The Remaining Useful Life Forecasting Method of Energy Storage Batteries Using Empirical Mode Decomposition to Correct the Forecasting Error of the Long Short-Term Memory Model

Abstract

Energy storage has a flexible regulatory effect, which is important for improving the consumption of new energy and sustainable development. The remaining useful life (RUL) forecasting of energy storage batteries is of significance for improving the economic benefit and safety of energy storage power stations. However, the low accuracy of the current RUL forecasting method remains a problem, especially the limited research on forecasting errors. In this paper, a method for forecasting the RUL of energy storage batteries using empirical mode decomposition (EMD) to correct long short-term memory (LSTM) forecasting errors is proposed. Firstly, the RUL forecasting model of energy storage batteries based on LSTM neural networks is constructed. The forecasting error of the LSTM model is obtained and compared with the real RUL. Secondly, the EMD method is used to decompose the forecasting error into many components. The time series of EMD components are forecasted by different LSTM models. The forecasting values of different time series are added to determine the corrected forecasting error and improve the forecasting accuracy. Finally, a simulation analysis shows that the proposed method can effectively improve the forecasting effect of the RUL of energy storage batteries.

1. Introduction

Traditional power generation consumes fossil fuels such as oil and coal; this has a negative impact on the environment and is not conducive to sustainable development. Therefore, new energy power generation has developed rapidly in recent years, with clean and pollution-free characteristics. However, due to the influence of weather conditions, new energy power generation has the characteristic of uncertainty [1,2,3]. Therefore, the large-scale integration of new energy generation into the grid will bring new challenges to the power quality and safe and stable operation of the power grid [4,5,6]. In addition, due to the rapid development of the economy and society, the electricity consumption in many countries has also shown a rapid growth trend, and the large load and peak valley difference will also bring new problems.

Electrochemical energy storage plays an important role in alleviating the above problems. It has been widely applied on the new energy side, power grid side, and user side in recent years, which is conducive to new energy consumption and sustainable development. The current high price of energy storage systems has become one of the main reasons limiting their development and application [7,8]. By studying the remaining useful life (RUL) of batteries, energy management methods for energy storage systems can be formulated, thereby extending the useful life of energy storage batteries and improving the economic benefits of energy storage power station owners. In addition, the safety of energy storage plants is very important, and there have been some accidents, such as fires and explosions, in energy storage stations before [9,10]. The forecasting of RUL can avoid this issue in advance.

Therefore, it is very necessary to forecast the RUL of energy storage batteries, and many scholars have also conducted related research. The main methods are divided into model-based methods [11,12] and data-driven methods [13]. The data-driven model is currently the most popular method, because it has the advantage of being able to analyze the data to obtain the relationships between various parameters and forecast the RUL of energy storage batteries. These methods mainly include neural networks (NN), support vector machines (SVM), long short-term memory (LSTM) neural networks, and so on.

Sun et al. [14] propose a simultaneous estimation scheme using SVM for state of charge (SOC) and state of health (SOH) based on shock response characteristics. Simulation results show that the proposed method can accurately estimate the SOH and SOC of a battery, with strong robustness and generalization ability. Li et al. [15] propose a lithium-ion health online estimation method based on particle swarm optimization (PSO) and SVM. The PSO was used to optimize the kernel function of the SVM. From experiments (such as dynamic stress tests), it can be seen that it has good adaptability and feasibility. Lin et al. [16] propose an RUL forecasting model for lithium-ion batteries that combines variational mode decomposition (VMD) and SVM. Compared with a single SVM regression model and a Gaussian process regression model, the VMD–SVM method achieved more accurate forecasting results. However, SVM methods are prone to fall into a local optimal state, making it difficult to obtain the most accurate forecasting results or ensure the stability of the forecasting results.

A recurrent neural network (RNN) considers the influence of the information of diffident time and is often used for time series prediction or language processing. Song et al. [17] propose a battery RUL forecasting method based on a new RNN, which overcomes the disadvantage of dealing with the long-term relationships of RNN. The average error of different battery cells is less than 3%, which means that the proposed method is accurate and robust for battery RUL forecasting. The RNN is prone to have problems of gradient vanishing or gradient explosion, and many scholars have improved it. LSTM is a highly successful improved model. Zhao et al. [18] propose a joint forecasting method for health status and RUL based on LSTM neural networks and Gaussian process regression. They established a Gaussian process regression forecasting model for remaining useful life. On this basis, an LSTM neural network is used to forecast the trend of health factors over time. Li et al. [19] propose an online forecasting method for electric vehicle battery fault based on LSTM. The model based on LSTM can effectively forecast battery fault with an accuracy rate of over 85%. It can complete online preprocessing of vehicle operation data and fault forecasting of power batteries, improve vehicle monitoring capabilities, and ensure the safety of electric vehicle use. In addition to the battery RUL, LSTM is also used for other battery-related research. Wang et al. [20] propose a fault diagnosis method based on a hybrid model, which estimates the internal temperature and SOC of the battery through its physical model. It combines the surface temperature, voltage, and current of the battery as inputs to the LSTM to accurately forecast the surface temperature and internal temperature. In the above literature, the RUL of energy storage batteries is mostly forecasted by using a single method. We can find that LSTM has good forecasting performance, but there is still room for improvement.

A soft-shared multitask deep learning method for multi-node load prediction in power systems was proposed to achieve the simultaneous prediction of multi-node loads [21]. The simulation results showed that this method can effectively explore the spatiotemporal coupling characteristics of multi-node load data and improve prediction performance. Wang et al. [22] combined the hybrid convolutional neural network (CNN)–Bidirectional Gated Recursive Unit (BiGRU) model with the Bootstrap method, endowing deep learning (DL)-based prediction methods with the ability to quantify prediction intervals. Experimental verification was conducted on a bearing dataset, and this method outperformed the other four methods in most cases. Guo et al. [23] propose a deep feature learning method that combines a convolutional neural network (CNN)–convolutional block attention module (CBAM) and a transformer network into a parallel channel method to predict the RUL of drilling pumps, confirming that the proposed method has higher accuracy. Zhang et al. [24] propose a combination of offline global models developed by different machine learning methods and online adaptive cellular personalized models. Training and testing were conducted on three large datasets, demonstrating the predictive performance. A new dual Gaussian process regression (GPR) framework was proposed in reference [25], and quantitative experimental results show that the state of charge estimation is significantly improved compared to traditional methods. Liu et al. [26] propose an effective prediction of battery calendar aging trajectory by deriving a knowledge-driven data-driven model with transfer concepts. The results show that the model has good prediction accuracy under known conditions. A reliable cycle aging-prediction method based on data-driven models was proposed in reference [27]. A multi-core RVM model containing two different feature kernel functions was constructed. Quantitative experimental results showed that the proposed model can accurately predict the failure cycle and capacity decay trajectory of different types of batteries.

Although the above literature combines multiple models, there is no relevant research focusing on the forecasting error of the RUL of energy storage batteries. This article explores how to improve the forecasting accuracy by dealing with the forecasting error. We propose the method that uses empirical mode decomposition (EMD) to correct the forecasting error of LSTM, thereby improving the forecasting accuracy of RUL. Firstly, we use the LSTM model to forecast the RUL of energy storage batteries and obtain the RUL forecasting error. Then, EMD is used to decompose the forecasting error to obtain components with different characteristics. Finally, we use the LSTM model to forecast the time series of each component, perform inverse transformation on the forecasting results to obtain the corrected forecasting error, and add it to the original RUL forecasting result to obtain the forecasting result of LSTM–EMD. The research in this article will accurately forecast the RUL of energy storage batteries, which is beneficial for improving the safety of new energy power plants containing energy storage batteries.

The main contributions of this paper are as follows:

(1)

This paper proposes a novel framework for forecasting the remaining useful life of the energy storage battery, which includes the LSTM model for forecasting the RUL and the EMD model for correcting the forecasting error.

(2)

The EMD method is proposed to decompose the LSTM forecasting error into multiple components. Each error component is trained separately to correct the forecasting error, which improves the forecasting accuracy.

(3)

The established forecasting model uses simple input data to solve the forecasting accuracy problem in the case of insufficient data types.

The rest of this paper are as follows: Section 2 introduces the framework of the RUL forecasting of the energy storage battery. Section 3 is the RUL forecasting method of the energy storage battery, which is the main part of this paper. Section 4 is the simulation analysis and verification. Section 5 is the conclusion.

2. Framework for Predicting the Remaining Useful Life of Energy Storage Batteries

The framework of the RUL forecasting of energy storage batteries is shown in Figure 1, which is mainly divided into three parts.

Part A: We have collected the data of different batteries. Before using the LSTM model for forecasting, we divide the data into training set and test set and carry out normalization processing. The normalization formula is shown in the equation below. The LSTM model is trained by using the data in the training set. The specific model is explained in Section 3.1. When the expected results are achieved by using training set, the test set is used to forecast the RUL and verify the proposed method. The forecasting value of the remaining capacity of the battery is obtained. In this paper, we assume that the remaining capacity represents the RUL. However, the forecasting results have a forecasting error, which is used as the input in Part B.

Part B: In this part, the forecasting error is obtained by using the forecasting value minus the real value. We use the method of empirical mode decomposition to decompose the forecasting error of the RUL, where several components can be obtained. For each component, we divide the training set and the test set and construct the corresponding LSTM model. The LSTM models are used for time series forecasting of several components. The method of empirical mode decomposition is described in Section 3.2.

Part C: Multiple trained LSTM models are used for time series forecasting of several components. Then, we invert the forecasting component to determine the correction value of the LSTM forecasting error in Part A. We add the correction value to the forecasting value by the LSTM in Part A. We determine the forecasting result of the correction, forecasting the remaining capacity of the battery, and the forecasting effect has been significantly improved.

3. Forecasting Method of Remaining Useful Life of Energy Storage Batteries

3.1. Forecasting Model Based on LSTM

Long short-term memory (LSTM) is a special kind of recurrent neural network. There may be lags of unknown duration between important events in the time series. The ordinary recurrent neural network has only one processing function in the neural unit, which can cause the problem of gradient disappearing or gradient explosion. The special designs in the cells of LSTM can avoid such problems. Therefore, LSTM networks are suited for classification, processing, and forecasting based on time series data. In this paper, the LSTM neural network is used to construct the relationship between the remaining useful life of a battery and the number of cycles. An ordinary LSTM cell consists of four parts: a forgetting gate, an input gate, an information update, and an output gate, as shown in Figure 2.

The first component of LSTM is the forgetting gate, in which parts of the information are discarded from the output of the previous time and the input value of the current time through the sigmoid function. Its expression is as follows:

$$f_t=\sigma \left({\omega }_f\left[h_{t-1},x_t\right]+b_f\right)$$

(1)

The second component is the input gate. The function is to determine what information needs to be updated. The output values of the input gate are selected and filtered by the sigmoid and tanh functions, respectively.

The expression of handling by function $\sigma$ is as follows:

$$i_t=\sigma \left({\omega }_i\left[h_{t-1},x_t\right]+b_i\right)$$

(2)

The expression of handling by function tanh is as follows:

$${\tilde{c}}_t=\tanh \left({\omega }_C\left[h_{t-1},x_t\right]+b_C\right)$$

(3)

The third part is the information update, which multiplies the forgetting gate and the information update value of the previous time and adds the product of the two values of the output gate. The update formula is as follows:

$$c_t=f_t{c}_{t-1}+i_t{\tilde{c}}_t$$

(4)

The fourth component is the output gate, which is based on the above three parts. First, part of the input gate is selected by the sigmoid function. Secondly, the tanh function is used to select and filter the updated information. Finally, the two selected information values are multiplied to determine the cell output value at this moment. The expression is as follows:

$$o_t=\sigma \left({\omega }_o\left[h_{t-1},x_t\right]+b_o\right)$$

(5)

$$h_t=o_t\tanh (c_t)$$

(6)

In the above formulas, $x_t$ is the input value at time t, $h_{t-1}$ is the output value at time t − 1, $c_t$ is the cell status update value, ${\omega }_{[·]}$ is the weight value, and $b_{[·]}$ is the bias value.

In this paper, the sigmoid function commonly used in neural networks is selected as the function $\sigma$, and the tanh function is also used in the neural networks. Their expressions are shown in (7) and (8), respectively.

$$s(x)=\frac{1}{1+e^{-x}}$$

(7)

$$\tanh (x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$$

(8)

3.2. Forecasting Error Correction Model

3.2.1. Basic Framework

In the above section, the forecasting model of RUL based on the LSTM is established. However, there are errors in the forecasting of the time series or the relationship between the cycles and RUL. In order to reduce the forecasting error, in this part, we will establish the error correction model based on the empirical mode decomposition method for the first time in the RUL forecasting.

First, the empirical mode decomposition is used to decompose the time series of the forecasting errors into several components, which have their own laws. Then, the time series forecasting model is established for each component; that is, the relationship between the number of cycles and the value of the component is established. When the number of cycles is given, we can forecast the value of the component through this relationship. Finally, the forecasting values of all the components are inversely transformed to determine the correction value of the forecasting error. Thus, the forecasting accuracy of the remaining useful life of the battery is improved.

3.2.2. Empirical Mode Decomposition

Empirical mode decomposition can be applied to any type of time series decomposition and has obvious advantages when dealing with nonlinear non-stationary time series. EMD can decompose the trend of different scales in the forecasting error sequence of RUL step by step, reduce the volatility and non-stationary nature of the time series, and obtain the intrinsic mode component containing local characteristic signals of different time scales, also known as the Intrinsic Mode Function (IMF).

The difference between the forecasting value and the actual value of the remaining useful life of the energy storage battery is recorded as the forecasting error sequence $E(t)$, $t=1,2,\dots ,\mathrm{n}$. The EMD steps of the forecasting error sequence of RUL are as follows:

(1)

Determine all the local maximum points and local minimum points. Connect all the maximum points and minimum points, respectively, with the cubic spline interpolation method to form the upper envelope line $S_{+}(t)$ and the lower envelope line $S_{-}(t)$. Calculate the mean value of the two envelope lines to determine the mean envelope line $M_1(t)$:

$$M_1(t)=\frac{S_{+}(t)+S_{-}(t)}{2}$$

(9)

where $S_{+}(t)$ is the maximum point and $S_{-}(t)$ is the minimum point.

(2)

Calculate the difference between $E(t)$ and $M_1(t)$, denoted as $H_1(t)$:

$$H_1(t)=E(t)-M_1(t)$$

(10)

(3)

Determine whether the conditions of the eigenmode function are met. If met, $H_1(t)$ is taken as an IMF. If not, $H_1(t)$ is taken as the original sequence, and the first step is repeated. After k repetitions, until the selected one $H_{1k}(t)$ meets the conditions of IMF, $H_{1k}(t)$ is taken as an IMF, denoted as $x_1(t)=H_{1k}(t)$.

(4)

Subtract $x_1(t)$ from the original signal $E(t)$ to determine the residual value $r_1(t)$:

$$r_1(t)=E(t)-x_1(t)$$

(11)

(5)

Take the residual remaining value as the new original sequence, repeat the above steps, and decompose gradually to obtain IMF $x_2(t)$, $x_3(t)$, etc. The relationship between the RUL forecasting error sequence $E(t)$ and each IMF $x_i(t)$ and the residual component is as follows:

$$E(t)={\displaystyle \sum _{i=1}^n{x}_i(t)}+r_n(t)$$

(12)

where $x_i(t)$ is the i-th IMF component obtained by EMD, which represents the parts of characteristics of the original signal at different time scales. $r_n(t)$ is the residual component, which reflects the change trend of the original signal. When the residual component becomes a monotone function with no extreme point, the decomposition process ends. In practice, when the residual component sequence cannot converge, it is discarded, and the decomposition terminating condition is press $r_n(t)$.

$$S={\displaystyle \sum \frac{{[x_{i-1}(t)-x_i(t)]}^2}{{[x_{i-1}(t)]}^2}}\le \delta$$

(13)

where $S$ is the decomposition convergence coefficient. When it is smaller than $\delta$ or equal to $\delta$, the decomposition process terminates. In this paper, the value of $\delta$ is 0.1. After the calculation in this section, the forecasting error sequence of RUL is decomposed into several relatively stable IMF components, which contain the complete information of the original time series. Then, we can forecast each IMF by using the time serious forecasting method to correct the LSTM forecasting error in Section 3.1.

3.3. Evaluation Index

The RUL forecasting results of different forecasting models, such as traditional neural networks, support vector machines, and LSTM neural networks, are different. In addition, the number of hidden layers of a neural network can be used for sensitivity analysis through evaluation indexes. This section summarizes the following different indexes to evaluate the forecasting results:

(1)

Root mean square error (RMSE). The smaller it is, the better the forecasting effect.

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left({\widehat{Y}}_i-Y_i\right)}^2}}$$

(14)

(2)

Symmetric mean absolute percentage error (SMAPE). The smaller the value of this index, the smaller the forecasting error.

$$SMAPE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\frac{\left|{\widehat{Y}}_i-Y\right|}{\frac{\left|\widehat{Y}\right|+\left|Y_i\right|}{2}}\times 100\%}$$

(15)

(3)

Mean absolute error (MAE), which is used to evaluate the closeness of forecasting results to real data sets. The smaller the value, the better the effect.

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|{\widehat{Y}}_i-Y_i\right|}$$

(16)

where $n$ is the number of the RUL data, ${\widehat{Y}}_i$ is the forecasting value of the RUL, and $Y_i$ is the real value of the RUL.

4. Simulation Analysis

4.1. Data Introduction

This paper selects an experimental data set of lithium-ion batteries from the University of Maryland as an example. The average voltage, current, and number of cycles are selected as the input, and the discharge energy or capacity is selected as the output. The discharge energy can reflect the RUL of an energy storage battery. In this data set, we use the first 1000 sets of data for training and the 1500th to 2000th sets for testing.

4.2. RUL Forecasting Result

For the LSTM model, the number of inputs and outputs has been determined, but the number of neural units in the hidden layer of the model is uncertain. Therefore, sensitivity analysis is needed to determine the number of neural units in the hidden layer. As shown in Figure 3, this paper conducted a comparative analysis on the number of neural units in the hidden layer under different indexes. The vertical axis is the value of the index, and the horizontal axis is the number of hidden layer units. As can be seen from the figure, compared with SMAPE and MAE, the indicator RMSE is the most unstable when it changes with the number of neural units, but it is consistent with the changing trend of SMAPE and MAE. The smaller the value of the three indexes, the higher the forecasting accuracy. When the number of hidden layer neural units is 30, the index value is the smallest. In this paper, when the number of neural units is 30, the RUL forecasting results based on LSTM have the best effect. It is worth noting that we also carried out sensitivity analysis on the other number of neural units, and the results show that when the number difference is small, the difference in the forecasting effect is small.

The forecasting model is trained by using the data of the first 1000 cycles in the data set to forecast the remaining capacity of 1500–2000 cycles. The forecasting result of the remaining useful life of the energy storage battery is obtained. Figure 4 shows the comparison between the forecasting value and the real value by different methods. Figure 5 shows the scatter plot between the forecasting value and the real value by different methods. In Figure 4, NN is the forecasting value of the traditional neural network method, SVM is the forecasting result of the support vector machine, and LSTM is the forecasting method in this paper. We conducted the subsequent simulation, in which the neural units of the hidden layer of the LSTM model total 30. It can be seen that the forecasting results of the three methods are similar in the cycles 1500–1800, and there is an obvious gap in the cycles 1800–2000 and the forecasting results using LSTM are closer to the real value. Its forecasting accuracy is the highest.

The scatter plot shows the distribution of data points on the plane of a cartesian coordinate system. The scatter plot represents the approximate trend of the forecasting value changing with the real value. According to the trend, the appropriate logarithmic data points of the function can be selected for fitting. The yellow, blue, and red dotted lines in Figure 5 are roughly the boundaries of the three methods’ scatters. From the scatters and their corresponding boundaries, we can see that the yellow one—that is, the scatters of the forecasting methods in this paper—are roughly distributed around the diagonal lines, which represents that this forecasting value is the closest to the real RUL value. The right part of the blue scatter deviates from the diagonal, and the red scatter deviates even more. We can see from the above analysis that LSTM is a better forecasting model than NN and SVM.

Table 1. Comparison of different indicators of the five forecasting methods.

	NN	SVM	ARIMA	CNN	LSTM
RMSE	0.25	0.31	0.45	0.23	0.21
SMAPE	0.06	0.08	0.18	0.05	0.05
MAE	0.19	0.26	0.36	0.18	0.16

shows the comparison of the different indexes of the three forecasting methods. Taking RMSE as an example, the forecasting effect of LSTM is improved by 16%, 32.26%, 53.33%, and 8.70% when compared with the NN model, SVM model, ARIMA model, and CNN model, respectively.

4.3. Forecasting Error Correction Results

When forecasting the remaining useful life of the battery, we found that there would always be forecasting errors no matter what kind of method. Another innovation or contribution of this paper is that we used the EMD method to deal with the forecasting errors, and then made time series forecasting for the different components, so as to achieve the purpose of correcting the forecasting errors. In this paper, the forecasting error of LSTM was decomposed into five components through empirical mode decomposition. Figure 6 shows the decomposed results, where Signal represents the forecasting error, IMF1-3 represents the three components of EMD, and Residual represents the residual value after decomposition. Compared with the original signal, each component shows a certain rule or trend. We made a time series forecasting for each component, and the forecasting results are shown in Figure 7.

Figure 7a–c are the comparisons between the real values of the three components and their forecasting values, and Figure 7d–f are the scatter plots of the actual values of the three components and the forecasting values of the time series. As can be seen from Figure 7a–c, among the three components, IMF2 and IMF3 have better forecasting effect. IMF1 has poor regularity, but its influence is not too serious to impede its ability to correct the forecasting error. From the scatter plot perspective, the scatter distribution range of IMF1 is relatively large, and the distribution on the diagonal is also concentrated in the range of [−0.2, 0.2]. The scatter plot of IMF2 and IMF3 is mainly distributed on the diagonal line, and its regression effect is very good. For IMF4 and IMF5, their regularity is better than IMF2 and IMF3 and they have better forecasting values.

After obtaining the forecasting time series value of each component, it can be reversed to obtain the corrected forecasting error. As shown in Figure 8, it can be seen that the forecasting error of the remaining useful life of the energy storage using the LSTM method is very close to the error correction value obtained by the EMD method. This represents that the correct effect is good. By adding the corrected error to the forecasting value of LSTM, the forecasting result of LSTM–EMD can be obtained. As shown in Figure 9, the blue line is the actual value of the remaining useful life of the energy storage, the red line is the forecasting result of LSTM, and the yellow line is the forecasting result of LSTM–EMD. It can be seen that the combination of LSTM and EMD obtained a better forecasting effect.

Table 2. Indexes of LSTM and LSTM–EMD.

	RMSE	SMAPE	MSE
LSTM	0.21	0.05	0.16
LSTM–EMD	0.15	0.04	0.12

shows three indexes of LSTM and LSTM–EMD. Taking RMSE as an example, the forecasting effect of LSTM–EMD is improved by 28.57% compared with that of LSTM.

5. Conclusions

For the current problems in the process of determining the RUL forecasting error, this paper proposes a method for forecasting the RUL of energy storage batteries using EMD to correct the LSTM forecasting error. An RUL forecasting model for energy storage batteries based on the LSTM neural network was constructed, and the EMD method was used to process the forecasting error of LSTM, thereby improving RUL forecasting accuracy. The following conclusions have been drawn through this study: (1) By using different evaluation indexes, similar numbers of hidden layers can be obtained; (2) Taking RMSE as the index, the forecasting effect of LSTM is improved by 16% compared with the NN method and 32.26% compared with the SVM method; (3) The forecasting effects of each component obtained through EMD are good, providing a good foundation for error correction; (4) The forecasting effect of LSTM–EMD is improved by 28.57% compared with that of LSTM, which verifies the effectiveness of this method of correcting forecasting errors.

In future research, we will further analyze the statistical patterns of forecasting errors and develop a more accurate forecasting model based on deep learning. Furthermore, the factors that impact the RUL of batteries will also be considered and analyzed. The energy management strategies for energy storage plants based on the forecasting results will be studied. Combining RUL forecasting with energy management will delay the lifespan decay of energy storage battery.