Lithium ion battery RUL prediction method based on MBGD-WGAN-GRU

Abstract

The invention discloses a lithium ion battery RUL prediction method based on MBGD-WGAN-GRU (Model-Based Graphics Decomposition-Wavelet German-Based Graphics According to the method, firstly, health factors highly related to the aging characteristics of the lithium ion battery are mined from original monitoring data through a grey relational analysis method, a characteristic space reflecting the degradation trend of the battery is constructed, and a data set is divided into a training set and a test set according to the proportion; then, a small-batch stochastic gradient descent optimization generative adversarial network is adopted, and high-fidelity synthetic data is generated; then training a GRU (Gated Recirculation Unit) model by using the extracted health factor and the extended training set, capturing a dynamic evolution law of battery aging, and realizing high-precision prediction of the RUL; and finally, battery RUL prediction and verification of the GRU model are realized through a public test data set. According to the method, the data expansion of the lithium ion training set is realized by optimizing the WGAN through the MBGD, the GRU model is trained by using the health factor sequence and the expanded training set, the dynamic evolution law of the aging of the lithium ion battery is captured, and the high-precision prediction of the RUL is realized.

Description

Technical Field

[0001] The present invention relates to a lithium ion battery RUL prediction method based on MBGD-WGAN-GRU. Background Art

[0002] With the rapid adoption of electric vehicles, safety risks caused by power battery performance degradation are becoming increasingly severe. In particular, the frequent occurrence of fires caused by aging lithium-ion batteries has resulted in significant economic losses and risks. Therefore, accurate prediction of the remaining useful life (RUL) of lithium-ion batteries has become crucial. Under real-world operating conditions, the charging and discharging processes of electric vehicles are complex and variable, influenced by numerous factors, such as mileage uncertainty, differences in user charging habits, and changes in ambient temperature. These factors make it difficult to obtain complete battery charge and discharge data. The lack of complete charge and discharge cycle data poses challenges for training and optimizing lithium-ion battery RUL prediction models, limiting improvements in prediction accuracy. Therefore, data augmentation methods have emerged to address this data shortage. Traditional methods, such as data interpolation and data augmentation, can augment data to a certain extent, but they have significant limitations. Data interpolation methods generate new data by interpolating between existing data points. However, the samples generated by these methods are often limited to the distribution range of the original data, making it difficult to generate samples with high authenticity and diversity, and prone to model overfitting. In recent years, generative adversarial networks (GANs) and their improved model, Wasserstein GANs (WGANs), have performed well in data generation. However, the training process has problems such as instability and easy mode collapse, which affect the generation effect. Summary of the Invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a lithium-ion battery RUL prediction method based on MBGD-WGAN-GRU, which can fully obtain complete battery charge and discharge cycle data and improve the RUL prediction accuracy and reliability of lithium-ion batteries.

[0004] Technical solution: The MBGD-WGAN-GRU-based lithium-ion battery RUL prediction method of the present invention has the following operating steps:

[0005] (1) Using the grey correlation analysis method, the health factors (IHFs) highly correlated with aging characteristics are extracted from the original aging data of lithium-ion batteries, and the original aging data are divided into a training set and a test set.

[0006] (2) Use the mini-batch stochastic gradient descent method to optimize the Wasserstein generative adversarial network and expand the training set;

[0007] (3) Use the health factors extracted from the original data and the expanded training set to train the GRU model;

[0008] (4) The trained GRU model is applied to the online prediction of the remaining service life of lithium-ion batteries.

[0009] Furthermore, the implementation process of step (1) is as follows:

[0010] (11) The original aging data of lithium-ion battery is recorded as

[0011] Where t represents the number of cycles, T represents the total number of cycles, and x(t) represents the capacity data of the lithium-ion battery at the tth cycle;

[0012] (12) Using the grey correlation analysis method, the average correlation coefficient between each health factor sequence IHFs and the lithium-ion battery capacity sequence is calculated, and the health factors that are highly correlated with the aging characteristics of lithium-ion batteries are retained:

[0013] I i (t) = H i (x(t))

[0014]

[0015] Where H i represents the feature extraction function, i represents the number of health factors, ξ i (t) indicates that at the tth cycle, the health factor sequence I i The correlation coefficient between (t) and the original capacity sequence x(t), x(t), I i (t) represents the original capacity and health factor at the t-th cycle, ρ represents the resolution coefficient, GRA-Mean i represents the average value of the correlation coefficient of each health factor series;

[0016] (3) Divide the original data of lithium-ion batteries into training set C according to the proportion train and test set C test , let the ratio be β, the sequence is as follows:

[0017] C train ={x(1),x(2),...,x(a)},a∈{1,βT}

[0018] C test ={x(βT+1),x(βT+2),...,x(c)},c∈{βT+1,T}.

[0019] Furthermore, the implementation process of step (2) is as follows:

[0020] (21) Discriminator optimization:

[0021] In WGAN, the goal of the discriminator D is to maximize the Wasserstein distance:

[0022]

[0023] Where, x(a)~P real Indicates randomly extracting a small batch of real data from the real training set data distribution, represents the expected distribution, P real Represents the original probability distribution of the training set data, D(x(a), ) represents the score value of the discriminator on the input data, i.e. the original training data and the generated training data, Represents the training data generated by the discriminator, z~P z Represents a small batch of noise extracted from the noise distribution, and G(z) represents the generator converting the noise z into generated training data function;

[0024] (22) Generator optimization:

[0025] The goal of the generator G is to minimize the Wasserstein distance:

[0026]

[0027] Furthermore, in step (21), to optimize the discriminator, a small batch stochastic gradient descent is used, and the operation steps are as follows:

[0028] First, from the real training set data distribution P real Randomly extract a small batch of real data from m is the number of samples in a small batch; from the noise distribution P z Randomly sample a mini-batch of noise from

[0029] Then, generate the corresponding data

[0030] Next, calculate the loss function and loss L of the discriminator D For the discriminator parameters θ D Gradient:

[0031]

[0032] Where, L D represents the loss function of the discriminator, Represents the gradient operator, which represents the generator parameter θ D The gradient of , η represents the learning rate;

[0033] Finally, the discriminator parameters are updated using the gradient:

[0034]

[0035] Furthermore, in step (22), to optimize the generator, a small batch stochastic gradient descent is used, and the operation steps are as follows:

[0036] First, from the noise distribution P z Randomly sample a mini-batch of noise from

[0037] Next, calculate the generator's loss function and loss L G For the generator parameter θ G Gradient:

[0038]

[0039] Where, L D represents the loss function of the discriminator, represents the gradient operator, which represents the gradient of the generator parameter θ, and η represents the learning rate;

[0040] Finally, the discriminator parameters are updated using the gradient:

[0041]

[0042] Furthermore, in step (3), GRU is a neural network for processing sequence data, including an update gate z t , reset gate r t and candidate hidden states

[0043] Among them, the update gate determines the fusion ratio of the current input health factor data and the lithium ion aging status information at the previous moment. Its calculation formula is as follows:

[0044] z t =σ(W z ·[h t-1 ,I i (t)]+b z )

[0045] Where z t Represents the update gate, the output value is between 0 and 1, W z and b z represents the parameter matrix and bias vector of the update gate, h t-1 Indicates the aging state of the lithium-ion battery at the previous moment, I i (t) represents the current input health factor sequence, σ represents the Sigma activation function;

[0046] The reset gate controls the impact of the aging state information at the previous moment on the candidate aging state information. The calculation formula is as follows:

[0047] r t =σ(W r ·[h t-1 ,I i (t)]+b r )

[0048] Where r t Represents the reset gate, the output value is between 0 and 1, W r and b r Represents the parameter matrix and bias vector of the reset gate;

[0049] Combine the currently input health factor data and the aging state information at the previous moment to generate candidate aging states and update the final aging state. The calculation formula is as follows:

[0050]

[0051] Where, Indicates the candidate aging state; W h and b h denote the parameter matrix and bias vector of the hidden state respectively.

[0052] Furthermore, the implementation process of training the GRU model using the health factor and the training set is: the health factor of the lithium-ion battery is used as input, and the expanded training set of the lithium-ion battery is used as output to train the GRU model. The calculation formula is as follows:

[0053]

[0054] Where, represents the expanded training set; W o and b o denote the weight and bias of the output layer respectively.

[0055] Furthermore, in step (4), in order to ensure the reliability of the prediction results, the prediction performance is evaluated using a test set, and the mean absolute error (MAE) and root mean square error (RMSE) are used to measure the deviation between the predicted value and the true value.

[0056] Furthermore, the operation of step (4) is as follows:

[0057] (41) Model prediction:

[0058] The trained GUR model is used to make predictions using the test set. The calculation formula is as follows:

[0059] RUL(c)=W o·h t +b o

[0060] Where RUL(c) represents the predicted value of the remaining service life of the lithium-ion battery in the test set; W o and b o Represent the weight and bias of the output layer respectively;

[0061] (42) Model evaluation indicators:

[0062] The mean absolute error E MAE , mean absolute percentage error E MAOE , root mean square error E RMSE and the coefficient of determination R 2 Calculate the error between the predicted RUL(c) and the actual test set x(c):

[0063]

[0064]

[0065] Where β represents the ratio of the divided training set, βT+1 represents the number of cycles at the start of the test set, (1-β)T represents the number of samples in the test set, RUL(c) represents the RUL prediction result of the test set, and x(c) represents the real data of the test set.

[0066] Beneficial effects: Compared with the existing technology, the present invention has the following significant features: By integrating MBGD, Wasserstein generative adversarial network WGAN and GRU model, the present invention significantly improves the accuracy and reliability of lithium-ion battery RUL prediction; specifically, Wasserstein generative adversarial network WGAN combines with MBGD to generate high-quality synthetic data, effectively alleviating the problem of small sample overfitting and enhancing the model's generalization ability; GRU accurately captures the nonlinear time series characteristics of battery aging and improves long-term prediction stability; the three work together to achieve end-to-end optimization, reduce computational complexity, and improve engineering practicality. This technology provides BMS with a high-precision life prediction tool that can provide early warning of failure risks, optimize charging and discharging strategies, reduce operation and maintenance costs, and provide key technical support for safe and efficient battery operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is a flow chart for predicting RUL of lithium-ion batteries in the present invention;

[0068] Figure 2 This is a data enhancement comparison diagram of B0005, B0006 and B0007 in the present invention;

[0069] Figure 3 It is a comparison chart of the prediction results in the present invention. DETAILED DESCRIPTION

[0070] The specific technical solutions of the present invention are further described in detail below with reference to specific examples.

[0071] As shown in the figure, the MBGD-WGAN-GRU-based lithium-ion battery RUL prediction method of the present invention has the following operating steps:

[0072] (1) Using Grey Relational Analysis (GRA), we extract health factors (IHFs) that are highly correlated with aging characteristics from the original aging data of lithium-ion batteries, and divide the original aging data into training and test sets.

[0073] (2) Use mini-batch stochastic gradient descent (MBGD) to optimize the Wasserstein generative adversarial network (WGAN) to expand the training set and improve data diversity;

[0074] (3) The GRU model is trained using the health factors extracted from the original data and the expanded training set, giving full play to the advantages of GRU in processing sequence data and learning the time series characteristics of lithium-ion battery aging;

[0075] (4) Apply the trained GRU model to the online prediction of the remaining useful life (RUL) of lithium-ion batteries;

[0076] In order to ensure the reliability of the prediction results, the test set is used to evaluate the prediction performance, and indicators such as mean absolute error (MAE) and root mean square error (RMSE) are used to measure the deviation between the predicted value and the true value.

[0077] The specific operation method of step (1) is:

[0078] (11) The original aging data of lithium-ion battery is recorded as

[0079] Where t represents the number of cycles, T represents the total number of cycles, and x(t) represents the capacity data of the lithium-ion battery at the tth cycle;

[0080] (12) Using the grey relational analysis (GRA) method, the average correlation coefficient between each health factor sequence IHFs and the lithium-ion battery capacity sequence is calculated, i.e., (GRA-Mean), and the health factors that are highly correlated with the aging characteristics of lithium-ion batteries are retained:

[0081] I i (t) = H i (x(t))

[0082]

[0083] Where H i represents the feature extraction function, i represents the number of health factors, ξ i (t) indicates that at the tth cycle, the health factor sequence I i The correlation coefficient between (t) and the original capacity sequence x(t), x(t), I i (t) represents the value of the original capacity and health factor at the t-th cycle, ρ represents the resolution coefficient, which ranges from 0 to 1 and is usually 0.5. The resolution coefficient is used to adjust the calculation of the correlation coefficient and affects the resolution of the correlation degree. i represents the average value of the correlation coefficient of each health factor series;

[0084] (3) Divide the original data of lithium-ion batteries into training set C according to a certain ratio train and test set C test , let the ratio be β, the sequence is as follows:

[0085] C train ={x(1),x(2),...,x(a)},a∈{1,βT}

[0086] C test ={x(βT+1),x(βT+2),...,x(c)},c∈{βT+1,T}.

[0087] The specific operation method of step (2) is:

[0088] (21) Optimize the discriminator:

[0089] In WGAN, the goal of the discriminator D is to maximize the Wasserstein distance:

[0090]

[0091] Where, x(a)~P real Indicates randomly extracting a small batch of real data from the real training set data distribution, represents the expected distribution, P real represents the original probability distribution of the training set data, It represents the score value of the discriminator on the input data, i.e. the original training data and the generated training data, and reflects the authenticity of the generated data. Represents the training data generated by the discriminator, z~P z Represents a small batch of noise extracted from the noise distribution, and G(z) represents the generator converting the noise z into generated training data function;

[0092] (22) Generator optimization:

[0093] The goal of the generator G is to minimize the Wasserstein distance:

[0094]

[0095] In step (21), in order to optimize the discriminator, a small batch stochastic gradient descent is used, and the specific operation steps are as follows:

[0096] First, from the real training set data distribution P real Randomly extract a small batch of real data from m is the number of samples in a small batch, from the noise distribution P z Randomly sample a mini-batch of noise from

[0097] Then, generate the corresponding data

[0098] Next, calculate the loss function and loss L of the discriminator D For the discriminator parameters θ D Gradient:

[0099]

[0100] Where, L D represents the loss function of the discriminator, Represents the gradient operator, which represents the generator parameter θ D The gradient of the loss function L D θ D The partial derivative of , η represents the learning rate, which is used to control the step size of parameter update;

[0101] Finally, the discriminator parameters are updated using the gradient:

[0102]

[0103] In step (22), in order to optimize the generator, a small batch stochastic gradient descent is used, and the specific operation steps are as follows:

[0104] First, from the noise distribution P z Randomly sample a mini-batch of noise from

[0105] Next, calculate the generator's loss function and loss L G For the generator parameter θ G Gradient:

[0106]

[0107] Where, LD represents the loss function of the discriminator, Represents the gradient operator, which represents the gradient of the generator parameter θ, that is, the loss function L G θ G The partial derivative of , η represents the learning rate, which is used to control the step size of parameter update;

[0108] Finally, the discriminator parameters are updated using the gradient:

[0109]

[0110] The expanded results are shown in Table 1:

[0111] Table 1

[0112]

[0113] In step (3), the gated recurrent unit GRU is a neural network for processing sequence data, and its structure includes updating gate z t , reset gate r t and candidate hidden states

[0114] The update gate determines the fusion ratio of the current input health factor data and the lithium ion aging status information at the previous moment. The calculation formula is as follows:

[0115] z t =σ(W z ·[h t-1 ,I i (t)]+b z )

[0116] Where z t It is the update gate, whose output value is between 0 and 1, and determines how much aging state history information is retained. z and b z is the parameter matrix and bias vector of the update gate, h t-1 is the aging state of the lithium-ion battery at the previous moment, I i (t) is the current input health factor sequence, σ is the Sigma activation function;

[0117] The reset gate controls the impact of the aging state information at the previous moment on the candidate aging state information. The calculation formula is as follows:

[0118] r t =σ(W r ·[h t-1 ,I i (t)]+b r )

[0119] Where rt It is the reset gate, and its output value is between 0 and 1, which determines how much historical aging information is forgotten. r and b r is the parameter matrix and bias vector of the reset gate;

[0120] Combine the currently input health factor data and the aging state information at the previous moment to generate candidate aging states and update the final aging state. The calculation formula is as follows:

[0121]

[0122] Where, is a candidate aging state; W h and b h is the parameter matrix and bias vector of the hidden state;

[0123] The implementation method of training the GRU model using the health factor and training set is as follows: the health factor of the lithium-ion battery is used as input and the expanded training set of the lithium-ion battery is used as output to train the GRU model. The calculation formula is as follows:

[0124]

[0125] Where, is the expanded training set, W o and b o are the weights and bias terms of the output layer, which are used to map the aging status information of the lithium-ion battery to the lithium-ion battery capacity data.

[0126] The operation mode of step (4) is as follows:

[0127] (41) Model prediction:

[0128] The trained GUR model is used to make predictions using the test set. The calculation formula is as follows:

[0129] RUL(c)=W o ·h t +b o

[0130] Where RUL(c) is the predicted value of the remaining service life of the lithium-ion battery in the test set; W o and b o are the weights and bias terms of the output layer, which map the aging status information of the lithium-ion battery to the remaining service life of the lithium ion;

[0131] (42) Model evaluation indicators:

[0132] The mean absolute error E MAE , mean absolute percentage error E MAPE , root mean square error ERMSE and the coefficient of determination R 2 Calculate the error between the predicted RUL(c) and the actual test set x(c):

[0133]

[0134] In the formula, β is the ratio of the divided training set, βT+1 represents the number of cycles at the start of the test set, (1-β)T is the number of samples in the test set, RUL(c) is the RUL prediction result of the test set, and x(c) is the real data of the test set. The final prediction results are shown in Table 2:

[0135] Table 2

[0136]

[0137]

[0138] This method combines mini-batch stochastic gradient descent (MBGD), generative adversarial networks (WGAN) and gated recurrent units (GRU) to achieve data enhancement of lithium-ion battery capacity and accurate prediction of service life; this technical path provides an efficient and reliable solution for lithium-ion battery health assessment, helps to improve the state monitoring accuracy and life prediction capabilities of battery management systems, and provides key technical support for battery life cycle management.

Claims

1. A lithium-ion battery RUL prediction method based on MBGD-WGAN-GRU, characterized by: The steps are as follows: (1) Using the grey correlation analysis method, the health factors (IHFs) highly correlated with aging characteristics are extracted from the original aging data of lithium-ion batteries, and the original aging data are divided into a training set and a test set. (2) Use the mini-batch stochastic gradient descent method to optimize the Wasserstein generative adversarial network and expand the training set; (3) Use the health factors extracted from the original data and the expanded training set to train the GRU model; (4) The trained GRU model is applied to the online prediction of the remaining service life of lithium-ion batteries.

2. The MBGD-WGAN-GRU-based RUL prediction method for lithium-ion batteries according to claim 1, characterized in that: The implementation process of step (1) is as follows: (11) The original aging data of lithium-ion battery is recorded as Where t represents the number of cycles, T represents the total number of cycles, and x(t) represents the capacity data of the lithium-ion battery at the tth cycle; (12) Using the grey correlation analysis method, the average correlation coefficient between each health factor sequence IHFs and the lithium-ion battery capacity sequence is calculated, and the health factors that are highly correlated with the aging characteristics of lithium-ion batteries are retained: I i (t)=H i (x(t)) Where H i represents the feature extraction function, i represents the number of health factors, ξ i (t) indicates that at the tth cycle, the health factor sequence I i The correlation coefficient between (t) and the original capacity sequence x(t), x(t), I i (t) represents the original capacity and health factor at the t-th cycle, ρ represents the resolution coefficient, GRA-Mean i represents the average value of the correlation coefficient of each health factor series; (3) Divide the original data of lithium-ion batteries into training set C according to the proportion train and test set C test , let the ratio be β, the sequence is as follows: C train ={x(1),x(2),...,x(a)},a∈{1,βT} C test ={x(βT+1),x(βT+2),...,x(c)},c∈{βT+1,T}。 3. The MBGD-WGAN-GRU-based RUL prediction method for lithium-ion batteries according to claim 1, characterized in that: The implementation process of step (2) is as follows: (21) Discriminator optimization: In WGAN, the goal of the discriminator D is to maximize the Wasserstein distance: Where, x(a)~P real Indicates randomly extracting a small batch of real data from the real training set data distribution, represents the expected distribution, P real represents the probability distribution of the original training set data, Represents the score value of the discriminator on the input data, i.e., the original training data and the generated training data, Represents the training data generated by the discriminator, z~P z Represents a small batch of noise extracted from the noise distribution, and G(z) represents the generator converting the noise z into generated training data function; (22) Generator optimization: The goal of the generator G is to minimize the Wasserstein distance:

4. The MBGD-WGAN-GRU-based RUL prediction method for lithium-ion batteries according to claim 3, characterized in that: In step (21), to optimize the discriminator, a small batch stochastic gradient descent is used, and the operation steps are as follows: First, from the real training set data distribution P real Randomly extract a small batch of real data from m is the number of samples in a small batch; from the noise distribution P z Randomly sample a mini-batch of noise from Then, generate the corresponding data Next, calculate the loss function and loss L of the discriminator D For the discriminator parameters θ D Gradient: Where, L D represents the loss function of the discriminator, Represents the gradient operator, which represents the generator parameter θ D The gradient of , η represents the learning rate; Finally, the discriminator parameters are updated using the gradient:

5. The MBGD-WGAN-GRU-based RUL prediction method for lithium-ion batteries according to claim 3, characterized in that: In step (22), to optimize the generator, a small batch stochastic gradient descent is used, and the operation steps are as follows: First, from the noise distribution P z Randomly sample a mini-batch of noise from Next, calculate the generator's loss function and loss L G For the generator parameter θ G Gradient: Where, L D represents the loss function of the discriminator, represents the gradient operator, which represents the gradient of the generator parameter θ, and η represents the learning rate; Finally, the discriminator parameters are updated using the gradient:

6. The MBGD-WGAN-GRU-based lithium-ion battery RUL prediction method according to claim 1, characterized in that: In step (3), GRU is a neural network for processing sequence data, including an update gate z t , reset gate r t and candidate hidden states 7. The MBGD-WGAN-GRU-based RUL prediction method for lithium-ion batteries according to claim 6, characterized in that: In the GRU, the update gate determines the fusion ratio of the current input health factor data and the lithium ion aging status information at the previous moment. The calculation formula is as follows: z t =σ(W z ·[h t-1 ,I i (t)]+b z ) Where z t Represents the update gate, the output value is between 0 and 1, W z and b z represents the parameter matrix and bias vector of the update gate, h t-1 Indicates the aging state of the lithium-ion battery at the previous moment, I i (t) represents the current input health factor sequence, σ represents the Sigma activation function; The reset gate controls the impact of the aging state information at the previous moment on the candidate aging state information. The calculation formula is as follows: r t =σ(W r ·[h t-1 ,I i (t)]+b r ) Where r t Represents the reset gate, the output value is between 0 and 1, W r and b r Represents the parameter matrix and bias vector of the reset gate; Combine the currently input health factor data and the aging state information at the previous moment to generate candidate aging states and update the final aging state. The calculation formula is as follows: Where, Indicates the candidate aging state; W h and b h denote the parameter matrix and bias vector of the hidden state respectively.

8. The MBGD-WGAN-GRU based lithium-ion battery RUL prediction method according to claim 1, characterized in that: In step (3), the implementation process of training the GRU model using the health factor and the training set is: the health factor of the lithium-ion battery is used as input, and the expanded training set of the lithium-ion battery is used as output to train the GRU model, and the calculation formula is as follows: Where, represents the expanded training set; W o and b o denote the weight and bias of the output layer respectively.

9. The MBGD-WGAN-GRU based lithium-ion battery RUL prediction method according to claim 1, characterized in that: In step (4), in order to ensure the reliability of the prediction results, the prediction performance is evaluated using a test set, and the mean absolute error (MAE) and root mean square error (RMSE) are used to measure the deviation between the predicted value and the true value.

10. The MBGD-WGAN-GRU based lithium-ion battery RUL prediction method according to claim 1, characterized in that: The operation mode of step (4) is as follows: (41) Model prediction: The trained GUR model is used to make predictions using the test set. The calculation formula is as follows: RUL(c)=W o ·h t +b o Where RUL(c) represents the predicted value of the remaining service life of the lithium-ion battery in the test set; W o and b o Represent the weight and bias of the output layer respectively; (42) Model evaluation indicators: The mean absolute error E MAE , mean absolute percentage error E MAPE , root mean square error E RMSE and the coefficient of determination R 2 Calculate the error between the predicted RUL(c) and the actual test set x(c): Where β represents the ratio of the divided training set, βT+1 represents the number of cycles at the start of the test set, (1-β)T represents the number of samples in the test set, RUL(c) represents the RUL prediction result of the test set, and x(c) represents the real data of the test set.

Images