A device life prediction method based on a particle filtering LSTM model

Abstract

The application discloses a kind of equipment life prediction methods based on particle filtering's LSTM model, it is related to system reliability field.The method proposes the RUL prediction method of fusion PF and LSTM, state transition model in PF filtering process is established using LSTM, the resampling method in PF is improved so that resampling can retain sampling gradient information for network model update.PF-LSTM model realized can give full play to LSTM on time series modeling and the state estimation capability of PF to nonlinear, non-stationary and non-Gaussian system.Original data is directly sent into network after standardization processing, and end-to-end learning ensures that the network only focuses on features related to the prediction target during the learning process, improving network sequence efficiency and accuracy.

Description

[0001] Field of study

[0002] This invention relates to the field of system reliability, and more specifically to high-dimensional data remaining lifetime prediction and reliability management of complex equipment. Existing technology

[0003] Predictive maintenance and health management (PHM) is a technology used to monitor the health status of in-service equipment, enabling maintenance decisions based on machine operating conditions. Compared to routine or periodic preventative maintenance, it is more cost-effective, performing maintenance only when deemed necessary. Therefore, it has gained recognition and is being widely adopted across various industries globally, particularly in industrial manufacturing. Remaining Useful Life (RUL) prediction is a crucial component of PHM, and its accuracy is critical for subsequent maintenance decisions and ensuring safe equipment operation. This has led to a surge in research on RUL prediction methods in recent years. While different methods have improved prediction accuracy to some extent, they lack interpretive representations of the uncertainties in the prediction results. RUL estimation with quantified uncertainty can provide a more comprehensive reference for practical equipment management and is of significant research value.

[0004] Currently, methods for predicting RUL (Recovery Limitation) can be mainly divided into three categories: physical model-based methods, data-driven methods, and hybrid methods. Physical model-based methods are suitable for specific objects with well-defined failure mechanisms, relying on the combination and application of prior data and empirical knowledge. If an accurate physical model can be established based on system characteristics, high RUL prediction accuracy can be achieved. However, with the increasing complexity and precision of equipment, different monitoring components possess different degradation mechanisms, limiting the versatility of physical model-based methods in real-world environments. Conversely, data-driven methods are free from the constraints of domain knowledge, directly building system models based on data and extracting the potential relationship between the original data and RUL by mining degradation information from the data. Hybrid methods aim to integrate the advantages of both physical model-based and data-driven methods to improve prediction accuracy, but they face numerous challenges in application, such as: how to determine the correct fusion mechanism; how to reconcile the contradictions between data and the model; and how to manage the uncertainties of hybrid prediction methods. Therefore, research on hybrid methods is currently the least extensive compared to the former two.

[0005] Currently, data-driven methods mainly include statistical learning and machine learning. The former uses mathematical statistics to provide support for quantifying prediction uncertainty, enhancing the reliability of prediction results, while the latter establishes a mapping relationship between data and prediction targets. Furthermore, a reliable prediction algorithm provides not only a RUL estimate but also a corresponding confidence representation. In fact, handling uncertainty in predictive science is even more important than degenerate modeling. Currently, the most researched methods for uncertainty in prediction mainly rely on statistical models, among which the Particle Filter (PF) method under Bayesian statistics is a particularly useful tool for exploring RUL prediction uncertainty. Using the PF method for prediction can easily generate outputs in the form of probability distributions, thereby characterizing and managing uncertainty. In addition, the adaptive learning capability of deep network models reduces the dependence on empirical knowledge in building degenerate models. Long Short-Term Memory (LSTM) neural networks, in particular, perform excellently in handling time series prediction problems and have become one of the more popular deep models. Summary of the Invention

[0006] The objective of this invention is to propose a RUL prediction method that integrates Power Filtering (PF) and LSTM. It utilizes LSTM to establish a state transition model during the PF filtering process and improves the resampling method in PF so that resampling retains sampling gradient information for network model updates. The implemented PF-LSTM model fully leverages the time series modeling capabilities of LSTM and the state estimation capabilities of PF for nonlinear, non-stationary, and non-Gaussian systems. The raw data is directly fed into the network after standardization, and end-to-end learning ensures that the network focuses only on features relevant to the prediction target during the learning process, improving the network's sequence efficiency and accuracy. The main contributions of the proposed method are as follows:

[0007] (1) A method for describing uncertainty is proposed. PF uses a set of weighted particles to represent the probability distribution, which enables the estimation of nonlinear, non-smooth, and non-Gaussian state-space models.

[0008] (2) A dynamically updated degradation model is proposed. LSTM is used to build the degradation model without requiring expert experience, and the differentiable particle filter enables the training and parameter update of the LSTM model to be carried out simultaneously.

[0009] (3) High prediction accuracy and confidence interval representation are given. The prediction method combines PF and LSTM and develops both to improve prediction accuracy. Finally, the corresponding confidence interval representation is given for uncertain information.

[0010] The technical solution of this invention is: a device lifetime prediction method based on particle filtering using an LSTM sequence model, comprising the following steps:

[0011] Step 1: Data acquisition and preprocessing, including the following sub-steps:

[0012] Step 1.1: Data Acquisition;

[0013] Sensors 1, 2, 3, ..., m are deployed on the monitored equipment to collect operational data with different changing trends, denoted as the original degradation sequence x. 1 ,x 2 ,x 3 ,...,x m The sensor sequence length is L, i.e., x i =[x1,x2,x3,...,x L ].

[0014] Step 1.2: Dataset partitioning;

[0015] The original degradation sequences collected by similar monitoring equipment form the original dataset. The original dataset is randomly divided into three parts: training set, validation set, and test set. The training set is used to train the model; the validation set is used to test the performance of the trained model, adjust the model parameters, and verify the model's generalization ability in order to determine the selection and preservation of the optimal model; the test set is used to evaluate the final predictive performance of the model.

[0016] Step 1.3: Data preprocessing;

[0017] The original degenerate sequence x 1 ,x 2 ,x 3 ,...,x m After sensor selection and standardization, the input sample sequences and labels are divided. The variance σ of the sequence variation is calculated for the same sensor. 1 ,σ 2 ,σ 3 ,...,σ m Remove variables with variance σ less than 10. -3 After the sensor is used, retain the valid sensor sequence x 1 ,x 2 ,x 3 ,...,x m , n≤m. The zero-mean normalization method (Z-score) standardizes the data for the same sensor. The specific processing method is as follows:

[0018]

[0019] in Let u be the standardized sensor feature value.i and σ i Let X and Y represent the mean and standard deviation of the i-th sensor, respectively. Let L be the RUL of the first collected data point, and 0 be the RUL of the L-th data point. The original degraded sequence is two-dimensional data X. L×n The input sample sequence is generated using a sliding window with a size of tw. The time window is slid across the two-dimensional data with a step size of 1, resulting in the following k-th input sample sequence:

[0020] X k =[x k ,x k ,x k ,...,x k+tw-1 ]

[0021] Where, x k It is an n-dimensional vector. The label of the k-th input sample sequence. RUL: Lk-tw+2 is the last data point in the sequence. The two-dimensional sensor sequence is transformed into a three-dimensional input sequence after being processed by a sliding window, where the first dimension is the sample size, the second dimension is the sample sequence length tw, and the third dimension is the sensor feature size n.

[0022] Step 2: Implementation of the PF-LSTM algorithm, including the following sub-steps:

[0023] Step 2.1: State initialization;

[0024] The input sample sequence and its corresponding label are fed into the feedforward neural network f in batches M. em (·) Reconstructing the degenerate state space to extract deep degenerate features is represented as:

[0025] (X' t =[x' t ,x' t+1 ,x' t+2 ,...,x' t+tw-1 ])=f em (X t =[x t ,x t+1 ,x t+2 ,...,x t+tw-1 ])

[0026] X t =[x t ,x t+1 ,x t+2 ,...,x t+tw-1 ] and X' t =[x' t ,x' t+1 ,x' t+2 ,...,x' t+tw-1The distribution represents the input sample sequence and the extracted depth feature sequence at time t. Then, the depth feature sequence is copied N times to obtain a set of depth feature sequences with the same number of particles N. It is a p-dimensional vector, where p represents the dimension of the deep feature embedding within the reconstructed degenerate state space. The particle state set is randomly initialized. Let the hidden state and long-term memory state of the i-th particle at the previous time step t-1 be represented respectively, and initialize the particle weight set.

[0027] Step 2.2: Building the PF-LSTM model;

[0028] Set of deep feature sequences Feed into the feedforward neural network f act (·) and f obs (·) Extract transfer information separately and measurement information Represented as:

[0029]

[0030]

[0031] and Given a sequence of length tw, use the reparameterization technique to transition from the current time t. The hidden state at time t-1 Learning process noise

[0032]

[0033] k(·) represents the feedforward neural network used for noise extraction, which is used to build the degenerate hidden state transition model for LSTM. The internal calculation formula of LSTM is as follows:

[0034]

[0035]

[0036]

[0037] f t i, These represent the input gate, forget gate, and output gate information, respectively; w i w f w o and b i b f b oThis represents the weight parameters and bias terms of the input gate, forget gate, and output gate, where σ(·) is the sigmoid function. Process noise. Replace candidate gate Update to obtain the long-term memory state at time t.

[0038]

[0039] Update the hidden state at time t to:

[0040]

[0041] tanh(·) is the hyperbolic tangent function.

[0042] Next, we will utilize the updated hidden state at time t. Measurement Weights Update:

[0043]

[0044] η is the regularization term, f like (·) is the likelihood generation relation p(z) learned using a feedforward neural network. t |h t At this point, the particle state set from the previous time step t-1 is complete. and particle weight set The update yields the particle state set at time t. and particle weight set

[0045] To prevent particle degradation from wasting computational resources, resampling methods are introduced. Traditional resampling directly starts from... After sampling the particle states according to their weights, the weights are normalized to... This results in the loss of sampling gradient information. An improvement to traditional resampling methods is needed, addressing the issue of mixed distributions. After sampling, the particle weights are recalculated as follows:

[0046]

[0047] λ is a harmonic parameter representing the resampling rate.

[0048] Transfer information Sequence and measurement information The sequence is recursively fed into the PF-LSTM to calculate and update the particle set.

[0049] Step 2.3: Model loss calculation and update;

[0050] The update of the last data point within a single sample sequence is obtained through recursive computation. via feedforward neural network f out (·) Output prediction RUL

[0051]

[0052] y t The weighted predicted RUL, corresponding to the sample label Compare and calculate the model loss:

[0053]

[0054] Let l be the model loss value with M samples. The model is trained using the backpropagation algorithm, adjusting network weights and biases to continuously minimize the model loss value l. Early stopping is used to reduce the risk of overfitting during model training. The training set loss l is calculated separately. train And validation set loss l valid A pre-set waiting time T is used when the training set loss l train As the waiting time T decreases, the validation set loss l valid If the model stops decreasing within the waiting time T, it can be considered that the model is overfitting. At this time, model training should be stopped and the model parameters should be saved.

[0055] Step 3: The PF-LSTM model is used to predict lifetime.

[0056] After building the PF-LSTM model, load the saved model parameters. Obtain the RUL prediction point output y on the test set. t and RUL prediction distribution characterization

[0057] The beneficial effects of this invention are: the fusion method not only completes the quantitative calculation of uncertainty in the modeling process, but also improves the model's prediction accuracy and robustness, solving the problem of difficulty in modeling degradation of complex equipment, and at the same time making up for the shortcomings of existing prediction algorithms in terms of insufficient accuracy and lack of uncertainty management. The proposed PF-LSTM algorithm has improved prediction accuracy and precision to a certain extent, and the model prediction performance has been greatly improved. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of a typical LSTM network structure;

[0059] Figure 2 This is a schematic diagram of the iterative update process of PF;

[0060] Figure 3 This is a schematic diagram of the internal structure of the PF-LSTM based invention.

[0061] Figure 4 This is a flowchart of the prediction process based on PF-LSTM;

[0062] Figure 5 This is a diagram of the model training loss trajectory in the embodiment;

[0063] Figure 6 This is a schematic diagram of the prediction results for 100 test set engines in FD001 in the embodiment;

[0064] Figure 7 This is a graph showing the prediction results for the entire work cycle in the embodiment;

[0065] Figure 8 This is a schematic diagram illustrating the exploration of the embedding dimension of deep features in the embodiment;

[0066] Figure 9 This is a schematic diagram illustrating the impact of particle number on the performance of the proposed network in the embodiment;

[0067] Figure 10 This is a schematic diagram illustrating the impact of the time window size on network performance in the embodiment. Specific Implementation

[0068] The following is an example verification of the device lifetime prediction method based on particle filtering and LSTM sequence model described in this invention. The process is as follows:

[0069] 1. Data Collection and Preprocessing:

[0070] (1) Data acquisition;

[0071] The FD001 dataset from the publicly available NASA Commercial Modular Aero-Propulsion System Simulation Data (C-MAPSS) will be used as the benchmark for evaluating the predictive performance of the PF-LSTM model. The CMAPSS dataset contains 21 sensors, and Table 1 provides detailed information on these 21 sensors.

[0072] Table 1. Detailed information on CMAPSS engine sensors.

[0073]

[0074]

[0075] (2) Dataset partitioning;

[0076] The FD001 has 100 training set engines and 100 test set engines. All engines can be considered to come from the same batch, but each engine has a slightly different degradation trajectory due to initial wear and tear and manufacturing deviations. The 100 training set engines are further divided for model training and validation in a ratio of 8:2, that is, 80 engines are used to generate training set data and 20 engines are used to generate validation set samples.

[0077] (3) Data preprocessing;

[0078] Of these 21 sets of sensor monitoring signals, the sequence variance σ of 14 sensors, including T24, T30, T50, P30, Nf, Nc, Ps30, phi, NRf, Nrc, BPR, htBleed, W31, and W32, was calculated. i Greater than 10 -3 The first sensor showed a relatively obvious degradation trend, while seven sensors, including T2, P20, P15, epr, farB, Nf_dmd, and PCNfR_dmd, remained almost unchanged after monitoring began and were subsequently removed. Calculate the mean u of each sensor sequence in the training set. i and variance σ i Then, the Z-Score method is used to standardize the training, validation, and test sets. Finally, a sliding window is used to generate the input sample sequences and labels.

[0079] 2. PF-LSTM algorithm implementation;

[0080] (1) State initialization

[0081] The training sample X t→train and validation sample X t→valid Feeding 128 at a time into the feedforward neural network f em (·) Extract deep degradation features X' t→train 、X' t→valid The depth feature embedding dimension was set to 32 through model parameter tuning. Next, the depth feature sequence was copied to obtain a set of depth feature sequences with the same number of particles. The particle set was then initialized.

[0082] (2) Constructing a PF-LSTM degeneracy model

[0083] Set of deep feature sequences Feed into the feedforward neural network f act (·) and f obs (·) Extract transfer information separately and measurement information Next, based on the reparameterization technique, noise is gradually extracted from the feature sequence using the noise of the network k(·) learning process. Particle states are predicted step by step using the calculation formulas of the internal cells of the LSTM. And combined with a feedforward neural network f like (·) Particle weights The algorithm is updated and improved, and then applied to posterior distribution resampling to obtain the particle set.

[0084] (3) Model loss calculation and update;

[0085] The particle set updated from the last data point in each sample sequence is fed into the feedforward neural network f. out (·) After predicting the RUL, the training set loss and validation set loss are calculated by comparing the RUL label value. The model parameters are updated based on backpropagation, and the model is trained using early stopping and the optimal parameters are saved.

[0086] The basic configuration of some structural and functional parameters of the network is shown in Table 2, including batch size, hidden unit dimension, learning rate, etc. After initializing the network and particle parameters and states, the standardized samples are input into the network for model training.

[0087] Table 2 Model Parameter Settings

[0088]

[0089] 3. PF-LSTM model for lifetime prediction

[0090] After building the PF-LSTM model, initialize the particle set. And load the model parameters saved during training. Input test set sample X t→test The forward computation is performed on the PF-LSTM model to obtain the RUL prediction weighted output y for each test sample. t→test and RUL prediction distribution characterization

[0091] 4. Performance Validation of PF-LSTM Model

[0092] (1) Validation of prediction results

[0093] The prediction results for the 100 test set engines in FD001 are as follows: Figure 6 As shown in the figure, the predicted RUL values ​​for most engines are close to the actual RUL values, especially for engines nearing failure with smaller actual RUL labels, where the predictions are quite accurate. For example, the red dots in the figure mark the predicted RUL values ​​for engines with actual labels less than 20; it can be seen that over 50% of the predicted results overlap with the actual values. This indicates that for engines with complete degradation history information, sufficient prior information can further improve the accuracy of the predictions.

[0094] Furthermore, we know that for critical and valuable mechanical equipment, we should perform advance maintenance to reduce the enormous economic losses caused by sudden equipment failures. It is known that the test set engines randomly stopped operating for a period of time before reaching failure, resulting in incomplete degradation life trajectory information for each unit. The prediction results for the entire working cycle as the engine operates until near failure are... Figure 7 As the results show, initially, due to missing information, the predicted results differed significantly from the true labels. Furthermore, the model was affected by random factors such as initialization, resulting in considerable estimation uncertainty and significant fluctuations in the predicted curve around the true degradation curve. With continuous input of information, the degradation curve gradually converged, and the prediction interval decreased. Especially near the failure point, the predicted value almost perfectly matched the true value, minimizing uncertainty. This aligns with our expectation of achieving higher prediction accuracy as we approach the failure point.

[0095] (2) Model parameter evaluation

[0096] In studies on the remaining life prediction of aero-engines, the root mean square error (RMSE) is a commonly used evaluation metric. The RMSE formula is defined as follows:

[0097]

[0098] In the formula, n is the number of test units. and y t→test Let RUL and RUL represent the predicted RUL and the actual RUL of the i-th test unit, respectively.

[0099] Figure 8 This study explores the depth feature embedding dimension to achieve better prediction performance. Considering the impact of time window size on prediction results, we conducted four sets of experiments, selecting time windows of lengths 20, 40, 60, and 80 to investigate the effect on the same depth feature embedding dimension. It can be seen that when the time window is small, such as 20 or 40, the prediction performance is significantly improved by increasing the depth feature embedding dimension, as the network obtains limited information from the degradation trajectory, and the RMSE shows a decreasing trend within a certain range. When the sequence length increases, such as to 60 or 80, the network further reduces the prediction error by drawing knowledge from historical information. Overall, appropriately increasing the depth feature embedding dimension can lead to better prediction results. Based on the experimental results, we determined the depth feature embedding dimension to be 32 for our subsequent experiments.

[0100] For particle filtering methods, the number of particles affects the spatial representation capability of the filter and the convergence of the results. Figure 9The impact of particle number on the proposed network performance is demonstrated. With a small particle count, such as 30, the prediction performance is insufficient. As the particle count increases, the estimation accuracy gradually improves. However, with further increases in particle count, the RMSE decreases somewhat, but the model training time becomes significantly longer. Overall, the network exhibits stable prediction performance, with the best results achieved at 100 particles.

[0101] After selecting appropriate feature dimensions and particle number, we further tested the impact of the time window size on prediction performance. The time window size determines the length of the input sequence; a longer sequence contains more known information, indicating a more accurate prediction. Figure 10 The study demonstrates the impact of time window size on network performance. As the time window gradually increases, the accuracy of RUL estimation continuously improves. This shows that prior information has a significant impact on improving prediction accuracy. When the time window is within the range of 70–90, the prediction performance is relatively stable, indicating that within the corresponding time length, the network is able to simulate the degradation trend reflected in the learned data.

Claims

1. A device lifetime prediction method based on LSTM sequence model with particle filtering, characterized in that, Includes the following steps: Step 1: Data acquisition and preprocessing, including the following sub-steps: Step 1.1: Data Acquisition; Sensors 1, 2, 3, ..., m are deployed on the monitored equipment to collect operational data with different changing trends, denoted as the original degradation sequence x. 1 ,x 2 ,x 3 ,...,x m The sensor sequence length is L, i.e., x i =[x1,x2,x3,...,x L ]; Step 1.2: Dataset partitioning; The original degradation sequences collected by similar monitoring equipment form the original dataset. The original dataset is randomly divided into three parts: training set, validation set, and test set. The training set is used to train the model; the validation set is used to test the performance of the trained model, adjust the model parameters, and verify the model's generalization ability to determine the selection and preservation of the optimal model; the test set is used to evaluate the final predictive performance of the model. Step 1.3: Data preprocessing; The original degenerate sequence x 1 ,x 2 ,x 3 ,...,x m After sensor selection and standardization, the input sample sequences and labels are divided; the variance σ of sequence variation is calculated for the same sensor. 1 ,σ 2 ,σ 3 ,...,σ m Remove variables with variance σ less than 10. -3 After the sensor is used, retain the valid sensor sequence x 1 ,x 2 ,x 3 ,...,x m , n≤m; The zero-mean normalization method (Z-score) standardizes the same sensor, and the specific processing method is as follows: in Let u be the standardized sensor feature value. i and σ i Let X be the mean and standard deviation of the i-th sensor, respectively; let L be the RUL of the first collected data point and 0 be the RUL of the L-th data point; the original degraded sequence is two-dimensional data X. L×n The input sample sequence is generated using a sliding window with a size of tw. The time window is slid across the two-dimensional data with a step size of 1, resulting in the following k-th input sample sequence: X k =[x k ,x k ,x k ,...,x k+tw-1 ] Where, x k It is an n-dimensional vector; the label of the k-th input sample sequence. RUL:Lk-tw+2 is the last data point in the sequence; the two-dimensional sensor sequence is transformed into a three-dimensional input sequence after being processed by a sliding window, where the first dimension is the sample size, the second dimension is the sample sequence length tw, and the third dimension is the sensor feature size n; Step 2: Implementation of the PF-LSTM algorithm, including the following sub-steps: Step 2.1: State initialization; The input sample sequence and its corresponding label are fed into the feedforward neural network f in batches M. em (·) Reconstructing the degenerate state space to extract deep degenerate features is represented as: (X' t =[x' t ,x' t+1 ,x' t+2 ,...,x' t+tw-1 ])=f em (X t =[x t ,x t+1 ,x t+2 ,...,x t+tw-1 ]) X t =[x t ,x t+1 ,x t+2 ,...,x t+tw-1 ] and X' t =[x' t ,x' t+1 ,x' t+2 ,...,x' t+tw-1 The distribution represents the input sample sequence and the extracted depth feature sequence at time t; then, the depth feature sequence is copied N times to obtain a set of depth feature sequences with the same number of particles N. It is a p-dimensional vector, where p represents the dimension of the deep feature embedding within the reconstructed degenerate state space; the particle state set is randomly initialized. Let the hidden state and long-term memory state of the i-th particle at the previous time step t-1 be represented respectively, and initialize the particle weight set. Step 2.2: Building the PF-LSTM model; Set of deep feature sequences Feed into the feedforward neural network f act (·) and f obs (·) Extract transfer information separately and measurement information Represented as: and Given a sequence of length tw; use the reparameterization technique to transition from the current time t. The hidden state at time t-1 Learning process noise k(·) represents the feedforward neural network used for noise extraction, which is used to build the degenerate hidden state transition model for LSTM. The internal calculation formula of LSTM is as follows: These represent the input gate, forget gate, and output gate information, respectively; w i w f w o and b i b f b o This represents the weight parameters and bias terms of the input gate, forget gate, and output gate, where σ(·) is the sigmoid function; process noise. Replace candidate gate Update to obtain the long-term memory state at time t. Update the hidden state at time t to: tanh(·) is the hyperbolic tangent function; Next, we will utilize the updated hidden state at time t. Measurement Weights Update: η is the regularization term, f like (·) is the likelihood generation relation p(z) learned using a feedforward neural network. t |h t At this point, the particle state set from the previous time step t-1 is completed. and particle weight set The update yields the particle state set at time t. and particle weight set Improvements to traditional resampling methods, based on mixed distributions After sampling, the particle weights are recalculated as follows: In the formula, λ is a harmonic parameter representing the resampling rate; Transfer information Sequence and measurement information The sequence is recursively fed into the PF-LSTM to calculate and update the particle set. Step 2.3: Model loss calculation and update; The update of the last data point within a single sample sequence is obtained through recursive computation. via feedforward neural network f out (·) Output prediction y t The weighted predicted RUL, corresponding to the sample label Compare and calculate the model loss l: Let l be the model loss value with M samples. The model is trained using the backpropagation algorithm, adjusting network weights and biases to continuously minimize the model loss value l. Early stopping is used to reduce the risk of overfitting during model training. The training set loss l is calculated separately. train And validation set loss l valid A pre-set waiting time T is used when the training set loss l train As the waiting time T decreases, the validation set loss l valid If the model stops decreasing within the waiting time T, it can be considered that the model is overfitting. At this time, model training should be stopped and the model parameters should be saved. Step 3: The PF-LSTM model is used to predict lifetime. After building the PF-LSTM model, load the saved model parameters; obtain the RUL prediction point output y on the test set. t and RUL prediction distribution characterization

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