Residual life prediction method and system combining recurrent neural network and filtering algorithm

Abstract

The application provides a remaining life prediction method and system combining a recurrent neural network and a filtering algorithm, comprising the following steps: S1, collecting measured operation observation data and selecting characteristic data; S2, performing product performance degradation state mining and low-dimensional fusion feature extraction on the selected characteristic data; S3, constructing a state space model based on the low-dimensional fusion features, estimating model parameters, and establishing a filtering remaining life prediction model; S4, taking the low-dimensional fusion features as a training set, training a recurrent neural network, and establishing a product degradation state prediction model based on an LSTM algorithm; S5, constructing a remaining life prediction fusion algorithm combining an LSTM recurrent neural network and a filtering algorithm; and S6, realizing online prediction of the remaining life of a product equipment system by using the constructed fusion algorithm. The application improves the accuracy and effectiveness of product degradation data analysis.

Description

Technical Field

[0001] This invention relates to the field of remaining service life prediction for in-service equipment. Specifically, it relates to a method and system for predicting remaining service life by combining a recurrent neural network and a filtering algorithm. More specifically, it relates to a method and system for predicting the remaining service life of product equipment by combining an LSTM recurrent neural network and a filtering algorithm. Background Technology

[0002] Traditional product life prediction methods mostly rely on reliability test data to calculate the MTBF of key components or to model a specific characteristic parameter of the product to assess relevant reliability indicators. For complex systems, such as large-scale control systems, traditional evaluation methods typically involve analyzing components and then using methods such as establishing system reliability block diagrams, fault trees, and system state transition models to extrapolate relevant system reliability indicators from the reliability data of each component and subsystem. However, as the functions of various products and equipment become increasingly rich and the corresponding system compositions become more complex, coupled with the limitations of traditional testing methods in data acquisition (complex system failure mechanisms, difficulty in experimental simulation, inability to meet the requirements of a large number of test samples, and long testing cycles), and the uncertainties in the coupling relationships between components and subsystems in complex systems due to the updating of materials and technologies, previous empirical models have led to problems such as one-sided conclusions and a lack of accurate system life prediction in system reliability assessment and life prediction.

[0003] Complex electromechanical products often contain key system components with a large amount of operational observation data. For such products, effectively utilizing the large amount of observation data of the system itself for degradation analysis can improve the accuracy of the remaining service life prediction. Based on the comprehensive analysis of the current mainstream technical theory research and engineering application of product equipment remaining service life prediction, the remaining service life prediction technology mainly includes (1) remaining service life prediction method based on failure physics model, (2) remaining service life prediction method based on statistical model, (3) remaining service life prediction method based on machine learning model, and (4) remaining service life prediction method based on hybrid model. The first three types of prediction methods have their own advantages and disadvantages for different application scenarios in the field of product remaining service life prediction. At present, many studies have proposed fusion prediction models in the hope of combining the advantages of various models to improve the applicability and accuracy of the prediction model. In the fusion model, the machine learning model is often combined with the random coefficient model. Since the fusion model can give full play to the advantages of various prediction models in different application scenarios, improve the applicability of the model and improve the accuracy of the prediction results, the fusion model is also one of the key research directions of the current remaining service life prediction model.

[0004] Patent document CN113536671A discloses a lithium battery lifetime prediction method based on LSTM, comprising: acquiring a lithium battery capacity degradation dataset; preprocessing the capacity degradation dataset; constructing an LSTM-based remaining lifetime prediction model; and after constructing the LSTM-based remaining lifetime prediction model, further constructing three local lithium battery lifetime prediction models and a central server-side global lifetime prediction model. The LSTM is a network structure, where each LSTM unit includes a forget gate, an input gate, and an output gate. The three local lithium battery lifetime prediction models have identical structures, each including two LSTM layers, two dropout layers to prevent overfitting, and a top-level prediction output layer. This patent only involves LSTM models, requires full-lifecycle data acquisition, and the method outputs point estimates lacking uncertainty expression capabilities, indicating room for improvement in these aspects.

[0005] Patent document CNIO395575OA discloses a method for predicting the remaining life of rolling bearings based on feature fusion and particle filtering. The method includes: extracting original features from bearing vibration signals; clustering the extracted features using a correlation clustering method; selecting a typical feature from each cluster to form an optimal feature set; fusing the feature set into a final degradation index using a weighted fusion method; smoothing and resampling the degradation index; adjusting the time interval to the expected value; calculating the initial parameters of the state-space model using least-squares fitting; updating the model parameters in real time based on new observation data; and predicting the remaining bearing life. This patent only relates to a filtered life prediction method. The filtering algorithm can be updated in real time and has the ability to express uncertainty. However, its prediction and updating are heavily dependent on the establishment of the state-space model. When dealing with nonlinear problems, its ability to track and predict the degradation state of the system is weaker than that of the LSTM model, and there is still room for improvement in these aspects. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for predicting remaining lifetime that combines recurrent neural networks and filtering algorithms.

[0007] A remaining lifetime prediction method combining recurrent neural networks and filtering algorithms, provided by the present invention, includes:

[0008] Step S1: Collect operational observation data and select characteristic data;

[0009] Step S2: Min the product performance degradation status and extract low-dimensional fusion features from the selected feature data;

[0010] Step S3: Construct a state-space model based on low-dimensional fusion features, estimate the model parameters, and establish a filter remaining lifetime prediction model;

[0011] Step S4: Using low-dimensional fusion features as the training set, train a recurrent neural network to establish a product degradation state prediction model based on the LSTM algorithm;

[0012] Step S5: Construct a fusion algorithm for remaining lifetime prediction that combines an LSTM recurrent neural network and a filtering algorithm;

[0013] Step S6: Use the constructed fusion algorithm to realize online prediction of the remaining life of the product equipment system.

[0014] Preferably, in step S1:

[0015] Collect operational observation data measured by sensors on product equipment components, and select preset characteristic data that can reflect the trend of product performance degradation:

[0016] Based on the correlation between observed data and product degradation trends, the data with the most significant trend characteristics are selected to characterize the system degradation state;

[0017] Identifying candidate subsets from the data and optimized evaluation criteria ;

[0018] A filtering-based feature selection method is used to extract key features, and a candidate subset for feature selection is defined. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest;

[0019] The selected feature data includes both homogeneous and heterogeneous data.

[0020] Preferably, in step S2:

[0021] Step S2.1: Identify the product performance degradation status;

[0022] A regularized particle filter algorithm is used to detect performance degradation states. The specific steps of the regularized particle filter algorithm include:

[0023] Step S2.1.1: The degradation state is a separable process. The state-space model established for the component sensor is represented as follows:

[0024]

[0025] In the formula, Let be the degenerate state variable at time t, where t is the current observation time. Here, i represents the sensor observation value, and i is the sensor number. For the error of the constant term, the coefficient The constant value obtained by fitting the data increment curve of calibration data obtained from past observations; This is process noise, reflecting the inherent uncertainty of the degradation state. This represents observed noise, which has zero mean and variance. Gaussian distribution;

[0026] Step S2.1.2: Sample N particles from the initial distribution. Given the same weights, ; express Time of the first The weight of each particle;

[0027] Step S2.1.3: Given In the prior probability density function Collect N particles ;

[0028] Step S2.1.4: Obtain the observed values ,according to Update particle weights, at which point the proposed distribution is selected. The weights are normalized. ;

[0029] Step S2.1.5: When the number of effective particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A; A is the state transition matrix;

[0030] From particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution; Let i be the number of the i-th sensor of the j-th type, under the standard Gaussian kernel function. =1;

[0031] Step S2.1.6: Update the... The estimate makes Returning to c enables dynamic updates;

[0032] The Monte Carlo method is used to construct the posterior probability density by sampling particles and their corresponding weights:

[0033] From the probability density p(z)t |x 1：t If N particles are sampled from a given sample, the posterior probability density is:

[0034]

[0035] in Let z be the Dirac function. t i For sampled particles, for any function f( The expected Monte Carlo estimate is:

[0036]

[0037] Sequential importance sampling is used to sample the posterior probability density function distribution.

[0038] in This is called the proposal distribution. For the filtering problem, the weights of the sampling points corresponding to each observation time of the dynamic system are:

[0039] Solving particle degradation problem using resampling method:

[0040] In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation.

[0041]

[0042] In the formula, Effective particle count, var(w) t ) for w t The second-order moment;

[0043] when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​is expressed as:

[0044] Where j is the corresponding number of the component sensor, Let i be the number of sensors of type i. express Time of the first The weight of each particle, This represents the Dirac delta function;

[0045] Estimation is performed using the standard Gaussian kernel function:

[0046]

[0047]

[0048] In the formula, Let be the continuous approximate probability density of the state variables of a nonlinear dynamic system at time t. For kernel density function, Let z be the state vector t The dimension of the sample is given by det, which is the determinant obtained by solving for the empirical covariance matrix of the sampled data. ;

[0049] Step S2.2: Low-dimensional fusion feature extraction specifically includes fusing homogeneous data using a distributed filtering algorithm and extracting low-dimensional fusion features from heterogeneous data using kernel principal component analysis.

[0050] Step S2.2.1: The weight allocation method for each filter does not use the product of the observed value minus the state estimate and the relation matrix as the standard for weight allocation. Instead, it uses the number of effective particles in the particle filtering process of each filter as the basis for weight allocation.

[0051]

[0052] in, Number each sub-filter;

[0053] Step S2.2.2: Kernel principal component analysis in subspace learning is used to achieve heterogeneous data fusion. Nonlinear data is mapped to a high-dimensional feature space through a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. The k-th principal component of the data is obtained by mapping with a Gaussian kernel. for:

[0054]

[0055] in, Let be the eigenvector corresponding to the covariance matrix of the k-th principal component. It is a nonlinear mapping function. The constant term coefficients of the eigenvectors are represented by the mapping function.

[0056] Preferably, in step S3:

[0057] The system The degradation process of the remaining lifetime prediction at time point is represented as follows:

[0058]

[0059] In the formula, for Time-degradation state estimate, This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. Indicates Brownian motion;

[0060] exist The remaining lifetime at a given time is expressed as:

[0061]

[0062] in, This is the failure threshold;

[0063] The probability density function of the system's remaining lifetime is then expressed as:

[0064]

[0065] in, The diffusion coefficient during the degradation process;

[0066] In step S4:

[0067] Step S4.1: Calculate the forget gate input for the model:

[0068]

[0069] in, This is the connection weight matrix between the forget gate and the input gate. A matrix of constant terms, h t-1 This represents the output of the previous node, x. t This represents the input of the current node, and σ represents the sigmoid function;

[0070] Step S4.2: Calculate the input gate input:

[0071]

[0072]

[0073]

[0074] in, The information that needs to be updated is determined by the sigmoid layer. The vector generated by the tanh layer is used as a candidate for update. For each connection weight matrix, For each constant term, This is the updated node state value. The coefficients of the constant term;

[0075] Step S4.3: Calculate the output gate output to determine the node output value:

[0076]

[0077]

[0078] in, The portion to be output for the sigmoid layer. To connect the weight matrix, The coefficient of the constant term, To update the node state value after input at time t, h t To output information.

[0079] Preferably, in step S5:

[0080] Step S5.1: Select observation feature data;

[0081] Step S5.2: Implement system degradation information mining and low-dimensional fusion feature extraction;

[0082] Step S5.3: Train the LSTM model using the extracted low-dimensional comprehensive degradation feature data to determine the model parameters;

[0083] Step S5.4: Establish a dynamic system state-space model for the system degradation characteristics and determine the model parameters;

[0084] Step S5.5: Predict the degradation state at time t+1 using the LSTM model with determined model parameters. ;

[0085] Step S5.6: Utilize algorithms based on the system state-space model to obtain system observations. For the predicted state Perform the update and calculate the updated mean squared error;

[0086] Step S5.7: Implement system remaining lifetime prediction, return to step S5.5, and implement online dynamic prediction;

[0087] In step S6:

[0088] Step S6.1: The constructed fusion model can achieve short-term prediction of the system's degradation state;

[0089] Step S6.2: The remaining lifetime prediction results output by the fusion model method include point estimates and interval estimates;

[0090] Step S6.3: The constructed fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy.

[0091] A remaining lifetime prediction system combining a recurrent neural network and a filtering algorithm, provided by the present invention, includes:

[0092] Module M1: Collects operational observation data from measurements and selects characteristic data;

[0093] Module M2: Performs product performance degradation state mining and low-dimensional fusion feature extraction on the selected feature data;

[0094] Module M3: Constructs a state-space model based on low-dimensional fusion features, estimates model parameters, and establishes a filter remaining lifetime prediction model;

[0095] Module M4: Using low-dimensional fused features as the training set, a recurrent neural network is trained to establish a product degradation state prediction model based on the LSTM algorithm;

[0096] Module M5: Constructs a fusion algorithm for remaining lifetime prediction that combines an LSTM recurrent neural network with a filtering algorithm;

[0097] Module M6: Uses a constructed fusion algorithm to achieve online prediction of the remaining lifespan of product equipment systems.

[0098] Preferably, in module M1:

[0099] Collect operational observation data measured by sensors on product equipment components, and select preset characteristic data that can reflect the trend of product performance degradation:

[0100] Based on the correlation between observed data and product degradation trends, the data with the most significant trend characteristics are selected to characterize the system degradation state;

[0101] Identifying candidate subsets from the data and optimized evaluation criteria ;

[0102] A filtering-based feature selection method is used to extract key features, and a candidate subset for feature selection is defined. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest;

[0103] The selected feature data includes both homogeneous and heterogeneous data.

[0104] Preferably, in module M2:

[0105] Module M2.1: Product performance degradation status detection;

[0106] A regularized particle filter algorithm is used to detect performance degradation states. The specific steps of the regularized particle filter algorithm include:

[0107] Module M2.1.1: The degradation state is a separable process. The state-space model established for the component sensor is represented as follows:

[0108]

[0109] In the formula, Let be the degenerate state variable at time t, where t is the current observation time. Here, i represents the sensor observation value, and i is the sensor number. For the error of the constant term, the coefficient The constant value obtained by fitting the data increment curve of calibration data obtained from past observations; This is process noise, reflecting the inherent uncertainty of the degradation state. This represents observed noise, which has zero mean and variance. Gaussian distribution;

[0110] Module M2.1.2: Sample N particles from the initial distribution Given the same weights, ; express Time of the first The weight of each particle;

[0111] Module M2.1.3: Given In the prior probability density function Collect N particles ;

[0112] Module M2.1.4: Obtaining Observations ,according to Update particle weights, at which point the proposed distribution is selected. The weights are normalized. ;

[0113] Module M2.1.5: When the effective number of particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A; A is the state transition matrix;

[0114] From particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution; Let i be the number of the i-th sensor of the j-th type, under the standard Gaussian kernel function. =1;

[0115] Module M2.1.6: Updates to The estimate makes Returning to c enables dynamic updates;

[0116] The Monte Carlo method is used to construct the posterior probability density by sampling particles and their corresponding weights:

[0117] From the probability density p(z) t |x 1：t If N particles are sampled from a given sample, the posterior probability density is:

[0118]

[0119] in Let z be the Dirac function. t i For sampled particles, for any function f( The expected Monte Carlo estimate is:

[0120]

[0121] Sequential importance sampling is used to sample the posterior probability density function distribution.

[0122] in This is called the proposal distribution. For the filtering problem, the weights of the sampling points corresponding to each observation time of the dynamic system are:

[0123] Solving particle degradation problem using resampling method:

[0124] In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation.

[0125]

[0126] In the formula, Effective particle count, var(w) t ) for w t The second-order moment;

[0127] when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​is expressed as:

[0128] Where j is the corresponding number of the component sensor, Let i be the number of sensors of type i. express Time of the first The weight of each particle, This represents the Dirac delta function;

[0129] Estimation is performed using the standard Gaussian kernel function:

[0130]

[0131]

[0132] In the formula, Let be the continuous approximate probability density of the state variables of a nonlinear dynamic system at time t. For kernel density function, Let z be the state vector t The dimension of the sample is given by det, which is the determinant obtained by solving for the empirical covariance matrix of the sampled data. ;

[0133] Module M2.2: Low-dimensional fusion feature extraction specifically includes using a distributed filtering algorithm to fuse data from the same source and using kernel principal component analysis to extract low-dimensional fusion features from data from different sources.

[0134] Module M2.2.1: The weight allocation method for each filter does not use the product of the observed value minus the state estimate and the relation matrix as the standard for weight allocation. Instead, it uses the number of effective particles in the particle filtering process of each filter as the basis for weight allocation.

[0135]

[0136] in, Number each sub-filter;

[0137] Module M2.2.2: This module employs kernel principal component analysis (KPI) from subspace learning to achieve heterogeneous data fusion. Nonlinear data is mapped to a high-dimensional feature space using a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. A Gaussian kernel is used for mapping to determine the k-th principal component of the data. for:

[0138]

[0139] in, Let be the eigenvector corresponding to the covariance matrix of the k-th principal component. It is a nonlinear mapping function. The constant term coefficients of the eigenvectors are represented by the mapping function.

[0140] Preferably, in module M3:

[0141] The system The degradation process of the remaining lifetime prediction at time point is represented as follows:

[0142]

[0143] In the formula, for Time-degradation state estimate, This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. Indicates Brownian motion;

[0144] exist The remaining lifetime at a given time is expressed as:

[0145]

[0146] in, This is the failure threshold;

[0147] The probability density function of the system's remaining lifetime is then expressed as:

[0148]

[0149] in, The diffusion coefficient during the degradation process;

[0150] In module M4:

[0151] Module M4.1: Computational Model Forget Gate Input:

[0152]

[0153] in, This is the connection weight matrix between the forget gate and the input gate. A matrix of constant terms, h t-1 This represents the output of the previous node, x. t This represents the input of the current node, and σ represents the sigmoid function;

[0154] Module M4.2: Calculation Input Gate Input:

[0155]

[0156]

[0157]

[0158] in, The information that needs to be updated is determined by the sigmoid layer. The vector generated by the tanh layer is used as a candidate for update. For each connection weight matrix, For each constant term, This is the updated node state value. The coefficients of the constant term;

[0159] Module M4.3: Calculates the output gate output to determine the node output value.

[0160]

[0161]

[0162] in, The portion to be output for the sigmoid layer. To connect the weight matrix, The coefficient of the constant term, To update the node state value after input at time t, h t To output information.

[0163] Preferably, in module M5:

[0164] Module M5.1: Select observation feature data;

[0165] Module M5.2: Enables system degradation information mining and low-dimensional fusion feature extraction;

[0166] Module M5.3: Trains the LSTM model using extracted low-dimensional comprehensive degradation feature data to determine the model parameters;

[0167] Module M5.4: Establish a dynamic system state-space model for system degradation characteristics and determine the model parameters;

[0168] Module M5.5: Predicts the degenerate state at time t+1 using an LSTM model with defined parameters. ;

[0169] Module M5.6: Implementing system observations using algorithms based on the system state-space model. For the predicted state Perform the update and calculate the updated mean squared error;

[0170] Module M5.7: Implements system remaining lifetime prediction, returns to module M5.5, and implements online dynamic prediction;

[0171] In module M6:

[0172] Module M6.1: The constructed fusion model can achieve short-term prediction of the system's degradation state;

[0173] Module M6.2: The remaining lifetime prediction results output by the fusion model method include point estimates and interval estimates;

[0174] Module M6.3: The constructed fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy.

[0175] Compared with the prior art, the present invention has the following beneficial effects:

[0176] This invention establishes a product remaining life prediction fusion model based on the filtering prediction method in statistical models and the LSTM recurrent neural network prediction method in machine learning technology. Compared with the existing product equipment remaining life prediction algorithms, the fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy, thereby improving the accuracy and effectiveness of product degradation data analysis. Attached Figure Description

[0177] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0178] Figure 1 For the dynamic system model of filtering;

[0179] Figure 2 Training process for parameters of a recurrent neural network model;

[0180] Figure 3 For the network structure modules of the LSTM model;

[0181] Figure 4 This is a block diagram of the LSTM model and filter fusion algorithm.

[0182] Figure 5 The remaining lifetime prediction result of a system based on a filtering algorithm;

[0183] Figure 6 For tracking and predicting observation data of a certain system based on an LSTM model;

[0184] Figure 7 For tracking and predicting observation data of a certain system based on an LSTM and filter fusion model;

[0185] Figure 8 For predicting the remaining lifetime of a certain system based on an LSTM and filter fusion model;

[0186] Figure 9 Comparison of the mean square error of each model in predicting the degradation state of a certain system;

[0187] Figure 10 The mean square error of each model in predicting the remaining lifetime of a certain system is compared. Detailed Implementation

[0188] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0189] Example 1:

[0190] This invention provides an optimized fusion algorithm for online remaining life prediction of complex equipment. Addressing the problems of scarce product failure life data and poor adaptability of various degradation process analysis models to product performance observation data in predicting the remaining life of critical system components with abundant operational observation data, this invention fully mines component degradation data and, based on relevant degradation analysis techniques, establishes a fusion model for product remaining life prediction using a combination of filtering prediction methods in statistical models and LSTM recurrent neural network prediction methods in machine learning. This fusion model combines the ability of filtering prediction models to mine product degradation states and express uncertainty with the good data adaptability and prediction accuracy of LSTM recurrent neural network models, improving the accuracy and effectiveness of product degradation data analysis. It can effectively predict the life of critical components and provide reliable fault warnings and auxiliary references for fault repair for critical system components with abundant operational observation data.

[0191] According to the present invention, a method for predicting remaining lifetime combining a recurrent neural network and a filtering algorithm is provided, such as... Figures 1-10 As shown, it includes:

[0192] Step S1: Collect operational observation data and select characteristic data;

[0193] Specifically, in step S1:

[0194] Collect operational observation data measured by sensors on product equipment components, and select preset characteristic data that can reflect the trend of product performance degradation:

[0195] Based on the correlation between observed data and product degradation trends, the data with the most significant trend characteristics are selected to characterize the system degradation state;

[0196] Identifying candidate subsets from the data and optimized evaluation criteria ;

[0197] A filtering-based feature selection method is used to extract key features, and a candidate subset for feature selection is defined. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest;

[0198] The selected feature data includes both homogeneous and heterogeneous data.

[0199] Step S2: Min the product performance degradation status and extract low-dimensional fusion features from the selected feature data;

[0200] Specifically, in step S2:

[0201] Step S2.1: Identify the product performance degradation status;

[0202] A regularized particle filter algorithm is used to detect performance degradation states. The specific steps of the regularized particle filter algorithm include:

[0203] Step S2.1.1: The degradation state is a separable process. The state-space model established for the component sensor is represented as follows:

[0204]

[0205] In the formula, Let be the degenerate state variable at time t, where t is the current observation time. Here, i represents the sensor observation value, and i is the sensor number. For the error of the constant term, the coefficient The constant value obtained by fitting the data increment curve of calibration data obtained from past observations; This is process noise, reflecting the inherent uncertainty of the degradation state. This represents observed noise, which has zero mean and variance. Gaussian distribution;

[0206] Step S2.1.2: Sample N particles from the initial distribution. Given the same weights, ; express Time of the first The weight of each particle;

[0207] Step S2.1.3: Given In the prior probability density function Collect N particles ;

[0208] Step S2.1.4: Obtain the observed values ,according to Update particle weights, at which point the proposed distribution is selected. The weights are normalized. ;

[0209] Step S2.1.5: When the number of effective particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A; A is the state transition matrix;

[0210] From particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution; Let i be the number of the i-th sensor of the j-th type, under the standard Gaussian kernel function. =1;

[0211] Step S2.1.6: Update the... The estimate makes Returning to c enables dynamic updates;

[0212] The Monte Carlo method is used to construct the posterior probability density by sampling particles and their corresponding weights:

[0213] From the probability density p(z) t |x 1：t If N particles are sampled from a given sample, the posterior probability density is:

[0214]

[0215] in Let z be the Dirac function. t i For sampled particles, for any function f( The expected Monte Carlo estimate is:

[0216]

[0217] Sequential importance sampling is used to sample the posterior probability density function distribution.

[0218] in This is called the proposal distribution. For the filtering problem, the weights of the sampling points corresponding to each observation time of the dynamic system are:

[0219] Solving particle degradation problem using resampling method:

[0220] In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation.

[0221]

[0222] In the formula, Effective particle count, var(w) t ) for w t The second-order moment;

[0223] when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​is expressed as:

[0224] Where j is the corresponding number of the component sensor, Let i be the number of sensors of type i. express Time of the first The weight of each particle, This represents the Dirac delta function;

[0225] Estimation is performed using the standard Gaussian kernel function:

[0226]

[0227]

[0228] In the formula, Let be the continuous approximate probability density of the state variables of a nonlinear dynamic system at time t. For kernel density function, Let z be the state vector t The dimension of the sample is given by det, which is the determinant obtained by solving for the empirical covariance matrix of the sampled data. ;

[0229] Step S2.2: Low-dimensional fusion feature extraction specifically includes fusing homogeneous data using a distributed filtering algorithm and extracting low-dimensional fusion features from heterogeneous data using kernel principal component analysis.

[0230] Step S2.2.1: The weight allocation method for each filter does not use the product of the observed value minus the state estimate and the relation matrix as the standard for weight allocation. Instead, it uses the number of effective particles in the particle filtering process of each filter as the basis for weight allocation.

[0231]

[0232] in, Number each sub-filter;

[0233] Step S2.2.2: Kernel principal component analysis in subspace learning is used to achieve heterogeneous data fusion. Nonlinear data is mapped to a high-dimensional feature space through a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. The k-th principal component of the data is obtained by mapping with a Gaussian kernel. for:

[0234]

[0235] in, Let be the eigenvector corresponding to the covariance matrix of the k-th principal component. It is a nonlinear mapping function. The constant term coefficients of the eigenvectors are represented by the mapping function.

[0236] Step S3: Construct a state-space model based on low-dimensional fusion features, estimate the model parameters, and establish a filter remaining lifetime prediction model;

[0237] Specifically, in step S3:

[0238] The system The degradation process of the remaining lifetime prediction at time point is represented as follows:

[0239]

[0240] In the formula, for Time-degradation state estimate, This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. Indicates Brownian motion;

[0241] exist The remaining lifetime at a given time is expressed as:

[0242]

[0243] in, This is the failure threshold;

[0244] The probability density function of the system's remaining lifetime is then expressed as:

[0245]

[0246] in, The diffusion coefficient during the degradation process;

[0247] Step S4: Using low-dimensional fusion features as the training set, train a recurrent neural network to establish a product degradation state prediction model based on the LSTM algorithm;

[0248] In step S4:

[0249] Step S4.1: Calculate the forget gate input for the model:

[0250]

[0251] in, This is the connection weight matrix between the forget gate and the input gate. A matrix of constant terms, h t-1 This represents the output of the previous node, x. t This represents the input of the current node, and σ represents the sigmoid function;

[0252] Step S4.2: Calculate the input gate input:

[0253]

[0254]

[0255]

[0256] in, The information that needs to be updated is determined by the sigmoid layer. The vector generated by the tanh layer is used as a candidate for update. For each connection weight matrix, For each constant term, This is the updated node state value. The coefficients of the constant term;

[0257] Step S4.3: Calculate the output gate output to determine the node output value:

[0258]

[0259]

[0260] in, The portion to be output for the sigmoid layer. To connect the weight matrix, The coefficient of the constant term, To update the node state value after input at time t, h t To output information.

[0261] Step S5: Construct a fusion algorithm for remaining lifetime prediction that combines an LSTM recurrent neural network and a filtering algorithm;

[0262] Specifically, in step S5:

[0263] Step S5.1: Select observation feature data;

[0264] Step S5.2: Implement system degradation information mining and low-dimensional fusion feature extraction;

[0265] Step S5.3: Train the LSTM model using the extracted low-dimensional comprehensive degradation feature data to determine the model parameters;

[0266] Step S5.4: Establish a dynamic system state-space model for the system degradation characteristics and determine the model parameters;

[0267] Step S5.5: Predict the degradation state at time t+1 using the LSTM model with determined model parameters. ;

[0268] Step S5.6: Utilize algorithms based on the system state-space model to obtain system observations. For the predicted state Perform the update and calculate the updated mean squared error;

[0269] Step S5.7: Implement system remaining lifetime prediction, return to step S5.5, and implement online dynamic prediction;

[0270] Step S6: Use the constructed fusion algorithm to realize online prediction of the remaining life of the product equipment system.

[0271] In step S6:

[0272] Step S6.1: The constructed fusion model can achieve short-term prediction of the system's degradation state;

[0273] Step S6.2: The remaining lifetime prediction results output by the fusion model method include point estimates and interval estimates;

[0274] Step S6.3: The constructed fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy.

[0275] Example 2:

[0276] Example 2 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0277] Those skilled in the art can understand the remaining lifetime prediction method combining recurrent neural networks and filtering algorithms provided by the present invention as a specific implementation of the remaining lifetime prediction system combining recurrent neural networks and filtering algorithms. That is, the remaining lifetime prediction system combining recurrent neural networks and filtering algorithms can be implemented by executing the steps of the remaining lifetime prediction method combining recurrent neural networks and filtering algorithms.

[0278] A remaining lifetime prediction system combining a recurrent neural network and a filtering algorithm, provided by the present invention, includes:

[0279] Module M1: Collects operational observation data from measurements and selects characteristic data;

[0280] Specifically, in module M1:

[0281] Collect operational observation data measured by sensors on product equipment components, and select preset characteristic data that can reflect the trend of product performance degradation:

[0282] Based on the correlation between observed data and product degradation trends, the data with the most significant trend characteristics are selected to characterize the system degradation state;

[0283] Identifying candidate subsets from the data and optimized evaluation criteria ;

[0284] A filtering-based feature selection method is used to extract key features, and a candidate subset for feature selection is defined. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest;

[0285] The selected feature data includes both homogeneous and heterogeneous data.

[0286] Module M2: Performs product performance degradation state mining and low-dimensional fusion feature extraction on the selected feature data;

[0287] Specifically, in module M2:

[0288] Module M2.1: Product performance degradation status detection;

[0289] A regularized particle filter algorithm is used to detect performance degradation states. The specific steps of the regularized particle filter algorithm include:

[0290] Module M2.1.1: The degradation state is a separable process. The state-space model established for the component sensor is represented as follows:

[0291]

[0292] In the formula, Let be the degenerate state variable at time t, where t is the current observation time. Here, i represents the sensor observation value, and i is the sensor number. For the error of the constant term, the coefficient The constant value obtained by fitting the data increment curve of calibration data obtained from past observations; This is process noise, reflecting the inherent uncertainty of the degradation state. This represents observed noise, which has zero mean and variance. Gaussian distribution;

[0293] Module M2.1.2: Sample N particles from the initial distribution Given the same weights, ; express Time of the first The weight of each particle;

[0294] Module M2.1.3: Given In the prior probability density function Collect N particles ;

[0295] Module M2.1.4: Obtaining Observations ,according to Update particle weights, at which point the proposed distribution is selected. The weights are normalized. ;

[0296] Module M2.1.5: When the effective number of particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A; A is the state transition matrix;

[0297] From particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution; Let i be the number of the i-th sensor of the j-th type, under the standard Gaussian kernel function. =1;

[0298] Module M2.1.6: Updates to The estimate makes Returning to c enables dynamic updates;

[0299] The Monte Carlo method is used to construct the posterior probability density by sampling particles and their corresponding weights:

[0300] From the probability density p(z) t |x 1：t If N particles are sampled from a given sample, the posterior probability density is:

[0301]

[0302] in Let z be the Dirac function. t i For sampled particles, for any function f( The expected Monte Carlo estimate is:

[0303]

[0304] Sequential importance sampling is used to sample the posterior probability density function distribution.

[0305] in This is called the proposal distribution. For the filtering problem, the weights of the sampling points corresponding to each observation time of the dynamic system are:

[0306] Solving particle degradation problem using resampling method:

[0307] In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation.

[0308]

[0309] In the formula, Effective particle count, var(w) t ) for w t The second-order moment;

[0310] when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​is expressed as:

[0311] Where j is the corresponding number of the component sensor, Let i be the number of sensors of type i. express Time of the first The weight of each particle, This represents the Dirac delta function;

[0312] Estimation is performed using the standard Gaussian kernel function:

[0313]

[0314]

[0315] In the formula, Let be the continuous approximate probability density of the state variables of a nonlinear dynamic system at time t. For kernel density function, Let z be the state vector t The dimension of the sample is given by det, which is the determinant obtained by solving for the empirical covariance matrix of the sampled data. ;

[0316] Module M2.2: Low-dimensional fusion feature extraction specifically includes using a distributed filtering algorithm to fuse data from the same source and using kernel principal component analysis to extract low-dimensional fusion features from data from different sources.

[0317] Module M2.2.1: The weight allocation method for each filter does not use the product of the observed value minus the state estimate and the relation matrix as the standard for weight allocation. Instead, it uses the number of effective particles in the particle filtering process of each filter as the basis for weight allocation.

[0318]

[0319] in, Number each sub-filter;

[0320] Module M2.2.2: This module employs kernel principal component analysis (KPI) from subspace learning to achieve heterogeneous data fusion. Nonlinear data is mapped to a high-dimensional feature space using a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. A Gaussian kernel is used for mapping to determine the k-th principal component of the data. for:

[0321]

[0322] in, Let be the eigenvector corresponding to the covariance matrix of the k-th principal component. It is a nonlinear mapping function. The constant term coefficients of the eigenvectors are represented by the mapping function.

[0323] Module M3: Constructs a state-space model based on low-dimensional fusion features, estimates model parameters, and establishes a filter remaining lifetime prediction model;

[0324] Specifically, in module M3:

[0325] The system The degradation process of the remaining lifetime prediction at time point is represented as follows:

[0326]

[0327] In the formula, for Time-degradation state estimate, This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. Indicates Brownian motion;

[0328] exist The remaining lifetime at a given time is expressed as:

[0329]

[0330] in, This is the failure threshold;

[0331] The probability density function of the system's remaining lifetime is then expressed as:

[0332]

[0333] in, The diffusion coefficient during the degradation process;

[0334] Module M4: Using low-dimensional fused features as the training set, a recurrent neural network is trained to establish a product degradation state prediction model based on the LSTM algorithm;

[0335] In module M4:

[0336] Module M4.1: Computational Model Forget Gate Input:

[0337]

[0338] in, This is the connection weight matrix between the forget gate and the input gate. A matrix of constant terms, h t-1 This represents the output of the previous node, x. t This represents the input of the current node, and σ represents the sigmoid function;

[0339] Module M4.2: Calculation Input Gate Input:

[0340]

[0341]

[0342]

[0343] in, The information that needs to be updated is determined by the sigmoid layer. The vector generated by the tanh layer is used as a candidate for update. For each connection weight matrix, For each constant term, This is the updated node state value. The coefficients of the constant term;

[0344] Module M4.3: Calculates the output gate output to determine the node output value.

[0345]

[0346]

[0347] in, The portion to be output for the sigmoid layer. To connect the weight matrix, The coefficient of the constant term, To update the node state value after input at time t, h t To output information.

[0348] Module M5: Constructs a fusion algorithm for remaining lifetime prediction that combines an LSTM recurrent neural network with a filtering algorithm;

[0349] Specifically, in module M5:

[0350] Module M5.1: Select observation feature data;

[0351] Module M5.2: Enables system degradation information mining and low-dimensional fusion feature extraction;

[0352] Module M5.3: Trains the LSTM model using extracted low-dimensional comprehensive degradation feature data to determine the model parameters;

[0353] Module M5.4: Establish a dynamic system state-space model for system degradation characteristics and determine the model parameters;

[0354] Module M5.5: Predicts the degenerate state at time t+1 using an LSTM model with defined parameters. ;

[0355] Module M5.6: Implementing system observations using algorithms based on the system state-space model. For the predicted state Perform the update and calculate the updated mean squared error;

[0356] Module M5.7: Implements system remaining lifetime prediction, returns to module M5.5, and implements online dynamic prediction;

[0357] Module M6: Uses a constructed fusion algorithm to achieve online prediction of the remaining lifespan of product equipment systems.

[0358] In module M6:

[0359] Module M6.1: The constructed fusion model can achieve short-term prediction of the system's degradation state;

[0360] Module M6.2: The remaining lifetime prediction results output by the fusion model method include point estimates and interval estimates;

[0361] Module M6.3: The constructed fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy.

[0362] Example 3:

[0363] Example 3 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0364] A method for predicting the remaining life of product equipment by combining an LSTM recurrent neural network and a filtering algorithm includes the following steps:

[0365] (1) Collect operational observation data measured by sensors of key components of the product equipment, and select characteristic data that can reflect the trend of product performance degradation.

[0366] (2) Extract the features of the same source observation information and different source observation information to obtain low-dimensional fusion features.

[0367] (3) Construct a state space model based on low-dimensional fusion features, estimate the model parameters, and establish a filter remaining lifetime prediction model.

[0368] (4) Using low-dimensional fusion features as the training set, train a recurrent neural network and establish a product degradation state prediction model based on the LSTM algorithm.

[0369] (5) Construct a fusion algorithm for remaining lifetime prediction that combines LSTM recurrent neural network and filtering algorithm.

[0370] (6) The constructed fusion algorithm is used to realize online prediction of the remaining life of the product equipment system, which can realize the tracking and prediction of the degradation state of the system, and the point estimation and interval estimation of the remaining life of the product equipment.

[0371] Step 1 specifically includes:

[0372] (1) Based on the correlation between the observed data and the product degradation trend, select the data with the most significant trend characteristics to characterize the system degradation state;

[0373] (2) Determine candidate subsets from the data and optimized evaluation criteria ;

[0374] (3) The present invention uses a filtering feature selection method to extract key features and sets a candidate subset for feature selection. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest;

[0375] (4) The selected feature data includes data from the same source and data from different sources.

[0376] Step 2 specifically includes:

[0377] (1) Identifying the state of product performance degradation;

[0378] This invention employs a regularized particle filter algorithm to mine performance degradation states. The specific steps of the regularized particle filter algorithm include:

[0379] (a) Treating the degradation state as a separable process, the state-space model established for the component sensor can be expressed as:

[0380]

[0381] coefficients in the formula The data increment curve was obtained by fitting the calibration data obtained from previous observations. This is process noise, reflecting the inherent uncertainty of the degradation state. The noise represents the observed noise, which is assumed to have zero mean and variance. The Gaussian distribution.

[0382] (b) Sample N particles from the initial distribution. Given the same weights ;

[0383] (c) Given In the prior probability density function Collect N particles ;

[0384] (d) Obtaining observations ,according to Update particle weights (at this point, the proposed distribution is selected). The weights are normalized. ;

[0385] (e) When the number of effective particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A. From the particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution;

[0386] (f) Update the pair The estimate makes Returning to c enables dynamic updates.

[0387] The Monte Carlo method is used to construct a posterior probability density that approximates the true posterior probability density by sampling particles and their corresponding weights.

[0388] From the probability density p(z) t |x 1：t If N particles are sampled from a given sample, the posterior probability density is:

[0389]

[0390] in Let z be the Dirac function. t i For the sampled particle, the Monte Carlo estimate of the expectation of any function f(•) is:

[0391]

[0392] Sequential importance sampling is used to sample the posterior probability density function distribution.

[0393] in This is called the proposal distribution. Let w be the weight. For the filtering problem, the weight of the sampling point at each observation time of the dynamic system is:

[0394] Solving particle degradation problem using resampling method:

[0395] In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation.

[0396]

[0397] Set threshold when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​can be approximately expressed as:

[0398] in express Time of the first The weight of each particle, This represents the Dirac delta function.

[0399] The sampling samples in the standard particle filter iteration process are drawn from a discrete distribution, which reduces the diversity of particle samples. By performing a continuous approximation on the discrete distribution and resampling within the continuous distribution, the diversity of sampled particles is increased, mitigating the potential particle scarcity problem caused by resampling. Using kernel density estimation (KDE) to approximate the probability density function of the sampled particle set can achieve the continuation of discrete data. KDE is a non-parametric estimation method for estimating the probability density function of a sample distribution when the type of sample data distribution is unknown. KDE can estimate the probability distribution of a random variable based solely on information from the sample data itself. This invention uses a standard Gaussian kernel function for estimation.

[0400] The kernel function concept is used to address the problem of reduced particle sample diversity, and to approximate the probability density function of the sampled particle set.

[0401]

[0402]

[0403] In the formula For kernel density function, Let z be the state vector t The dimension of the sample is given by det, which is the determinant obtained by solving for the empirical covariance matrix of the sampled data.

[0404] This invention uses a standard Gaussian kernel function for regularization:

[0405]

[0406] (2) Low-dimensional fusion feature extraction specifically includes using distributed filtering algorithm to fuse data from the same source and using kernel principal component analysis to extract low-dimensional fusion features from data from different sources.

[0407] a. In this invention, the weight allocation method for each filter does not use the product of the observed value minus the state estimate and the relation matrix as the standard for weight allocation. Instead, it uses the number of effective particles in the particle filtering process of each filter as the basis for weight allocation.

[0408]

[0409] b. Methods for handling heterogeneous data mainly include feature selection, copula functions, and subspace learning. This invention uses kernel principal component analysis (KPM) in subspace learning to achieve heterogeneous data fusion. Specifically, nonlinear data is mapped to a high-dimensional feature space using a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. This invention uses a Gaussian kernel for mapping to obtain the k-th principal component of the data. for:

[0410]

[0411] Step 3 specifically includes:

[0412] The system The degradation process of the remaining lifetime prediction at time point can be represented as:

[0413]

[0414] In the formula This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. This represents Brownian motion. The remaining lifetime at a given time can be expressed as:

[0415]

[0416] The probability density function of the system's remaining lifetime can then be expressed as:

[0417]

[0418] Step 4 specifically includes:

[0419] a. Input to the forget gate in the computational model:

[0420]

[0421] in h t-1 This represents the output of the previous node, x.t This represents the input of the current node, and σ represents the sigmoid function.

[0422] b. Calculate the input gate input:

[0423]

[0424]

[0425]

[0426] c. Calculate the output gate output to determine the node output value:

[0427]

[0428]

[0429] Step 5 specifically includes:

[0430] a. Select observation feature data using the method in step (1);

[0431] b. Use the method in step (2) to mine system degradation information and extract low-dimensional fusion features;

[0432] c. Use step (4) to train the LSTM model using the extracted low-dimensional comprehensive degradation feature data to determine the model parameters;

[0433] d. Establish a dynamic system state-space model for the system degradation characteristics and determine the model parameters;

[0434] e. Predict the degradation state at time t+1 using an LSTM model with defined model parameters. ;

[0435] f. Based on the system state-space model, the step (3) algorithm is used to realize the system observation values. For the predicted state Perform the update and calculate the updated mean squared error;

[0436] g. Use the algorithm of step (3) to predict the remaining lifespan of the system, return to step e, and realize online dynamic prediction.

[0437] Step 6 specifically includes:

[0438] a. The constructed fusion model can achieve short-term prediction of the system's degradation state;

[0439] b. The remaining lifetime prediction results output by the fusion model method include point estimates and interval estimates.

[0440] c. The constructed fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy.

[0441] Example 4:

[0442] Example 4 is a preferred example of Example 1, which is used to illustrate the present invention in more detail.

[0443] This invention belongs to the field of remaining service life prediction for in-service equipment, specifically an optimized remaining service life prediction method for complex systems based on operational observation data.

[0444] The objective of this invention is to construct a model that integrates LSTM and filtering algorithms, combining the advantages of both models to improve the applicability and accuracy of system remaining lifetime prediction methods. This provides reliable fault early warning and auxiliary reference for fault repair of key system components in products and equipment with a large amount of operational observation data. The technical solution adopted to achieve the above objective includes the following steps:

[0445] (1) Collect operational observation data measured by sensors of key components of the product equipment, select feature data that can reflect the trend of product performance degradation, and based on the correlation between the observation data and the product degradation trend, the operational observation feature data includes relevant features, irrelevant features, and redundant features. In order to extract the data with the most significant trend features to characterize the system degradation state, feature selection is used to extract observation data. The main task of feature selection is to determine the candidate subset from the data. and optimized evaluation criteria The steps are as follows:

[0446] 1. Generate a subset of features from the original feature set and identify it as a candidate subset. ;

[0447] 2. Use evaluation functions For candidate feature subsets To conduct an evaluation;

[0448] 3. Check whether the evaluation results meet the termination conditions set by the optimization evaluation criteria. If the termination conditions are met, output the optimal feature subset. The feature selection process ends here; otherwise, steps 1 and 2 will be repeated.

[0449] Research on feature selection methods has gradually shown a trend of diversification and comprehensiveness, mainly divided into three categories: filtering, encapsulation, and embedding methods. This invention uses a filtering feature selection method to extract key features, and sets a candidate subset for feature selection. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the data set that arrives fastest, the selected feature data includes both homogeneous and heterogeneous data.

[0450] (2) The data preprocessing in this invention involves mining the product performance degradation state and extracting low-dimensional fusion features from the selected feature data. Since the collected system operation observation signals are usually noisy signals, it is necessary to preprocess the selected feature data to mine the true degradation state of the system. At the same time, the selected observation features include both homogeneous and heterogeneous data, with a wide variety of parameters and high dimensionality, resulting in excessive computational load for system performance data analysis. Furthermore, the information between multidimensional features overlaps and intersects, leading to redundancy in subsequent decision-making. In terms of data description, this may result in low accuracy, poor overall recognition, high computational load, and difficulty in visualization.

[0451] 1. This invention uses the particle filter algorithm to realize the mining of performance degradation states. The particle filter algorithm is a nonlinear state estimation algorithm based on the Monte Carlo sampling method. It can handle dynamic system problems with strong nonlinear characteristics and has good data adaptability. The core idea of ​​the algorithm is to use discrete random sampling samples (particles) to approximate the probability density function of the model, and use the average value of the samples to replace the integral operation to realize the estimation of the system state.

[0452] The state-space model of particle filtering can be expressed as follows:

[0453] In the formula z t x represents the state of the system degradation at time t. t u represents the measurement value of the observation system corresponding to time t. t v represents the random parameter describing the uncertainty in the system's state equation. k denoted by , g(•) represents the noise term in the observation equation, g(•) represents the state transition function in the state-space model, and h(•) represents the observation function describing the relationship between the observed value and the hidden state.

[0454] For the state estimation problem in nonlinear dynamic systems, the main objective is to utilize the prior distribution of the aforementioned model and the observed values ​​x during actual operation. 1：t =x{x1,x2,…x t To estimate the system state value z t The posterior probability density function p(z) t |x 1：t ).

[0455] From the perspective of recursive Bayesian filtering, assuming The posterior probability density function p(z) at time t t-1 |x1：t-1 It is known that z can be obtained through two steps: prediction and update. t The posterior probability density function p(z) t |x 1：t ).

[0456] a. Based on x{x1,x2,…x t-1 Predicting z from observed values ​​of} t Determine z t Prior distribution:

[0457] b. Using the new observation x t To update z t Predicting the probability density function, i.e., finding z. t The posterior probability density function:

[0458] Calculating the analytical solution of the above integral is typically very difficult, and the difficulty increases with each iteration. This invention employs Monte Carlo methods, sequential importance sampling, and resampling to implement particle filtering in solving the problem of determining the posterior probability density of state values.

[0459] a. Monte Carlo method

[0460] Assume that from the probability density p(z) t |x 1：t If N particles are sampled from a sample, the posterior probability density can be approximately expressed as:

[0461]

[0462] in Let z be the Dirac function. t i For the sampled particle, the Monte Carlo estimate of the expectation of any function f(•) is:

[0463]

[0464] b. Sequential importance sampling

[0465] The sequential importance sampling method can be used to sample p(z) t |x 1：t This allows for simple and effective direct sampling. If the probability density function q(z) t |x 1：t ) and p(z) t |x 1：t If the two have the same probability density distribution, and the one below is easier to sample, then from the distribution q(z) t |x1：t If N points are randomly sampled from a system, the expected value describing the distribution of the hidden states can be approximately expressed as:

[0466] in This is called the proposal distribution. Let w be the weight. For the filtering problem, the weight of the sampling point at each observation time of the dynamic system is:

[0467] Starting from the initial time, calculating the posterior distribution expectation at each observation time requires updating the weights w of each sampling point. Each update requires calculating the weights N times for the corresponding N samples, resulting in high computational complexity. The sequential importance sampling method addresses this by finding the correct weights. and The relationship between these factors reduces the computational complexity of model updates. (Probability density function) Belongs to function The marginal distribution function, therefore from The recursive relationship between weights is sought within the function:

[0468] Assuming a proposal distribution have:

[0469] but It can be represented as:

[0470] The normalized weights can be expressed as:

[0471] The sequential importance sampling method suffers from "particle degeneration," meaning that after multiple iterations, the variance of the weights corresponding to the sampled samples increases with each iteration. This results in larger weights for larger particles and smaller weights for smaller particles, making the sampled particle set and its corresponding weights unable to accurately approximate the actual posterior distribution. A resampling method is employed to address this particle degeneration problem.

[0472] c. Weight degradation and resampling

[0473] In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation.

[0474]

[0475] Set threshold when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​can be approximated as:

[0476] in express Time of the first The weight of each particle, This represents the Dirac delta function.

[0477] d. Regularized particle filter

[0478] To address the issue of reduced particle sample diversity caused by sampling from a discrete distribution, this invention employs a regularized particle filtering method, using kernel density estimation to approximate the probability density function of the sampled particle set:

[0479]

[0480]

[0481] In the formula For kernel density function, Let z be the state vector t The dimension of the sample is given by det, which is the determinant obtained by solving for the empirical covariance matrix of the sampled data. Standard kernel density function satisfy nuclear broadband This invention uses a standard Gaussian kernel function for regularization:

[0482]

[0483] The computational flow of the regularized particle filter algorithm is shown below:

[0484] (a) Sample N particles from the initial distribution Given the same weights ;

[0485] (b) Given In the prior probability density function Collect N particles ;

[0486] (c) Obtaining observations ,according to Update particle weights (at this point, the proposed distribution is selected). The weights are normalized. ;

[0487] (d) When the number of effective particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A. From the particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution;

[0488] (e) Update the The estimate makes Returning b enables dynamic updates.

[0489] Treating the degradation state as a separable process, the state-space model established for the component sensor can be represented as:

[0490]

[0491] coefficients in the formula The data increment curve was obtained by fitting the calibration data obtained from previous observations. This is process noise, reflecting the inherent uncertainty of the degradation state. The noise represents the observed noise, which is assumed to have zero mean and variance. The Gaussian distribution.

[0492] 2. This invention uses distributed filtering algorithm and kernel principal component analysis to achieve low-dimensional fusion feature extraction.

[0493] a. Distributed particle filtering assigns weights to the filtered estimates from each sensor and calculates the fused estimate. Typically, the product of the state estimate and the relation matrix is ​​subtracted from the observed value of each filter as the criterion for weight allocation.

[0494] However, the main purpose of filtering is to update the estimated state using observations. When the estimated state values ​​and observations generally differ significantly, it cannot accurately reflect the filter's performance. This invention uses the number of effective particles in the particle filtering process as the basis for weight allocation:

[0495]

[0496] The effective particle count represents the efficiency of the filter, and this value measures the distribution of particles in the sub-filters. After obtaining the effective particle count of each sub-filter, the weight of that sub-filter in the main filter can be calculated using the effective particle count of each sub-filter. This enables the fusion of information from the same source.

[0497] b. Kernel principal component analysis

[0498] KPCA maps nonlinear problems in the input space to a high-dimensional feature space using a nonlinear mapping method. PCA is then performed in this high-dimensional space to extract the nonlinear principal components between the original feature space data. Commonly used kernel functions include linear kernels, polynomial kernels, and Gaussian kernels. The specific KPCA algorithm is as follows.

[0499] First, let's assume the training data samples are... Where N is the number of samples. The basic idea of ​​KPCA is to calculate it through nonlinear mapping. Mapping the input space to a high-dimensional space F, the covariance matrix C of F is:

[0500]

[0501] In the formula, the nonlinear mapping function is: and Assuming the eigenvalues ​​of the covariance matrix are λ and the corresponding eigenvectors are V, the characteristic equation can be obtained as follows:

[0502]

[0503] Multiply both sides of the above expression by And by calculating the inner product, we get the following formula:

[0504]

[0505] Assume the coefficient exists This allows the eigenvector V in C to be derived from... Linear representation:

[0506]

[0507] In conclusion:

[0508]

[0509] in Let K be the inner product operator of x and y. Define the kernel function matrix as K, then:

[0510]

[0511] Data Mapping to feature vector Calculate the k-th principal component for:

[0512]

[0513] This invention achieves the fusion of heterogeneous information through the subspace learning method based on kernel principal component analysis described above.

[0514] (3) Construction of particle filter remaining lifetime prediction model

[0515] In the dynamic system assumption, filtering algorithms can utilize system observation information to recursively identify degenerate states and parameters over time while minimizing the computational complexity of online data accumulation. The filtering problem typically involves two steps:

[0516] (1) Based on Predicting based on observations Sure The prior distribution;

[0517] (2) Utilizing new observations To update the Predicting the probability density function, i.e., finding... The posterior probability density function.

[0518] When no observations update the predicted state, short-term predictions of the degenerate state can be achieved through the state transition equations in the state-space model. Based on the established state-space model of the observation system, the system... The degradation process of the remaining lifetime prediction at time point can be represented as:

[0519]

[0520] In the formula This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. This represents Brownian motion. The remaining lifetime at a given time can be expressed as:

[0521]

[0522] The probability density function of the system's remaining lifetime can then be expressed as:

[0523]

[0524] (4) Construction of LSTM recurrent neural network remaining lifetime prediction model

[0525] The computational model for data transmission in the LSTM model is as follows:

[0526]

[0527] The above formula is for calculating the forgetting gate, where h t-1 This represents the output of the previous node, x. t This represents the input of the current node. σ represents the sigmoid function.

[0528]

[0529]

[0530]

[0531] The above formula is for input gate calculation, which determines how much new information to add to the node state. This requires two steps: first, a sigmoid layer determines which information needs updating; then, a tanh layer generates a vector containing the candidate information for updating; finally, these two parts are combined to update the node state.

[0532]

[0533]

[0534] Finally, the output gate is calculated to determine the output. First, a sigmoid layer is run to determine which part of the node state will be output; then the node state is processed through a tanh layer (to obtain values ​​in the range [-1,1]) and multiplied with the output of the sigmoid layer to finally determine the part of the output.

[0535] (5) Construction of integrated remaining useful life prediction model

[0536] Based on the fusion algorithm, the implementation steps of the fusion model are as follows:

[0537] a. Select observation feature data using the method in step (1);

[0538] b. Use the method in step (2) to mine system degradation information and extract low-dimensional fusion features;

[0539] c. Train the LSTM model using the extracted low-dimensional comprehensive degradation feature data to determine the model parameters;

[0540] d. Establish a dynamic system state-space model that addresses the system's degradation characteristics;

[0541] e. Predict the degradation state at time t+1 using an LSTM model with defined model parameters. ;

[0542] f. Using a particle filter algorithm based on a system state-space model to obtain system observations For the predicted state Perform the update and calculate the updated mean squared error;

[0543] g. Use the algorithm of step (3) to predict the remaining lifespan of the system, return to step e, and realize online dynamic prediction.

[0544] Example 5:

[0545] Example 5 is a preferred embodiment of Example 1, which is used to illustrate the present invention in more detail.

[0546] like Figure 4 As shown, the steps of the product equipment remaining life prediction calculation method combining LSTM recurrent neural network and filtering algorithm are as follows:

[0547] (1) Select characteristic data that can reflect the trend of product performance degradation;

[0548] This step involves using a filtering-based feature selection method to extract key features, and setting a candidate subset for feature selection. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest;

[0549] (2) Mining of product and equipment degradation status and extraction of low-dimensional fusion features;

[0550] This step first uses a regularized particle filter algorithm to investigate the degradation state of the product equipment.

[0551] (a) Treating the degradation state as a separable process, the state-space model established for the component sensor can be expressed as:

[0552]

[0553] coefficients in the formula The data increment curve was obtained by fitting the calibration data obtained from previous observations. This is process noise, reflecting the inherent uncertainty of the degradation state. The noise represents the observed noise, which is assumed to have zero mean and variance. The Gaussian distribution.

[0554] (b) Sample N particles from the initial distribution. Given the same weights ;

[0555] (c) Given In the prior probability density function Collect N particles ;

[0556] (d) Obtaining observations ,according to Update particle weights (at this point, the proposed distribution is selected). The weights are normalized. ;

[0557] (e) When the number of effective particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A. From the particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution;

[0558] (f) Update the pair The estimate makes Returning to c enables dynamic updates;

[0559] The filtered data more closely approximates the true degradation state of the system.

[0560] Distributed filtering algorithms are used to fuse data from the same source, while kernel principal component analysis is used to extract low-dimensional fusion features from data from different sources.

[0561] a. In this invention, the weight allocation method for each filter does not use the product of the observed value minus the state estimate and the relation matrix as the standard for weight allocation. Instead, it uses the number of effective particles in the particle filtering process of each filter as the basis for weight allocation.

[0562]

[0563] b. Methods for handling heterogeneous data mainly include feature selection, copula functions, and subspace learning. This invention uses kernel principal component analysis (KPM) in subspace learning to achieve heterogeneous data fusion. Specifically, nonlinear data is mapped to a high-dimensional feature space using a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. This invention uses a Gaussian kernel for mapping to obtain the k-th principal component of the data. for:

[0564]

[0565] The extracted low-dimensional fusion features can be used to estimate model parameters for subsequent model building.

[0566] (3) Construct a filter remaining lifetime prediction model

[0567] This step involves constructing a state-space model based on low-dimensional fusion features, estimating model parameters, establishing a filtered remaining lifetime prediction model, and then... The degradation process of the remaining lifetime prediction at time point is represented as follows:

[0568]

[0569] In the formula This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. This represents Brownian motion. The remaining lifetime at a given time can be expressed as:

[0570]

[0571] The probability density function of the system's remaining lifetime can then be expressed as:

[0572]

[0573] (4) Constructing an LSTM model system degradation state prediction model

[0574] This step involves training a recurrent neural network using low-dimensional fused features as the training set to establish a product degradation state prediction model based on the LSTM algorithm. The steps include the following three:

[0575] a. Input to the forget gate in the computational model:

[0576]

[0577] in h t-1 This represents the output of the previous node, x. t This represents the input of the current node, and σ represents the sigmoid function.

[0578] b. Calculate the input gate input:

[0579]

[0580]

[0581]

[0582] c. Calculate the output gate output to determine the node output value:

[0583]

[0584]

[0585] (5) Construct a fusion algorithm for remaining lifetime prediction that combines LSTM recurrent neural network and filtering algorithm:

[0586] a. Select observation feature data using the method in step (1);

[0587] b. Use the method in step (2) to mine system degradation information and extract low-dimensional fusion features;

[0588] c. Use step (4) to train the LSTM model with the extracted low-dimensional comprehensive degradation feature data and determine the model parameters;

[0589] d. Use step (3) to establish a dynamic system state-space model for the system degradation characteristics and determine the model parameters;

[0590] e. Predict the degradation state at time t+1 using an LSTM model with defined model parameters. ;

[0591] f. Based on the system state-space model, the step (3) algorithm is used to realize the system observation values. For the predicted state Perform the update and calculate the updated mean squared error;

[0592] g. Use the algorithm of step (3) to predict the remaining lifespan of the system, return to step e, and realize online dynamic prediction.

[0593] (6) Through the above steps, the remaining lifetime of the system can be predicted using the fusion model:

[0594] a. Figure 5 The remaining life prediction results of a product are obtained by introducing a filtering algorithm based on the observation data of a certain system operation.

[0595] b. Figure 6 The remaining life prediction results of a product are obtained by introducing an LSTM model using the operational observation data of a certain system as an example.

[0596] c. Figure 7 The following is an example of the degradation state tracking and prediction results of a certain system based on the LSTM and filter fusion model, using the observation data of a certain system operation as an example;

[0597] d. Figure 8 The following is an example of the remaining lifetime prediction results of a system based on an LSTM and filter fusion model, using the system's operational observation data as an example.

[0598] e. Figure 9 Comparison of the mean square error of each model in predicting the degradation state of a certain system;

[0599] f. Figure 10 The mean square error of each model in predicting the remaining lifetime of a certain system is compared.

[0600] This demonstrates that the fusion model constructed in this invention exhibits high prediction accuracy for predicting the degradation state and lifespan of a certain system. It retains the ability of the filtering prediction model to mine the degradation state of the product, and its ability to express uncertainty also reflects the good data adaptability and prediction accuracy of the LSTM recurrent neural network model in the fusion model.

[0601] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0602] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for predicting remaining lifetime combining recurrent neural networks and filtering algorithms, characterized in that, include: Step S1: Collect operational observation data and select characteristic data; Step S2: Use the regularized particle filter algorithm to mine the product performance degradation state and extract low-dimensional fusion features on the selected feature data. The low-dimensional fusion feature extraction specifically includes using a distributed filtering algorithm to fuse data from the same source and using kernel principal component analysis to fuse data from different sources. Step S3: Construct a state-space model based on low-dimensional fusion features, estimate the model parameters, and establish a filter remaining lifetime prediction model; the state-space model is represented as: In the formula, Let be the degenerate state variable at time t, where t is the current observation time. Here, i represents the sensor observation value, and i is the sensor number. For the error of the constant term, the coefficient The constant value obtained by fitting the data increment curve of calibration data obtained from past observations; This is process noise, reflecting the inherent uncertainty of the degradation state. This represents observed noise, which has zero mean and variance. Gaussian distribution; In step S3: The system The degradation process of the remaining lifetime prediction at time point is represented as follows: In the formula, for Time-degradation state estimate, This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. Indicates Brownian motion; exist The remaining lifetime at a given time is expressed as: in, This is the failure threshold; The probability density function of the system's remaining lifetime is then expressed as: in, The diffusion coefficient during the degradation process; Step S4: Using low-dimensional fusion features as the training set, train a recurrent neural network to establish a product degradation state prediction model based on the LSTM algorithm; Step S5: Construct a fusion algorithm for remaining lifetime prediction that combines an LSTM recurrent neural network and a filtering algorithm; Step S6: Use the constructed fusion algorithm to achieve online prediction of the remaining life of the product equipment system; In step S5: Step S5.1: Select observation feature data; Step S5.2: Implement system degradation information mining and low-dimensional fusion feature extraction; Step S5.3: Train the LSTM model using the extracted low-dimensional comprehensive degradation feature data to determine the model parameters; Step S5.4: Establish a dynamic system state-space model for the system degradation characteristics and determine the model parameters; Step S5.5: Predict the degradation state at time t+1 using the LSTM model with determined model parameters. ; Step S5.6: Utilize algorithms based on the system state-space model to obtain system observations. For the predicted state Perform the update and calculate the updated mean squared error; Step S5.7: Implement system remaining lifetime prediction, return to step S5.5, and implement online dynamic prediction; In step S6: Step S6.1: The constructed fusion model can achieve short-term prediction of the system's degradation state; Step S6.2: The remaining lifetime prediction results output by the fusion model method include point estimates and interval estimates; Step S6.3: The constructed fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy.

2. The remaining lifetime prediction method combining recurrent neural networks and filtering algorithms according to claim 1, characterized in that, In step S1: Collect operational observation data measured by sensors on product equipment components, and select preset characteristic data that can reflect the trend of product performance degradation: Based on the correlation between observed data and product degradation trends, the data with the most significant trend characteristics are selected to characterize the system degradation state; Identifying candidate subsets from the data and optimized evaluation criteria ; A filtering-based feature selection method is used to extract key features, and a candidate subset for feature selection is defined. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest; The selected feature data includes both homogeneous and heterogeneous data.

3. The remaining lifetime prediction method combining recurrent neural networks and filtering algorithms according to claim 1, characterized in that, In step S2: Step S2.1: Identify the product performance degradation status; The specific steps of the regularized particle filter algorithm used include: Step S2.1.1: The degenerate state is a separable process; Step S2.1.2: Sample N particles from the initial distribution. Given the same weights, ; express Time of the first The weight of each particle; Step S2.1.3: Given In the prior probability density function Collect N particles ; Step S2.1.4: Obtain the observed values ,according to Update particle weights, at which point the proposed distribution is selected. The weights are normalized. ; Step S2.1.5: When the number of effective particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A; A is the state transition matrix; From particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution; Let i be the number of the i-th sensor of the j-th type, under the standard Gaussian kernel function. =1; Step S2.1.6: Update the... The estimate makes Return to step S2.1.3 to implement dynamic updates; The Monte Carlo method is used to construct the posterior probability density by sampling particles and their corresponding weights: From the probability density p(z) t |x 1：t If N particles are sampled from a given sample, the posterior probability density is: in Let z be the Dirac function. t i For sampled particles, for any function f( The expected Monte Carlo estimate is: Sequential importance sampling is used to sample the posterior probability density function distribution. in This is called the proposal distribution. As weights, for filtering problems, the weights of the sampling points corresponding to each observation time of the dynamic system are: Solving particle degradation problem using resampling method: In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation. In the formula, Effective particle count, var(w) t ) for w t The second-order moment; when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​is expressed as: Where j is the corresponding number of the component sensor, Let i be the number of sensors of type i. express Time of the first The weight of each particle, This represents the Dirac delta function; Estimation is performed using the standard Gaussian kernel function: In the formula, The continuous approximate probability density of the state variables at time t of a nonlinear dynamic system is given by the empirical covariance matrix of the sampled samples. ; Step S2.2: Low-dimensional fusion feature extraction specifically includes fusing homogeneous data using a distributed filtering algorithm and extracting low-dimensional fusion features from heterogeneous data using kernel principal component analysis. Step S2.2.1: Use the number of effective particles in the particle filtering process of each filter as the basis for weight allocation: in, Number each sub-filter; Step S2.2.2: Kernel principal component analysis in subspace learning is used to achieve heterogeneous data fusion. Nonlinear data is mapped to a high-dimensional feature space through a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. The k-th principal component of the data is obtained by mapping with a Gaussian kernel. for: in, Let be the eigenvector corresponding to the covariance matrix of the k-th principal component. It is a nonlinear mapping function. The constant term coefficients of the eigenvectors are represented by the mapping function.

4. The remaining lifetime prediction method combining recurrent neural networks and filtering algorithms according to claim 1, characterized in that: In step S4: Step S4.1: Calculate the forget gate input for the model: in, This is the connection weight matrix between the forget gate and the input gate. A matrix of constant terms, h t-1 This represents the output of the previous node, x. t This represents the input of the current node, and σ represents the sigmoid function; Step S4.2: Calculate the input gate input: in, The information that needs to be updated is determined by the sigmoid layer. The vector generated by the tanh layer is used as a candidate for update. For each connection weight matrix, For each constant term, This is the updated node state value. The coefficients of the constant term; Step S4.3: Calculate the output gate output to determine the node output value: in, The portion to be output for the sigmoid layer. To connect the weight matrix, The coefficient of the constant term, To update the node state value after input at time t, h t To output information.

5. A remaining lifetime prediction system combining recurrent neural networks and filtering algorithms, characterized in that, include: Module M1: Collects operational observation data from measurements and selects characteristic data; Module M2: The selected feature data is subjected to regularized particle filter algorithm for product performance degradation state mining and low-dimensional fusion feature extraction. The low-dimensional fusion feature extraction specifically includes fusion of data from the same source using a distributed filtering algorithm and fusion of data from different sources using kernel principal component analysis. Module M3: Constructs a state-space model based on low-dimensional fusion features, estimates model parameters, and establishes a filter remaining lifetime prediction model; the state-space model is represented as: In the formula, Let be the degenerate state variable at time t, where t is the current observation time. Here, i represents the sensor observation value, and i is the sensor number. For the error of the constant term, the coefficient The constant value obtained by fitting the data increment curve of calibration data obtained from past observations; This is process noise, reflecting the inherent uncertainty of the degradation state. This represents observed noise, which has zero mean and variance. Gaussian distribution; In module M3: The system The degradation process of the remaining lifetime prediction at time point is represented as follows: In the formula, for Time-degradation state estimate, This indicates a cumulative degradation process. This represents the diffusion coefficient during the degradation process. Indicates Brownian motion; exist The remaining lifetime at a given time is expressed as: in, This is the failure threshold; The probability density function of the system's remaining lifetime is then expressed as: in, The diffusion coefficient during the degradation process; Module M4: Using low-dimensional fused features as the training set, a recurrent neural network is trained to establish a product degradation state prediction model based on the LSTM algorithm; Module M5: Constructs a fusion algorithm for remaining lifetime prediction that combines an LSTM recurrent neural network with a filtering algorithm; Module M6: Utilizes the constructed fusion algorithm to achieve online prediction of the remaining lifespan of product equipment systems; In module M5: Module M5.1: Select observation feature data; Module M5.2: Enables system degradation information mining and low-dimensional fusion feature extraction; Module M5.3: Trains the LSTM model using extracted low-dimensional comprehensive degradation feature data to determine the model parameters; Module M5.4: Establish a dynamic system state-space model for system degradation characteristics and determine the model parameters; Module M5.5: Predicts the degenerate state at time t+1 using an LSTM model with defined parameters. ; Module M5.6: Implementing system observations using algorithms based on the system state-space model. For the predicted state Perform the update and calculate the updated mean squared error; Module M5.7: Implements system remaining lifetime prediction, returns to module M5.5, and implements online dynamic prediction; In module M6: Module M6.1: The constructed fusion model can achieve short-term prediction of the system's degradation state; Module M6.2: The remaining lifetime prediction results output by the fusion model method include point estimates and interval estimates; Module M6.3: The constructed fusion model combines the filtering prediction model's ability to mine product degradation status and express uncertainty with the LSTM recurrent neural network model's good data adaptability and prediction accuracy.

6. The remaining lifetime prediction system combining recurrent neural networks and filtering algorithms according to claim 5, characterized in that, In module M1: Collect operational observation data measured by sensors on product equipment components, and select preset characteristic data that can reflect the trend of product performance degradation: Based on the correlation between observed data and product degradation trends, the data with the most significant trend characteristics are selected to characterize the system degradation state; Identifying candidate subsets from the data and optimized evaluation criteria ; A filtering-based feature selection method is used to extract key features, and a candidate subset for feature selection is defined. The evaluation criteria are optimized based on the time it takes for the fitted curve to reach the failure threshold for each data point after nonlinear fitting. To select the set of data that arrives fastest; The selected feature data includes both homogeneous and heterogeneous data.

7. The remaining lifetime prediction system combining recurrent neural networks and filtering algorithms according to claim 5, characterized in that, In module M2: Module M2.1: Product performance degradation status detection; The specific steps of the regularized particle filter algorithm used include: Module M2.1.1: Degenerate state is a separable process; Module M2.1.2: Sample N particles from the initial distribution Given the same weights, ; express Time of the first The weight of each particle; Module M2.1.3: Given In the prior probability density function Collect N particles ; Module M2.1.4: Obtaining Observations ,according to Update particle weights, at which point the proposed distribution is selected. The weights are normalized. ; Module M2.1.5: When the effective number of particles Less than a certain set threshold At that time, by particle set Calculate the empirical covariance matrix S of the sample, by Calculate A; A is the state transition matrix; From particle set Medium resampling yields a new set of particles with equal weights. Then, N samples are drawn from the kernel density function. According to the optimal bandwidth and samples make , These are new particles obtained by resampling from a continuous approximate distribution; Let i be the number of the i-th sensor of the j-th type, under the standard Gaussian kernel function. =1; Module M2.1.6: Updates to The estimate makes Return to module M2.1.3 to implement dynamic updates; The Monte Carlo method is used to construct the posterior probability density by sampling particles and their corresponding weights: From the probability density p(z) t |x 1：t If N particles are sampled from a given sample, the posterior probability density is: in Let z be the Dirac function. t i For sampled particles, for any function f( The expected Monte Carlo estimate is: Sequential importance sampling is used to sample the posterior probability density function distribution. in This is called the proposal distribution. As weights, for filtering problems, the weights of the sampling points corresponding to each observation time of the dynamic system are: Solving particle degradation problem using resampling method: In particle filtering, the effective particle number index is used to quantitatively assess the degree of particle weight degradation. In the formula, Effective particle count, var(w) t ) for w t The second-order moment; when If the value is less than a pre-set threshold, resampling is performed. The posterior probability density function of the resampled weight values ​​is expressed as: Where j is the corresponding number of the component sensor. Let i be the number of sensors of type i. express Time of the first The weight of each particle, This represents the Dirac delta function; Estimation is performed using the standard Gaussian kernel function: In the formula, The continuous approximate probability density of the state variables at time t of a nonlinear dynamic system is given by the empirical covariance matrix of the sampled samples. ; Module M2.2: Low-dimensional fusion feature extraction specifically includes using a distributed filtering algorithm to fuse data from the same source and using kernel principal component analysis to extract low-dimensional fusion features from data from different sources. Module M2.2.1: The number of effective particles in the particle filtering process of each filter is used as the basis for weight allocation. in, Number each sub-filter; Module M2.2.2: This module employs kernel principal component analysis (KPI) from subspace learning to achieve heterogeneous data fusion. Nonlinear data is mapped to a high-dimensional feature space using a kernel function, and then principal component analysis is performed on this high-dimensional space to extract the nonlinear principal components between the original feature space data. A Gaussian kernel is used for mapping to determine the k-th principal component of the data. for: in, Let be the eigenvector corresponding to the covariance matrix of the k-th principal component. It is a nonlinear mapping function. The constant term coefficients of the eigenvectors are represented by the mapping function.

8. The remaining lifetime prediction system combining recurrent neural networks and filtering algorithms according to claim 5, characterized in that: In module M4: Module M4.1: Computational Model Forget Gate Input: in, This is the connection weight matrix between the forget gate and the input gate. A matrix of constant terms, h t-1 This represents the output of the previous node, x. t This represents the input of the current node, and σ represents the sigmoid function; Module M4.2: Calculation Input Gate Input: in, The information that needs to be updated is determined by the sigmoid layer. The vector generated by the tanh layer is used as a candidate for update. For each connection weight matrix, For each constant term, This is the updated node state value. The coefficients of the constant term; Module M4.3: Calculates the output gate output to determine the node output value. in, The portion to be output for the sigmoid layer. To connect the weight matrix, The coefficient of the constant term, To update the node state value after input at time t, h t To output information.

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