12), It is a constant value. It can be represented as: (13) Then: (14) For the constructed linear regression model, its total probability density function ,have: (15) 3-2-2-2) Update posterior distribution It can be represented as: In equation (16), If it is a constant, then, In equation (17), It is a diagonal matrix, and its posterior distribution is... It can be viewed as a Gaussian distribution: In equation (18), In equation (19), Defined as the expected operation; 3-2-2-3) Update 、 posterior distribution It can be represented as: (20) Posterior distribution This can be viewed as a gamma distribution: (21) According to the properties of gamma distribution, we have: (22) Similarly, the posterior distribution is obtained. ： (23) Parameters The expected value and variance are: （24）。 6. The method for predicting the remaining life of complex equipment based on sparse variational Bayes as described in claim 1, characterized in that, The specific steps for outputting the model coefficients and likelihood function values ​​in step 3-3) are as follows: 3-3-1) Maximize the first... log-likelihood function at time 1 ： (25) Fixed step 3-2) Updated Using lower bound functions In the The maximum value at time step is used to update the parameters, and the optimal solution of the parameters is applied. time: (26) 3-3-2) Solve for the lower bound function The value, if ,in: The output model parameters are set to the designed threshold. The value; if If the function returns to step 3-2), repeat steps 3-2 to 3-3 until the lower bound function is reached. The conditions are met.

7. The method for predicting the remaining life of complex equipment based on sparse variational Bayes as described in claim 1, characterized in that, The specific steps for outputting the optimal parameters of the model in step 3-4) to obtain the optimized linear regression model are as follows: 3-4-1) For the model parameters Assume that it follows a normal distribution with a mean of 0. It is its variance; using the variance value to characterize the importance of a parameter in the model is called automatic correlation to determine ARD variables. In sparse Bayesian analysis, the parameters are used... As a basis for variable selection, the number of iterations In the model, let the set of variables be... ,in: The model to be estimated is expressed as: (27) Obtain the model parameters and the ARD variable set, represented as Based on the ARD variables and their meanings, after each iteration, in Find the largest ARD value and remove the corresponding variable to obtain a new model; let This represents the variable index corresponding to the maximum ARD value; the new variable set is... The model is rebuilt based on the new set of variables, and the model parameters are solved. (3-4-2) The VB method, while obtaining the model parameters, also provides the likelihood function value of the corresponding model, i.e., the maximum lower bound function, expressed as... Then, the key variables are determined based on the largest lower bound function, and the selection of key variables is transformed into the following optimization problem: （28）。

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