Method for predicting residual life probability of key component of large wind turbine generator

By preprocessing and feature extraction of the SCADA data of wind turbines, using parallel LSTM neural networks to predict the remaining life of fan components, and combining linear regression and kernel density estimation for uncertainty quantification, the accuracy and reliability of life prediction of key components of wind turbines in the prior art are solved, and the accuracy of prediction and the reliability of operation and maintenance decisions are improved.

CN119647655AActive Publication Date: 2025-03-18ZHEJIANG UNIV +1
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Patent Information

Application Number
CN202411639105.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-15
Publication Date
2025-03-18
Estimated Expiration
2044-11-15

AI Technical Summary

Technical Problem

The prior art is difficult to accurately predict the remaining life of key components of wind turbines, and it is difficult to effectively capture the dynamic impact of the environment and workload. The multi-scale mixed noise timing data processing capability is insufficient, which affects the reliability of operation and maintenance decisions.

Method used

A method for predicting the residual life probability of key components of large wind turbines is proposed. SCADA data is obtained through data acquisition and monitoring control systems, data preprocessing and fast Fourier transform, feature vectors under different time scales are extracted, and processed through parallel LSTM neural networks, and uncertainty quantization is finally carried out through linear regression and kernel density estimation.

Benefits of technology

It improves the accuracy of fan components' remaining life prediction, can accurately capture the dynamic impact of the environment and workload, and provides a more robust reference for operation and maintenance decisions through uncertainty quantification.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention belongs to the technical field of fans, and relates to a method for predicting the residual life probability of key components of a large wind turbine generator, which comprises the following steps of: after obtaining fan SCADA (Supervisory Control and Data Acquisition) data through a data acquisition and monitoring control system, firstly performing variable screening and preprocessing, and then preliminarily searching different periodic changes of the fan SCADA data through Fourier transform; intercepting the multi-dimensional time sequence data according to different periods, carrying out parallel processing through the LSTM neural networks, deeply extracting the time features of the multi-dimensional time sequence data, splicing the output vectors of the LSTM neural networks together, obtaining a residual life prediction result through a linear output layer, and finally, carrying out the prediction of the residual life of the multi-dimensional time sequence data. The uncertainty quantization method based on linear regression and kernel density estimation is used for carrying out uncertainty quantization on an original residual life prediction result, and a more stable reference is provided for a fan maintenance decision. Compared with other methods, the method can effectively improve the prediction accuracy and reliability of the residual life of the fan component.
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Description

Technical Field

[0001] The invention belongs to the technical field of wind turbines and relates to a method for predicting the probability of remaining life of key components of a large wind turbine generator set. Background Art

[0002] With the rapid development of the wind power industry, wind turbines have become an important source of clean energy worldwide. However, due to the long-term operation of their key components (such as gearboxes, bearings, and blades) in complex natural environments, they are easily affected by factors such as fatigue and wear, which in turn cause failures. The failure of these components may lead to equipment downtime and high maintenance costs. Therefore, predicting their remaining life has become the key to ensuring efficient operation of wind turbines and reducing maintenance costs. However, the operating data of wind turbine components has the characteristics of multi-source, multi-scale, and nonlinear. Traditional physical models and statistical models are difficult to accurately describe their complex degradation processes, and it is difficult to effectively capture the dynamic effects of the environment and workload. At present, thanks to the rapid development of sensor and communication technologies, data-driven methods are widely used in remaining life prediction. These methods directly extract key information from a large amount of sensor data for condition monitoring to detect changes in system status. Among data-driven methods, machine learning and deep learning have been favored by researchers in recent years, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs). However, in actual scenarios, the time series data collected during the equipment degradation process usually show overlap and interaction between multiple cycles, and are often mixed with noise signals. Many existing models are still insufficient in processing time series data of such multi-scale mixed noise, making it difficult to extract comprehensive degradation features from the data. In addition, existing models mostly focus on predicting specific values, while ignoring the uncertainty in the prediction results, which will affect the reliability of operation and maintenance decisions. Summary of the invention

[0003] In order to solve the above technical problems existing in the prior art, the present invention proposes a method for predicting the remaining life probability of key components of large wind turbines, which can accurately predict the remaining life of wind turbine components and quantify the uncertainty to obtain reliable remaining life prediction results. The specific technical solution is as follows:

[0004] A method for predicting the probability of remaining life of key components of a large wind turbine generator system comprises the following steps:

[0005] Step S1: acquiring SCADA data of the wind turbine through a data acquisition and monitoring control system, screening out input variables related to the remaining life of target components of the wind turbine, and performing data preprocessing to obtain standardized time series data of multiple input variables;

[0006] Step S2: Perform fast Fourier transform on the standardized time series data of multiple input variables obtained in step S1, and cut them into time series data of different lengths according to multiple frequency components, and then input the time series data of different lengths into different LSTM neural networks for parallel processing, extract the feature vectors at different time scales and perform splicing and merging, and then input them into the linear output layer to obtain the predicted value of the remaining life of the fan components;

[0007] Step S3: performing uncertainty quantification processing on the predicted value of the remaining life of the wind turbine components obtained in step S2 based on the method of linear regression and kernel density estimation.

[0008] Furthermore, in step S1, the input variables related to the remaining life of the target components of the wind turbine are screened out, specifically: first, the initial input variables related to the remaining life of the target components are selected based on professional knowledge, and then the Pearson correlation coefficients of other variables and the initial input variables are calculated, and variables with correlation coefficients greater than a preset value p are selected from other variables, and used as input variables together with the initial input variables, thereby obtaining n input variables, where n is a positive integer.

[0009] Furthermore, in step S1, the data preprocessing specifically includes:

[0010] First, a threshold of 5 times the standard deviation is used to eliminate extreme outliers in SCADA data, and the shutdown state data is eliminated using the active power greater than zero as the threshold;

[0011] Then the Z-score standardization method is used to process the time series of each input variable;

[0012] Finally, a sliding window with a step size of 1 unit time and a width of t unit time is used to segment the standardized input variable time series.

[0013] Furthermore, the step S2 specifically includes:

[0014] Step S2.1: Use fast Fourier transform to process the time series signal with an input length of t and an input variable number of n after window segmentation to obtain n characteristic spectrum graphs, where n is a positive integer. Then, the amplitude dimensions of all characteristic spectrum graphs are averaged to obtain a new spectrum graph. Based on the conjugate characteristics of the spectrum, only half of the spectrum of the new spectrum graph is taken for analysis:

[0015]

[0016] In the formula, X i ∈R t×n , X irepresents a time series of an input variable, A represents the corresponding amplitudes of all frequency components, FFT(·) represents fast Fourier transform, and Amp(·) represents the calculated amplitude;

[0017] Step S2.2: Select the first k maximum amplitudes from A obtained in step S2.1, and find their corresponding frequencies and periods. The calculation formula is as follows:

[0018] [f1,…,f k ]=Fre(Topk(A))

[0019]

[0020] In the formula, Topk(·) means finding the first k maximum values, Fre(·) means taking the frequency value, [f1,…,f k ] represents the first k frequency values, [p1,…,p k ] represents the first k period values ​​corresponding to the frequency value;

[0021] Step S2.3: Based on the k periods obtained from step S2.2, start from the last moment of the input time series and cut forward to obtain k time segments with a length equal to the period value. l∈{1,…,k};

[0022] Step S2.4: Input the k time segments obtained in step S2.3 into different LSTM neural networks respectively to obtain the final output vectors [h1,…,h k ];

[0023] Step S2.5: concatenate the k final output vectors obtained in step S2.4 and input them into the linear output layer to obtain the predicted value of the remaining life of the fan components, which is expressed as:

[0024] y=W l ·cat([h1,…,h k ])

[0025] Where W l is the weight of the linear layer, y is the final prediction result, and the cat(·) function indicates that the vectors are concatenated by column.

[0026] Furthermore, in step S2.2, when the first k maximum amplitudes are selected from A, the frequency components therein do not include high-frequency components.

[0027] Furthermore, the step S3 specifically includes:

[0028] Step S3.1: Process the remaining life prediction value obtained in step S2.5 by using a sliding window with a step length of 1 unit time and a width of 1 unit time to obtain the original remaining life prediction value [y1,...,y l ] and consider each sliding window as a degradation stage;

[0029] Step S3.2: The original predicted value of the remaining life in the sliding window [y1,...,y l ] to perform linear regression. The slope of the fitted regression line is the estimated degradation rate of the component during this window predicted by the neural network. The ordinate value at the end of the regression line is the estimated remaining life at the last moment of the current window. The formula is:

[0030]

[0031] y end =wt end +b

[0032] In the formula, w and b are the slope and intercept of the regression line respectively. and are the mean of the original predicted value of the remaining life and the mean of the corresponding time, y end is the ordinate value at the end of the regression line in the window, i.e., the final predicted value of the remaining life, t end is the horizontal coordinate value at the end of the regression line;

[0033] Step S3.3: Project all the original predicted values ​​of the remaining life in the window obtained in step 3.2 to the last moment of the window at the same degradation rate, that is, along the direction of the regression line, to obtain the estimated values ​​of the remaining life at the end of the degradation stage. The formula is expressed as:

[0034]

[0035] In the formula, is one of the remaining lifetime estimates at the last moment of the window;

[0036] Step S3.4: Estimate the probability density function of the remaining life prediction distribution by kernel density estimation method for the remaining life prediction values ​​in a sliding window obtained in step S3.3. Assume its probability density function is f, and the kernel density estimation expression is:

[0037]

[0038] In the formula, K(·) represents the kernel function, and a represents the bandwidth;

[0039] After the probability density function of the predicted distribution of remaining life is estimated, the 95% confidence interval of the predicted distribution of remaining life is further obtained.

[0040] Compared with the prior art, the technical progress achieved by the present invention is:

[0041] The method of the present invention decomposes the multidimensional SCADA time series to perform decoupling analysis on the intra-cycle and inter-cycle changes caused by different cycles in the complex time pattern, thereby overcoming the problem that multiple cycles of the SCADA time series data of the wind turbine overlap and influence each other, making variable modeling difficult to handle, improving the accuracy of the remaining life prediction of the wind turbine components, and providing a more robust reference for wind turbine maintenance decision-making by quantifying the uncertainty of the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of a method for predicting the probability of remaining life of key components of a large wind turbine generator system according to an embodiment of the present invention;

[0043] Figure 2 : is a structural principle diagram of a multi-scale time feature extraction neural network MH-LSTM according to an embodiment of the present invention;

[0044] Figure 3a is a linear regression analysis diagram of the original predicted value of the remaining life within the sliding window of this embodiment;

[0045] Figure 3b yes Figure 3a Corresponding probability density analysis diagram of the predicted distribution of remaining life;

[0046] Figures 4a to 4d Schematic diagram of the remaining life prediction and uncertainty quantification results of the wind turbine gearbox using LSTM, BiLSTM, CNN-LSTM-AM, and MH-LSTM neural network methods respectively. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical scheme and technical effect of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0048] like Figure 1 As shown, a method for predicting the probability of remaining life of key components of a large wind turbine generator system in this embodiment includes the following steps:

[0049] Step S1: Obtain the SCADA data of the wind turbine, i.e., multivariate time series data, through the Supervisory Control And Data Acquisition (SCADA) system, screen the input variables that may be related to the remaining life of the target component, and perform data preprocessing to obtain multiple standardized input variable time series data as neural network training and testing samples, specifically including:

[0050] Step S1.1: Preliminarily select initial input variables that may be related to the remaining life of the target component based on professional knowledge, then calculate the Pearson correlation coefficient between other variables and the initial input variables, and additionally select variables with correlation coefficients greater than a preset value p as input variables together with the initial input variables, and finally obtain n input variables;

[0051] Step S1.2: Use a threshold of 5 times the standard deviation to remove extreme outliers in SCADA data, and use the threshold of active power greater than zero to remove shutdown state data;

[0052] Step S1.3: Use the Z-score standardization method to process the data of each input variable time series obtained. The calculation formula is as follows:

[0053]

[0054] Among them, μ is the mean of the sample data, σ is the standard deviation of the sample data;

[0055] Step S1.4: Use a sliding window with a step size of 1 unit time and a width of t unit time to segment the obtained standardized input variable time series, which can be used as a sample data set for neural network training and testing.

[0056] Step S2: Perform fast Fourier transform on the multiple standardized input variable time series data obtained in step S1, and cut them into time series data of different lengths according to multiple frequency components. Then, the time series data of different lengths are input into different LSTM neural networks in parallel, and the feature vectors at different time scales are extracted and spliced ​​and merged. After that, they are input into the linear output layer to obtain the predicted value of the remaining life of the fan components, such as Figure 2 As shown, specifically including:

[0057] Step S2.1: After window segmentation, the time series signal X with an input length of t and the number of input variables n is obtained. i ∈R t×nFast Fourier transform is used to process and obtain n characteristic spectrum graphs. In order to comprehensively consider the influence of each input variable, the amplitude dimension of all characteristic spectrum graphs is averaged to obtain a new spectrum graph. Due to the conjugate characteristics of the spectrum, only half of the spectrum of the new spectrum graph is taken for analysis:

[0058]

[0059] In the formula, X i represents a time series of an input variable, A represents the corresponding amplitudes of all frequency components, FFT(·) represents fast Fourier transform, and Amp(·) represents the calculated amplitude;

[0060] Step S2.2: Select the first k maximum amplitudes from A obtained in step S2.1, and find their corresponding frequencies and periods. It should be noted that in order to remove the influence of noise, high-frequency components are generally not considered when selecting frequency components. The calculation formula is as follows:

[0061] [f1,…,f k ]=Fre(Topk(A))

[0062]

[0063] In the formula, Topk(·) means finding the first k maximum values, Fre(·) means taking the frequency value, [f1,...,f k ] represents the first k frequency values, [p1,...,p k ] represents the period value corresponding to the above frequency value;

[0064] Step S2.3: Based on the k periods obtained from step S2.2, start from the last moment of the input time series and cut forward to obtain k time segments with a length equal to the period value. l∈{1,…,k};

[0065] Step S2.4: Input the k time segments obtained in step S2.3 into different LSTM neural networks respectively to obtain the final output vectors [h1,…,h k ];

[0066] Step S2.5: concatenate the k final output vectors obtained in step S2.4 and input them into the linear output layer to obtain the predicted value of the remaining life of the fan components, which is expressed as:

[0067] y=W l ·cat([h1,…,h k ])

[0068] Where W lis the weight of the linear layer, y is the final prediction result, and the cat(·) function indicates that the vectors are concatenated by column.

[0069] Step S3: quantifying the uncertainty of the predicted value of the remaining life of the wind turbine components obtained in step S2 based on the method of linear regression and kernel density estimation, specifically including:

[0070] Step S3.1: Process the remaining life prediction value obtained in step S2.5 by using a sliding window with a step length of 1 unit time and a width of 1 unit time to obtain the original remaining life prediction value [y1,…,y l ] and consider each sliding window as a small degradation stage;

[0071] Step S3.2: In order to estimate the degradation rate of the components within the window, it is necessary to calculate the original predicted values ​​of the remaining life in the sliding window [y1,…,y l ] to perform linear regression, such as Figure 3a As shown in the figure, the slope of the fitted regression line is the estimated degradation rate of the component during this window predicted by the neural network, and the ordinate value at the end of the regression line is the estimated remaining life at the last moment of the current window. This process can be expressed by the following formula:

[0072]

[0073] y end =wt end +b

[0074] In the formula, w and b are the slope and intercept of the regression line respectively. and are the mean of the original predicted value of the remaining life and the mean of the corresponding time, y end is the ordinate value at the end of the regression line in the window, i.e., the final predicted value of the remaining life, t end is the horizontal coordinate value at the end of the regression line;

[0075] Step S3.3: Project all the original predicted values ​​of the remaining life in the window obtained in step 3.2 to the last moment of the window at the same degradation rate, that is, along the direction of the regression line. In this way, all possible predicted values ​​of the remaining life at the end of this degradation stage are obtained, which can be mathematically expressed as:

[0076]

[0077] In the formula, is one of the remaining lifetime estimates at the last moment of the window;

[0078] Step S3.4: Reference Figure 3b, estimate the probability density function of the remaining life prediction distribution by the kernel density estimation method for all possible remaining life prediction values ​​in a sliding window obtained in step S3.3. Assume its probability density function is f, and the kernel density estimation expression is:

[0079]

[0080] Where K(·) represents the kernel function, usually a Gaussian kernel is selected, and a represents the bandwidth. After the probability density function of the remaining life prediction distribution is estimated, the 95% confidence interval of the distribution can be further obtained.

[0081] In order to verify the effectiveness of the method of the present invention, this embodiment uses the SCADA data set of a 4MW wind turbine in a wind farm in Jiangsu Province, China to evaluate the proposed method. In the fault records of the data set, it can be known that due to a gearbox failure, wind turbines No. 42 and No. 47 were shut down for maintenance at 2023-07-08 12:00 and 2023-07-08 13:18, respectively. This embodiment selects the SCADA data of the two wind turbines from four months before the failure to the failure for training and testing, respectively. The detailed information of the data set is shown in Table 1. Substitute the method MH-LSTM of the present invention into other LSTM, BiLSTM, CNN-LSTM-AM and other methods for comparison.

[0082] Table 1 Dataset details

[0083]

[0084] In this embodiment, the gearbox degradation data of fan No. 42 is used as training data to train the multi-scale time feature extraction neural network MH-LSTM proposed in the present invention, and the neural network hyperparameter settings are shown in Table 2. In the training process of the neural network, in order to speed up the convergence rate and reduce the training time, the learning rate decay strategy and the early stopping strategy are adopted.

[0085] Table 2 Neural network hyperparameter settings

[0086]

[0087] The gearbox degradation data of fan No. 47 was used as the test data. In order to verify the superiority of the method of the present invention, it was compared with several other neural network models, including LSTM, BiLSTM and CNN-LSTM-AM. Figures 4a to 4dAs shown in the figure, compared with other methods, the remaining life prediction value obtained by the method of the present invention is more accurate at each time point, the probability density function is more concentrated, and it is more in line with the law of change. 2 , interval coverage probability: PICP, average width: PINAW, comprehensive index: CWC, as the evaluation index of the gearbox remaining life prediction and uncertainty quantification effect, the calculation results are shown in Table 3. It can be seen that the method of the present invention has achieved the best results in the five evaluation indicators of RMSE, MAE, R2, PINAW, and CWC. In general, the remaining life probability prediction method of the present invention has a stronger ability to identify different stages of the degradation process, and has high prediction accuracy and stability in the whole life degradation process of the wind turbine gearbox.

[0088] Table 3 Comparison of evaluation indicators of different methods

[0089]

[0090] The above description is only a preferred implementation case of the present invention and does not limit the present invention in any form. Although the implementation process of the present invention is described in detail above, for those familiar with the art, they can still modify the technical solutions recorded in the above examples, or replace some of the technical features therein with equivalents. All modifications, equivalent replacements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the probability of remaining life of key components of a large wind turbine generator set, characterized in that: The following steps are involved: Step S1: acquiring SCADA data of the wind turbine through a data acquisition and monitoring control system, screening out input variables related to the remaining life of target components of the wind turbine, and performing data preprocessing to obtain standardized time series data of multiple input variables; Step S2: Perform fast Fourier transform on the standardized time series data of multiple input variables obtained in step S1, and cut them into time series data of different lengths according to multiple frequency components, and then input the time series data of different lengths into different LSTM neural networks for parallel processing, extract the feature vectors at different time scales and perform splicing and merging, and then input them into the linear output layer to obtain the predicted value of the remaining life of the fan components; Step S3: performing uncertainty quantification processing on the predicted value of the remaining life of the wind turbine components obtained in step S2 based on the method of linear regression and kernel density estimation.

2. The method for predicting the remaining life probability of key components of a wind turbine generator set according to claim 1 is characterized in that: In step S1, the input variables related to the remaining life of the target component of the wind turbine are screened out, specifically: first, the initial input variables related to the remaining life of the target component are selected based on professional knowledge, and then the Pearson correlation coefficients of other variables and the initial input variables are calculated, and variables with correlation coefficients greater than a preset value p are selected from other variables, and used as input variables together with the initial input variables, thereby obtaining n input variables, where n is a positive integer.

3. The method for predicting the remaining life probability of key components of a wind turbine generator set according to claim 1 is characterized in that: In step S1, the data preprocessing specifically includes: First, a threshold of 5 times the standard deviation is used to eliminate extreme outliers in SCADA data, and the shutdown state data is eliminated using the active power greater than zero as the threshold; Then the Z-score standardization method is used to process the time series of each input variable; Finally, a sliding window with a step size of 1 unit time and a width of t unit time is used to segment the standardized input variable time series.

4. The method for predicting the remaining life probability of key components of a wind turbine generator set according to claim 3 is characterized in that: The step S2 specifically includes: Step S2.1: Use fast Fourier transform to process the time series signal with an input length of t and an input variable number of n after window segmentation to obtain n characteristic spectrum graphs, where n is a positive integer. Then, the amplitude dimensions of all characteristic spectrum graphs are averaged to obtain a new spectrum graph. Based on the conjugate characteristics of the spectrum, only half of the spectrum of the new spectrum graph is taken for analysis: Where, X i ∈R t×n , X i represents a time series of an input variable, A represents the corresponding amplitudes of all frequency components, FFT(·) represents fast Fourier transform, and Amp(·) represents the calculated amplitude; Step S2.2: Select the first k maximum amplitudes from A obtained in step S2.1, and find their corresponding frequencies and periods. The calculation formula is as follows: [f1,…,fk]=Fre(Topk(A)) In the formula, Topk(·) means finding the first k maximum values, Fre(·) means taking the frequency value, [f1,…,f k ] represents the first k frequency values, [p1,…,p k ] represents the first k period values ​​corresponding to the frequency value; Step S2.3: Based on the k periods obtained from step S2.2, start from the last moment of the input time series and cut forward to obtain k time segments with a length equal to the period value. l∈{1,...,k}; Step S2.4: Input the k time segments obtained in step S2.3 into different LSTM neural networks respectively to obtain the final output vectors [h1,…,h k ]; Step S2.5: concatenate the k final output vectors obtained in step S2.4 and input them into the linear output layer to obtain the predicted value of the remaining life of the fan components, which is expressed as: y=W l ·cat([h1,…,h k ]) Where W l is the weight of the linear layer, y is the final prediction result, and the cat(·) function indicates that the vectors are concatenated by column.

5. The method for predicting the remaining life probability of key components of a wind turbine generator set according to claim 4 is characterized in that: In step S2.2, when the first k maximum amplitudes are selected from A, the frequency components thereof do not include high-frequency components.

6. The method for predicting the remaining life probability of key components of a wind turbine generator set according to claim 4 is characterized in that: The step S3 specifically includes: Step S3.1: Process the remaining life prediction value obtained in step S2.5 by using a sliding window with a step length of 1 unit time and a width of 1 unit time to obtain the original remaining life prediction value [y1, ..., y l ] and consider each sliding window as a degradation stage; Step S3.2: The original predicted value of the remaining life in the sliding window [y1, ..., y l ] to perform linear regression. The slope of the fitted regression line is the estimated degradation rate of the component during this window predicted by the neural network. The ordinate value at the end of the regression line is the estimated remaining life at the last moment of the current window. The formula is: y end =wt end +b In the formula, w and b are the slope and intercept of the regression line respectively. and are the mean of the original predicted value of the remaining life and the mean of the corresponding time, y end is the ordinate value at the end of the regression line in the window, i.e., the final predicted value of the remaining life, t end is the horizontal coordinate value at the end of the regression line; Step S3.3: Project all the original predicted values ​​of the remaining life in the window obtained in step 3.2 to the last moment of the window at the same degradation rate, that is, along the direction of the regression line, to obtain the estimated values ​​of the remaining life at the end of the degradation stage. The formula is expressed as: In the formula, is one of the remaining lifetime estimates at the last moment of the window; Step S3.4: Estimate the probability density function of the remaining life prediction distribution by kernel density estimation method for the remaining life prediction values ​​in a sliding window obtained in step S3.

3. Assume its probability density function is f, and the kernel density estimation expression is: In the formula, K(·) represents the kernel function, and a represents the bandwidth; After the probability density function of the predicted distribution of remaining life is estimated, the 95% confidence interval of the predicted distribution of remaining life is further obtained.

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