A New Hybrid Neural Network Method for State-of-Health Estimation of Lithium-Ion Battery

Abstract

Accurate estimation of lithium-ion battery state-of-health (SOH) is important for the safe operation of electric vehicles; however, in practical applications, the accuracy of SOH estimation is affected by uncertainty factors, including human operation, working conditions, etc. To accurately estimate the battery SOH, a hybrid neural network based on the dilated convolutional neural network and the bidirectional gated recurrent unit, namely dilated CNN-BiGRU, is proposed in this paper. The proposed data-driven method uses the voltage distribution and capacity changes in the extracted battery discharge curve to learn the serial data time dependence and correlation. This method can obtain more accurate temporal and spatial features of the original battery data, resulting higher accuracy and robustness. The effectiveness of dilated CNN-BiGRU for SOH estimation is verified on two publicly lithium-ion battery datasets, the NASA Battery Aging Dataset and Oxford Battery Degradation Dataset. The experimental results reveal that the proposed model outperforms the compared data-driven methods, e.g., CNN-series and RNN-series. Furthermore, the mean absolute error (MAE) and root mean square error (RMSE) are limited to within 1.9% and 3.3%, respectively, on the NASA Battery Aging Dataset.

1. Introduction

In recent years, the environmental impact of fossil fuel consumption has become more and more serious, and governments are promoting the development of electric vehicles (EVs), increasing the popularity of EVs [1]. An energy storage system (ESS) is one of the important components of EVs, which is the key point to ensure the safe operation of EVs. Lithium-ion batteries have been widely used as the main energy source for ESS because of their long service life and high energy density. However, as the operating time of EVs increases, the batteries will inevitably age, so it is critical to accurately estimate the degree of battery aging. The state-of-health (SOH) is influenced by a number of factors such as current and voltage, reflecting the degree of battery aging. Battery SOH refers to the capacity of the battery in its current state to store electrical energy relative to a new battery, and is generally used as a percentage to quantitatively describe the current SOH of the battery [2], with a new battery being 100% and a completely obsolete one being 0%. There are various variables that can be used to describe the battery SOH, such as capacity, charge, internal resistance, number of cycles, etc. SOH is usually defined as the percentage of capacity decay and power decay (i.e., increase in internal resistance) of the reacting cell, as in Equations (1) and (2). Between them, battery capacity decay is the most widely applied definition for SOH calculation:

$$\mathrm{S}\mathrm{O}\mathrm{H}=\frac{\mathrm{Q}}{{\mathrm{Q}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}}\times 100\%$$

(1)

$$\mathrm{S}\mathrm{O}\mathrm{H}=\frac{{\mathrm{R}}_{\mathrm{E}\mathrm{O}\mathrm{L}}-{\mathrm{R}}_{\mathrm{n}\mathrm{o}\mathrm{w}}}{{\mathrm{R}}_{\mathrm{E}\mathrm{O}\mathrm{L}}\mathrm{-}{\mathrm{R}}_{\mathrm{n}\mathrm{e}\mathrm{w}}}$$

(2)

where Q_rated represents the rated capacity of the battery, Q represents the current capacity of the battery, R_now represents the internal resistance of the battery at the current moment, R_new represents the internal resistance of the new battery at the current moment, and R_EOL represents the internal resistance of the battery when it reaches the end of life (EOL). The larger the SOH value of the battery, the healthier the lithium-ion battery. It is generally believed that when the SOH drops to 70~80%, the EOL of the battery is reached, and the battery needs to be replaced.

SOH cannot be measured directly by the device, so it often needs to be obtained by the designed estimation methods. The existing SOH estimation methods are divided into two main categories, which are model-based methods and data-driven methods. The model-based methods are mainly divided into the electrochemical model [3], equivalent circuit model (ECM) [4], and empirical model [5].

Electrochemical models analyze the internal reaction mechanism and external characteristics of lithium-ion batteries by constructing multiple sets of partial differential equations, so as to describe the ion movement in the battery. Electrochemical models are generally classified into pseudo-two-dimensional models [6] and single-particle models [7,8]. In [9], an electrochemical model is established to identify the thermodynamic attributes of capacity loss. The authors in [10] develop an SOH-prediction algorithm based on estimation of the parameters of an enhanced single particle model that could be implemented using vehicle charging data. However, this type of method requires too many parameters to be solved and is less practical. Even if the parameters are simplified, there are still more than 20 parameters to be solved. Therefore, the electrochemical model-based methods are difficult to adopt in practice. ECMs are constructed to describe the electrical characteristics and internal structural changes of a battery by using electrical components such as resistors, capacitors, and inductors. The authors in [11] present a novel ECM in which the effect of nonlinear solid-phase diffusion is considered, which outperforms the traditional second-order model. The authors in [12] establish a new ECM based on the principle of electrochemical impedance spectroscopy, to improve the stability of the full-cycle modeling of lithium-ion batteries. However, this type of method is more difficult to model than electrochemical models, and deviations in some parameters will lead to large prediction errors. Empirical models obtain the mathematical relationship between parameters and variables through statistical analysis based on minimum error. The authors in [13] propose an empirical model to represent the effect of SOH, SOC, and temperature on the ECM parameters, which can be easily integrated into real-world BMS applications. However, due to the complex degradation mechanism inside the cell, such methods are highly dependent on the quality of the data and have weak robustness. These model-based methods are often integrated with currently widely used filters to estimate the battery SOH, such as the Kalman filter [14], extended Kalman filter [15], and recursive least squares filter [16], etc. However, all of these are difficult for choosing the appropriate model to maintain the balance between SOH estimation accuracy and computational complexity, thus limiting the use in real life.

Data-driven methods are widely used in battery-SOH estimation tasks due to their high flexibility and robustness. This type of method does not consider the internal aging mechanism and electrochemical reactions of the battery, but learns a nonlinear mapping from features to SOH from a large amount of data. Traditional data-driven methods are mainly based on machine learning methods, such as support vector machine (SVM) [17], Gaussian process regression (GPR) [18], and grey relational analysis (GRA) [19]. The authors in [20] propose a short-term SOH prediction method, which is carried out by combining the GPR with probability predictions. In [21], a joint GRA-based SOH estimation method considering temperature effects is proposed to explore the degradation mechanism of lithium-ion batteries at different temperatures and a generic temperature regressive model is developed. However, machine learning-based methods rely on the accuracy of manually extracted features, i.e., the accuracy of feature engineering, yet useful information is easily obscured in the feature engineering process because of realistic environmental factors and the randomness of battery signals.

Based on the consideration of the above problems and the development of deep learning, a large number of neural network (NN)-based SOH estimation methods have emerged. Among them, the recurrent neural network (RNN) is widely used because of its superiority in processing time-series information. As a further development of RNN, long short-term memory (LSTM) [22] has received wide attention because of its superiority in accomplishing long-term memory tasks; the gate recurrent unit (GRU) [23] further improves on it and maintains the same functions as LSTM while the parameters are reduced, which is more suitable in practical applications. The authors in [24] use a backpropagation LSTM neural network to develop SOH estimation and remaining useful life (RUL) prediction models. The authors in [25] present a novel hybrid Elman-LSTM method for battery RUL prediction by combining the LSTM and Elman neural networks, which are established to predict high- and low-frequency sublayers, respectively. In addition, the authors in [26,27,28] et al. have also proposed many methods based on LSTM, GRU, and its variants bidirectional LSTM (BiLSTM) [29], bidirectional GRU (BiGRU) [30], to solve the RNN short-term dependency problem.

Different from all the above methods, we propose a novel hybrid network, namely a dilated convolutional neural network-bidirectional gate recurrent unit (dilated CNN-BiGRU), for extracting and modeling time-series information. Numerous studies have demonstrated that both dilated CNN and BiGRU can be used for the task of predicting time-series information with high robustness and accuracy. In this hybrid network, dilated CNN and BiGRU are used to extract and process local and global features from the battery aging process, respectively. The two network outputs are fused by a parallel structure and used as the final feature representation. The method is used to reason about the dependence of voltage and battery capacity in the original battery data. In fact, with this hybrid network structure, both dilated CNN and BiGRU networks can be utilized to obtain more accurate temporal and spatial features of the original battery data. We use this hybrid network in the SOH estimation task for lithium-ion batteries, where the method does not rely on the ECM or the electrochemical model and does not require an additional feature extraction network. To demonstrate the superiority of the proposed network structure for the SOH estimation task, extensive experiments are conducted on two public lithium-ion battery datasets, the NASA Battery Aging Dataset and Oxford Battery Degradation Dataset, and the experimental results reveal that the present network has high accuracy and robustness.

The remainder of this paper is constructed as follows: Section 2 introduces the basic structure of the dilated CNN-BiGRU model and the detail estimation procedure. Section 3 describes the experimental data and elaborates on the experimental verification. Conclusions are summarized in Section 4.

2. Model Structure and Estimation Algorithm

2.1. Dilated CNN

In traditional recognition tasks, pooling layers are usually used to increase the receptive filed, which reduces the feature map size, so it also needs to be reduced to the original size by upsampling. This process will cause some information loss, which affects the accuracy of the prediction results. Dilated CNN [31] was developed to increase the receptive field while keeping the feature map size unchanged, thus not causing information loss and other problems. The convolution kernel size and perceptual field of the dilated convolution layer are calculated as follows:

$${\mathrm{k}}^{*}=\left(\mathrm{k}-1\right)\left(\mathrm{d}-1\right)+\mathrm{k}$$

(3)

$${\mathrm{r}}_{\mathrm{n}}={\mathrm{r}}_{\mathrm{n}-1}+\left({\mathrm{k}}^{\ast }-1\right)\ast {\displaystyle \prod _{\mathrm{i}=1}^{\mathrm{n}-1}{\mathrm{S}}_{\mathrm{i}}}$$

(4)

where k* represents the size of the convolution kernel of the dilated convolution layer, k represents the size of the convolution kernel of the normal convolution layer, d represents the dilation rate, r_n represents the receptive field size of this dilated convolution, r_n−1 represents the receptive field size of the upper dilated convolution, S_i represents the strides of the i-th convolution or pooling layer, and n represents the number of convolution layers.

Dilated CNN increases the receptive field without losing feature map size, but there are new problems that arise. The inputs to the dilated CNN are spaced, so not all of them will be involved in the next step of the computation. When the dilation rates are the same, the problem of discontinuity of convolution centroids will occur on the overall feature map. Therefore, the most direct way to solve this problem is to use dilated convolutions with different dilation rates, so this paper uses five layers of dilated convolutions with dilation rates of 1, 3, 9, 27, and 81, respectively. The schematic diagram of the dilated convolutions with dilation rates of 1, 2 and 6 respectively is shown in Figure 1.

2.2. GRU and BiGRU

GRU: GRU, like LSTM, is a variant of RNN, which was proposed to solve problems such as long-term memory and gradient in back propagation. However, GRU is an altered form of LSTM that works better. Three gate functions are used in LSTM: input gate, forget gate, and output gate, which represent the input value, memory value, and output value, respectively. The simplified version of the LSTM, GRU, uses two gate functions: reset gate and update gate, which reduces the parameters and improves the efficiency.

For GRU, its input and output are the same as those of a normal RNN. As shown in Figure 2, the input is the input X_t at time t, and the hidden layer state H_t−1 at time t − 1, which contains the information about the previous nodes. The output is the hidden node output OUT_t at time t and the hidden layer state H_t passed to the next node. In addition, ResNet gate is used to capture short-term dependencies. Update gate is used to capture long-term dependencies. The update equation of GRU at moment t is as follows:

$${\mathrm{R}}_{\mathrm{t}}=\mathsf{\sigma }\left({\mathrm{X}}_{\mathrm{t}}{\mathrm{W}}_{\mathrm{x}\mathrm{r}}+{\mathrm{H}}_{\mathrm{t}-1}{\mathrm{W}}_{\mathrm{h}\mathrm{r}}+{\mathrm{b}}_{\mathrm{r}}\right)$$

(5)

$${\mathrm{Z}}_{\mathrm{t}}=\mathsf{\sigma }\left({\mathrm{X}}_{\mathrm{t}}{\mathrm{W}}_{\mathrm{x}\mathrm{z}}+{\mathrm{H}}_{\mathrm{t}-1}{\mathrm{W}}_{\mathrm{h}\mathrm{z}}+{\mathrm{b}}_{\mathrm{z}}\right)$$

(6)

The GRU obtains the state of two gates by the state H_t−1 transmitted down from the previous moment and the input X_t of the current node. Where R_t represents ResNet gate and Z_t represents Update gate. σ represents the sigmoid function by which the data can be transformed to a value from zero to one, thus acting as a gate control signal. W is the weight; b is the bias.

$$\tilde{\mathrm{H}}=\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left({\mathrm{X}}_{\mathrm{t}}{\mathrm{W}}_{\mathrm{h}\mathrm{x}}+{\mathrm{R}}_{\mathrm{t}}{\mathrm{H}}_{\mathrm{t}}\otimes -1{\mathrm{W}}_{\mathrm{h}\mathrm{h}}+{\mathrm{b}}_{\mathrm{h}}\right)$$

(7)

where $\tilde{\mathrm{H}}$ represents the candidate hidden layer state, $\otimes$ represents the multiplication by element, and tanh represents the activation function tanh. Here R_t and H_t−1 are multiplied by elements to determine whether the previous information has any effect on the future prediction result. When R_t tends to zero, the GRU unit discards the past hidden information; when R_t tends to one, the GRU unit considers the past information useful and therefore keeps it. Then the output of multiplying by elements is added to the input at the current time, and finally the candidate hidden state is calculated by the fully connected layer of the activation function tanh. $\tilde{\mathrm{H}}$ mainly contains the information of the input X_t at time t and the targeted retention of the hidden layer state H_t−1 at time t − 1.

$${\mathrm{H}}_{\mathrm{t}}=\left(1-{\mathrm{Z}}_{\mathrm{t}}\right)\otimes {\mathrm{H}}_{\mathrm{t}}-1+{\mathrm{Z}}_{\mathrm{t}}\otimes \tilde{\mathrm{H}}$$

(8)

The purpose of this step is to forget some dimensional information of H_t−1 passed down and add some dimensional information of the current node input. Z_t ranges from zero to one. The closer the gating signal is to zero, the more previous data are remembered, while the closer it is to one, the more previous data are forgotten. (1 − Z_t)$\otimes$H_t−1, represents the selective forgetting of the previously hidden state. Z_t$\otimes \tilde{\mathrm{H}}$, represents selective memory for the current hidden state. When Z_t tends to one, it means that long-term dependence is always present; when Z_t tends to zero, it means that some unimportant information in the hidden information is forgotten.

BiGRU: The traditional GRU is transmitted along a single direction, and the information it obtains is the historical information before the current time, which leads to the neglect of the future information and thus can cause the consequence of losing important information. To make full use of the contextual information, this paper adopts BiGRU, whose structure is shown in Figure 3. BiGRU uses forward and backward computation for sequence information, respectively, so as to obtain two different hidden layer states, and then sum up the two vectors to get the final output. Its structure consists of forward GRU and backward GRU, which has the function of capturing the features of previous and future information, making full use of the sequence information and facilitating the feature extraction.

$${\overrightarrow{\mathrm{H}}}_{\mathrm{t}}=\mathrm{G}\mathrm{R}\mathrm{U}\left({\mathrm{X}}_{\mathrm{t}},{\overrightarrow{\mathrm{H}}}_{\mathrm{t}-1}\right)$$

(9)

$${\overleftarrow{\mathrm{H}}}_{\mathrm{t}}=\mathrm{G}\mathrm{R}\mathrm{U}\left({\mathrm{X}}_{\mathrm{t}},{\overleftarrow{\mathrm{H}}}_{\mathrm{t}-1}\right)$$

(10)

$${\mathrm{H}}_{\mathrm{t}}={\mathsf{\alpha }}_{\mathrm{t}}{\overrightarrow{\mathrm{H}}}_{\mathrm{t}}+{\mathsf{\beta }}_{\mathrm{t}}{\overleftarrow{\mathrm{H}}}_{\mathrm{t}}+{\mathrm{b}}_{\mathrm{t}}$$

(11)

where H_t represents the state of the hidden layer at time t, X_t represents the input at time t, $\overrightarrow{\mathrm{H}}\mathrm{t}$ and $\overleftarrow{\mathrm{H}}\mathrm{t}$ represents the outputs of the hidden layer at time t for forward and backward propagation, respectively, α_t and β_t represents the output weights of the hidden layer at forward and backward propagation, respectively, and b_t is the bias of the hidden layer at time t.

2.3. The Proposed Overall Network Structure

Since both dilated CNN and BiGRU introduced in the previous two sections can extract features from time-series information and mining correlations, they are now heavily used in time-series detection tasks [32,33,34]. To make full use of both networks, this paper design a hybrid network, namely dilated CNN-BiGRU, to achieve the estimation of the battery SOH. The overall network structure of the proposed network is shown in Figure 4. Dilated CNN-BiGRU contains two streams, one is the dilated CNN stream and the other is the BiGRU stream. The dilated CNN stream contains five cascaded dilated CNN modules, each contains a dilated convolution layer, a ReLU activation function, a maxpooling layer, and the five cascaded dilated CNN modules are followed by connecting three fully connected layers. The BiGRU stream contains two BiGRU layers followed by three fully connected layers. The role of the fully connected layers is to reduce the dimensionality to one dimension before the final output for subsequent summation. Finally, the output of the two streams is added as the capacity prediction result.

The detailed architecture of the proposed network is shown in

Table 1. Specifications of the DCNN-BiGRU architecture.

Layer	Input [N, M]	Kernel Size	Kernel Number	Strides	Dilation Rate	Output [N, M]	Last/Next Layer
I0	[4000, 1]	N/A	N/A	N/A	N/A	[4000, 1]	N/A/D1, G1
DC1	[4000, 1]	3	72	2	1	[2000, 72]	I0/P1
P1	[2000, 72]	2	N/A	N/A	N/A	[2000, 72]	DC1/DC2
DC2	[2000, 72]	3	36	1	3	[2000, 36]	P1/DC3
DC3	[2000, 36]	3	18	1	9	[2000, 18]	DC2/DC4
DC4	[2000, 18]	3	36	1	27	[2000, 36]	DC3/DC5
DC5	[2000, 36]	3	72	1	81	[2000, 72]	DC4/F1
F1	[2000, 72]	N/A	N/A	N/A	N/A	2000 × 72	DC5/D1
D1	2000 × 72	N/A	100	N/A	N/A	100	F1/D2
D2	100	N/A	1	N/A	N/A	1	D1/A1
G1	[4000, 1]	N/A	8	N/A	N/A	[4000, 16]	I0/G2
G2	[4000, 1]	N/A	8	N/A	N/A	[4000, 16]	G1/F2
F2	[4000, 1]	N/A	N/A	N/A	N/A	4000 × 16	G2/D3
D3	4000 × 16	N/A	100	N/A	N/A	100	F2/D4
D4	100	N/A	1	N/A	N/A	1	D3/A1
A1	1	N/A	N/A	N/A	N/A	1	D2 + D4/O0
O0	1	N/A	N/A	N/A	N/A	1	A1/N/A

I denotes input layer, DC denotes dilated convolutional neural network layer, P denotes maxpooling layer, F denotes flatten layer, D denotes dense layer, G denotes bidirectional gate recurrent unit layer, A denotes element-wise add, and O denotes output layer.

. In particular, a series of experiments are conducted to determine the size of the hidden layer of the BiGRU in this paper, and the experimental results are shown in Figure 5. By changing the hidden layer size of the BiGRU while keeping other parameters constant, we can see that the loss decreases gradually as the epoch increases, and reaches the lowest and tends to be constant when the epoch is close to 150. At this time, the network with hidden layer 8 obtains the smallest loss, so the BiGRU with hidden layer size 8 is used in this paper.

2.4. SOH Estimation Algorithm Based on Proposed Network

The overall SOH prediction flowchart is described in Figure 6; specifically:

Step 1: Data acquisition and preprocessing. First, we use data from two public datasets as experimental samples and convert the discharge data samples into a vector of size 4000 × 1. Then, experimental samples are normalized by Equation (12), where x is the data in the data set sample, x_min is the minimum value in the data sample, and x_max is the maximum value in the data sample. Finally, the data samples are divided into the training set and the test set in a ratio of approximately 3:1.

$${\mathrm{x}}_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}}=\frac{2\left(\mathrm{x}-{\mathrm{x}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right)}{{\mathrm{x}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{x}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}-1$$

(12)

Step 2: Model setup and initialization. Set the dilation rate of the dilated CNN and the number of hidden layers of the BiGRU, set the hyperparameters, and set the optimization algorithm. First, to avoid the problem of discontinuity of centroids in the feature map, we set five dilated convolutions with different dilation rates, 1, 3, 9, 27, and 81, respectively. In addition, to obtain a lower loss, we conduct several sets of experiments and determine the hidden layer size of the BiGRU to be 8. Second, we set the network hyperparameters, including epoch, learning rate, and batch size. For the epoch, we can see from Figure 5 that the loss decreases as the epoch increases, and the loss reaches the lowest and tends to be constant when the epoch reaches 150, and a larger epoch leads to a meaningless increase in time, so we set the epoch to 150. For the learning rate, during the training process, when 10 epochs pass without the model performance improving on the test set (i.e., the loss function value is not improved), the learning rate is adjusted to 0.75 times the previous one. By this method of adaptively changing the learning rate, the convergence of the model is improved to some extent. Different initial learning rates and batch sizes will directly affect the convergence minimum of the objective function. Therefore, we determine the initial learning rate and batch size by the control variable method, and ensure that the other parameters are consistent during the experiments. The results are shown in Figure 7. Taking into account the time cost and the value of the loss function (the larger the batch size, the longer the training time), we set the batch size to 16 and the initial learning rate to 0.0005. Finally, we use the Adam optimizer to optimize Equation (13), which combines the advantages of AdaGrad and RMSProp, with fast convergence speed and easy parameter adjustment.

$$\mathrm{L}\mathrm{o}\mathrm{s}\mathrm{s}=\frac{1}{\mathrm{N}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}\left|\mathrm{f}({\mathrm{x}}_{\mathrm{i}})-{\mathrm{l}}_{\mathrm{i}}\right|}$$

(13)

where f denotes the proposed model, N denotes the number of training samples, i denotes i-th sample, x_i denotes the input, and l_i denotes the corresponding label.

Step 3: Training. The training set samples are input into the network for training and the network model is saved at the end of training.

Step 4: Testing. The test set samples are input into the network for testing. To evaluate the SOH estimation performance of this network model, the maximum absolute error (MAE) and root-mean-square error (RMSE) are used as the evaluation criteria in this paper. The MAE and RMSE judge the estimation performance, and the smaller the value, the better the estimation performance. These two criteria are defined by the following equations:

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{\mathrm{m}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{m}}\left|{\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{\mathrm{i}}\right|}$$

(14)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{\mathrm{m}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{m}}{\left({\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{\mathrm{i}}\right)}^2}}$$

(15)

where y_i represents the true value of the i-th sample data (i.e., battery capacity), ${\widehat{\mathrm{y}}}_{\mathrm{i}}$ represents the estimated value of the i-th sample data, and m represents the total number of data samples.

3. Experiment and Analysis

3.1. Experimantal Data

In this paper, two public lithium-ion battery datasets are used to verify the validity of the proposed dilated CNN-BiGRU network. The two datasets are described as follows:

NASA dataset: The NASA Li-ion Battery Aging Dataset was published by the NASA Ames Research Center [35]. The Ames Research Center first set up a battery accelerated-life experiment platform, and then conducted charge and discharge experiments on all battery cells. The battery type used in the experiment is the 18650 Li-ion battery, which has a rated capacity of 2 Ah, a charge cut-off voltage of 4.2 V, and a discharge cut-off voltage of 2.7 V. The EOL is reached when the capacity of the Li-ion battery degrades to 70% of the rated capacity. In this paper, the test data of Li-ion batteries B0007, B0028, B0032, and B0036 are used as the test set, and the test data of batteries B0005, B0006, B0018, B0025, B0027, B0029, B0030, B0031, and B0034 are used as the training set. Batteries B0005, B0006, B0007, and B0018 were discharged with 2 A constant current until the voltage drops to 2.7 V, 2.5 V, 2.2 V, 2.5 V, respectively; batteries B0025, B0027, and B0028 were discharged with 4 A, 50% duty cycle 0.05 Hz square wave load until the voltage drops to 2.0 V, 2.5 V, and 2.7 V, respectively; batteries B0034 and B0036 were discharged with 4 A, 2 A constant current until the voltage dropped to 2.2 V and 2.7 V, respectively. The above batteries were all tested at room temperature, 24 °C. The other battery data were obtained at a high temperature of 43 °C and discharged at a constant current of 4 A. By this method of dividing the test set and training set, the effect of the proposed network in different environments can be better verified.

Oxford dataset: The Oxford Battery Degradation Dataset 1 [36] was obtained by a team of researchers from the Department of Engineering Sciences at the University of Oxford. The battery type used in this battery-aging experiment was a 740 mAh lithium cobalt-acid battery from Kokam, which has a rated capacity of 740 mAh. The test platform was an MPG205 battery test system from Bio-Logic, France, which recorded battery voltage, current, temperature, and SOC at a constant frequency of 1 Hz. The battery test platform charged and discharged the lithium-ion batteries at a constant temperature of 40 °C according to Artemis city driving conditions, and the battery was charged and discharged at a constant current after every 100 cycles. The specific constant current charging and discharging process is as follows: The battery is charged at 1 C (0.74 A) constant current until the voltage rises to 4.2 V, and then discharged at 1 C constant current until the voltage drops to 2.7 V, during which the current capacity is recorded using the amperage integration method. A total of 150,000 data points were recorded for the whole charging and discharging process, of which 517 curves were available for SOH estimation. In this experiment, Cell 4 and Cell 8 are used as the test set, and the remaining six batteries are used as the training set.

The charging voltage curves for the NASA dataset and the Oxford dataset are shown in Figure 8a,b, respectively; and capacity decay curves of some batteries are shown in Figure 9a,b, respectively.

3.2. Experimental Platform

The experimental environment used in this paper is CPU Intel(R) Core(TM) i5-10400 F CPU @ 2.90 GHz, GPU NVIDIA GeForce RTX 3070 Ti, video card memory 8 GB, Cuda version 11.4, using the deep learning framework TensorFlow-GPU 2.5.0.

3.3. Experiment Result on NASA Dataset and Oxford Dataset

To verify the performance of the proposed dilated CNN-BiGRU hybrid network for battery SOH prediction, a series of comparison experiments both on NASA dataset and Oxford dataset are conducted in this paper. First, we remove dilated CNN and BiGRU separately and test their single network prediction performance to verify the superiority of this hybrid network; second, we replace dilated CNN with CNN to verify the superiority of dilated CNN; finally, we replace BiGRU with GRU and BiLSTM to verify the superiority of BiGRU.

NASA dataset: For the NASA dataset, B0007, B0028, B0032, and B0036 are used as the test set and the other nine cells as the training set in this paper. The experimental results are shown in Figure 10. Overall, all methods can achieve the estimation of battery SOH. Figure 10a–d represent the estimation results of B0007, B0028, B0032, and B0036, respectively. For Figure 10a,b, the errors of all six methods are small except for BiGRU, and the error of BiGRU is slightly larger, which may be due to the failure of a single BiGRU network to achieve adequate modeling of a relatively small amount of original data; in addition, the error of dilated CNN-GRU is a little larger than the other methods, which may be due to the disadvantage of GRU compared to BiGRU when dealing with time-series information. For Figure 10c,d, the estimation errors of all six methods increase significantly, but our proposed dilated CNN-BiGRU network still achieves an error within 5% on B0036 and within 3% in the last 20 cycles of B0032. The curves predicted by the other methods showed a large deviation, especially for the BiGRU-based method, which may be due to the failure of a single BiGRU network to achieve adequate modeling of a relatively small amount of original data.

In this paper, MAE and RMSE are used as evaluation criteria to quantitatively analyze the SOH estimation results and the evaluation results are shown in

Table 2. MAEs and RMSEs of SOH estimation on the NASA dataset.

Battery Number	Criteria	Dilated CNN	BiGRU	CNN-BiGRU	Dilated CNN-GRU	Dilated CNN-BiLSTM	Dilated CNN-BiGRU
B0007	MAE (%)	1.08	1.12	0.81	1.35	1.14	0.80
	RMSE (%)	2.07	1.94	1.42	2.16	2.37	1.43
B0028	MAE (%)	0.55	3.17	0.36	1.10	0.60	0.40
	RMSE (%)	0.98	4.78	0.73	1.75	0.98	0.78
B0032	MAE (%)	3.92	4.13	3.86	3.88	4.47	2.77
	RMSE (%)	5.75	6.03	5.66	5.72	6.58	4.76
B0036	MAE (%)	3.36	4.06	4.65	3.04	3.13	2.71
	RMSE (%)	4.95	6.57	6.83	4.54	4.58	4.01
Overall	MAE (%)	2.35	2.88	2.83	2.34	2.32	1.83
	RMSE (%)	4.00	5.11	5.03	3.80	3.97	3.21

. The overall MAEs based on dilated CNN, BiGRU, CNN-BiGRU, dilated CNN-GRU, dilated CNN-BiLSTM, and our method (dilated CNN-BiGRU) are 2.35%, 2.88%, 2.83%, 2.34%, 2.32%, and 1.83%, respectively; the RMSEs are 4.00%, 5.11%, 5.03%, 3.80%, 3.97%, and 3.21, respectively. Overall, our method is able to achieve more accurate results. In particular, for B0032, the MAEs based on dilated CNN, BiGRU, CNN-BiGRU, dilated CNN-GRU, dilated CNN-BiLSTM, and our method are 3.92%, 4.13%, 3.86%, 3.88%, 4.47%, and 2.77%, respectively, and our method reduces the MAE by more than 40% compared to the other methods, which further demonstrates the superiority of the proposed method for the SOH estimation task.

Oxford dataset: For the Oxford dataset, Cell 4 and Cell 8 are used as the test set and the other six cells are used as the training set in this paper. The experimental results are shown in Figure 11. Overall, all six methods can achieve the estimation of battery SOH, and the error can be kept within 2.5%, which are all lower than those in the NASA dataset. This is due to the fact that the cell data in the Oxford dataset are all obtained under the same simple operating conditions, without extreme operating conditions such as high temperature and low temperature. From Figure 11a,b, it can be seen that the errors obtained by BiGRU are larger compared to the other five methods, which may be due to the limitations of BiGRU as a single neural network for time-series estimation, which further proves the advantages of the proposed hybrid dilated CNN-BiGRU network over the single network. For overall comparison, it can be concluded that the proposed network is superior in estimating the battery SOH and the errors can all be kept within 0.5%.

In this paper, MAE and RMSE are used as evaluation criteria to quantitatively ana-lyze the SOH estimation results, and the evaluation results are shown in

Table 3. MAEs and RMSEs of SOH estimation on the Oxford dataset.

Battery Number	Criteria	Dilated CNN	BiGRU	CNN-BiGRU	Dilated CNN-GRU	Dilated CNN-BiLSTM	Dilated CNN-BiGRU
Cell 4	MAE (%)	0.078	0.275	0.147	0.054	0.129	0.041
	RMSE (%)	0.145	0.494	0.309	0.117	0.291	0.073
Cell 8	MAE (%)	0.108	0.128	0.097	0.120	0.100	0.052
	RMSE (%)	0.177	0.241	0.177	0.187	0.176	0.083
Overall	MAE (%)	0.097	0.184	0.116	0.095	0.111	0.048
	RMSE (%)	0.165	0.359	0.236	0.164	0.227	0.080

. The over-all MAEs based on dilated CNN, BiGRU, CNN-BiGRU, dilated CNN-GRU, dilated CNN-BiLSTM, and our method (dilated CNN-BiGRU) are 0.097%, 0.184%, 0.116%, 0.095%, 0.111%, and 0.048%, respectively, and RMSEs are 0.165%, 0.359%, 0.236%, 0.164%, 0.227%, and 0.080%, respectively. Specifically, on Cell 4, the MAEs based on dilated CNN, BiGRU, CNN-BiGRU, dilated CNN-GRU, dilated CNN-BiLSTM, and our method are 0.078%, 0.275%, 0.147%, 0.054%, 0.129%, 0.041%, respectively, and the RMSEs are 0.145%, 0.494%, 0.309%, 0.117%, 0.291%, and 0.073%, respectively. On Cell 8, the MAE based on dilated CNN, BiGRU, CNN-BiGRU, dilated CNN-GRU, dilated CNN-BiLSTM, and our method are 0.108%, 0.128%, 0.097%, 0.120%, 0.100%, and 0.052%, respectively, and RMSEs of 0.177%, 0.241%, 0.177%, 0.187%, 0.176%, and 0.083%, respectively.

4. Conclusions

Accurate estimation of SOH is important for the safe operation of EVs, and establishing a reliable network model is a major key to estimate the SOH of the battery. In this paper, a novel hybrid network is proposed for SOH estimation based on the dilated CNN and the BiGRU, which fuses these two networks that are currently more effective in prediction tasks to obtain a more accurate result. The network model captures the long-term information of the time series, i.e., the long-term characteristics of battery capacity degradation. Based on this network, extensive experiments are conducted on both the NASA dataset and Oxford dataset, where the MAEs and RMSEs are 1.83% and 3.21% on the NASA dataset, and 0.048% and 0.08% on the Oxford dataset, respectively. The experimental results reveal that our proposed network can accurately predict the battery SOH without the additional complex feature-extraction process.