The rapid adoption of electric vehicles (EVs) in China has positioned the country as a global leader in sustainable transportation. Lithium-ion batteries are the cornerstone of China’s EV industry due to their high energy density and longevity. However, predicting the remaining useful life (RUL) of these batteries remains a critical challenge, as inaccurate forecasts can lead to safety risks and reduced efficiency. In this article, I propose a hybrid deep learning model that integrates Empirical Mode Decomposition (EMD), Multilayer Long Short-Term Memory (MLSTM) networks, and Elman neural networks to enhance RUL prediction accuracy for China’s electric vehicle batteries. By decomposing battery data into high-frequency and low-frequency components, the model captures complex degradation patterns, enabling more reliable forecasts. Experimental results demonstrate the model’s superiority over traditional methods, with an average absolute percentage error of only 1.438%. This approach not only supports the maintenance and safety of electric vehicles in China but also contributes to the broader goals of sustainable mobility.
The growth of China’s electric vehicle market is driven by government policies and technological advancements, making battery management a priority. Lithium-ion batteries in electric vehicles degrade over time due to factors like charge-discharge cycles and environmental conditions. Accurate RUL prediction helps in scheduling maintenance, reducing costs, and enhancing the reliability of China’s EV fleet. Traditional methods, such as support vector machines (SVM) and logistic regression (LR), often fall short in handling the non-linear and noisy data typical of battery degradation. In contrast, deep learning models, like recurrent neural networks (RNN) and LSTM, offer improved performance but still face limitations in capturing multi-scale features. My hybrid model addresses these issues by combining EMD for data decomposition with specialized neural networks for component-specific learning, resulting in a robust framework for China’s electric vehicle applications.
The core of my approach lies in the decomposition of battery capacity sequences using EMD. Given a raw time-series data sequence $x(t)$, the EMD process iteratively extracts intrinsic mode functions (IMFs) and a residual trend. The steps are as follows: First, identify all local maxima and minima, and use cubic spline interpolation to form the upper envelope $x_H(t)$ and lower envelope $x_L(t)$. The mean envelope $m(t)$ is computed as:
$$m(t) = \frac{x_H(t) + x_L(t)}{2}$$
Then, the difference between the raw data and the mean envelope is calculated as $x_1(t) = x(t) – m(t)$. If $x_1(t)$ satisfies the IMF conditions—having the same number of extrema and zero crossings, and symmetric envelopes—it is considered the first IMF, denoted $c_1(t)$. Otherwise, the process repeats until an IMF is obtained. The residual $r_1(t)$ is derived as $r_1(t) = x(t) – c_1(t)$. This screening continues for $n$ iterations, with the standard deviation (SD) serving as a stopping criterion:
$$SD = \sum_{t=0}^{N} \left| \frac{c_{i-1}(t) – c_i(t)}{c_{i-1}^2(t)} \right|, \quad i=1,2,\dots$$
where $N$ is the total number of data points, and $SD$ is typically set between 0.2 and 0.3. The final decomposition reconstructs the original data as:
$$x(t) = \sum_{i=1}^{n} c_i(t) + r_n(t)$$
Here, $c_i(t)$ represents the IMFs (high-frequency components), and $r_n(t)$ is the residual (low-frequency trend). This decomposition allows the model to handle non-stationary battery data effectively, which is common in electric vehicle operations in China.
For predicting the low-frequency components and trend, I employ an Elman neural network, which incorporates contextual memory units to capture temporal dependencies. The Elman network processes input sequences $x_n$ and hidden states $h_n$ as follows:
$$h_n = \sigma_h(W_h x_n + U_h h_{n-1} + b_h)$$
$$y_n = \sigma_y(W_y h_n + b_y)$$
where $W_h$, $U_h$, $W_y$ are weight matrices, $b_h$ and $b_y$ are bias vectors, and $\sigma$ is the sigmoid activation function defined as $\sigma(x) = \frac{1}{1 + e^{-x}}$. This network is particularly suited for the slowly varying low-frequency components, as it maintains historical context through its recurrent connections, enhancing prediction stability for China’s electric vehicle battery data.
In parallel, the high-frequency components are processed using a multilayer LSTM (MLSTM) network. The LSTM unit employs gates to control information flow, with the forget gate $f_n$ determining how much of the previous state $h_{n-1}$ to retain:
$$f_n = \sigma(W_f \cdot [h_{n-1}, x_n] + b_f)$$
The input gate $i_n$ and candidate state $\tilde{S}_n$ update the current state $S_n$:
$$i_n = \sigma(W_i \cdot [h_{n-1}, x_n] + b_i)$$
$$\tilde{S}_n = \tanh(W_c \cdot [h_{n-1}, x_n] + b_c)$$
$$S_n = f_n S_{n-1} + i_n \tilde{S}_n$$
Finally, the output gate $O_n$ and hidden state $h_n$ are computed as:
$$O_n = \sigma(W_o [h_{n-1}, x_n] + b_o)$$
$$h_n = O_n \tanh(S_n)$$
The MLSTM network consists of multiple LSTM layers to learn hierarchical features from high-frequency data. The loss function for training is the cross-entropy loss:
$$L_1 = \sum_{x_i} – y_i \log(\hat{y}_i)$$
where $y_i$ is the true label and $\hat{y}_i$ is the predicted value. This setup enables the model to capture short-term fluctuations in battery capacity, which are critical for accurate RUL prediction in electric vehicles.
The predictions from the Elman and MLSTM networks are combined using a stacking rule. If the MLSTM produces $n$ high-frequency predictions $y^{\text{MLSTM}}_i$ and the Elman network produces $m$ low-frequency predictions $y^{\text{Elman}}_j$, along with the residual trend prediction $y^{\text{Res}}_0$, the final RUL prediction $y_{\text{all}}$ is:
$$y_{\text{all}} = \sum_{i=1}^{n} y^{\text{MLSTM}}_i + \sum_{j=1}^{m} y^{\text{Elman}}_j + y^{\text{Res}}_0$$
This integration ensures that both rapid changes and long-term trends in battery degradation are accounted for, providing a comprehensive solution for China’s electric vehicle industry.
To validate the model, I used a dataset from battery aging tests, which included cycles under different discharge rates. The batteries had a rated capacity of 1.1 Ah and were tested at 25°C with charge and discharge cutoff voltages of 4.2 V and 2.7 V, respectively. The dataset comprised approximately 360 samples of battery capacity, temperature, and humidity data. For training, I used data from cells CS2#33 and CS2#36, while CS2#34 and CS2#37 were reserved for testing, with a train-test split ratio of 2:1. The experimental setup involved Python with PyTorch on an Ubuntu system, using an Intel i9 CPU and NVIDIA GPUs for acceleration.
| Parameter | Value |
|---|---|
| Rated Capacity | 1.1 Ah |
| Chemical Composition | LiCoO2 Cathode, Graphite Anode |
| Weight | 21.1 g |
| Size | 5.4 mm × 33.6 mm × 50.6 mm |
| Charge Current | 0.55 A (Constant) |
| Discharge Rates | 0.5C, 1C |
During training, I configured the MLSTM with two layers, a learning rate of $10^{-3}$, batch size of 50, and Adam optimizer. The maximum iterations were set to 15,000, with regularization to prevent overfitting. The input sequence length was 128, incorporating historical capacity data and environmental factors like temperature and humidity, which are vital for electric vehicle batteries in varying Chinese climates.
I evaluated the model using metrics such as Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE). The hybrid model was compared against SVM, LR, RNN, and LSTM baselines. The results showed that the proposed model achieved a training loss of approximately 7.87% and a test loss of 11.13%, with a minimal gap indicating good generalization. In contrast, RNN and LSTM had higher losses, around 18.43% and 16.69% respectively, due to overfitting on training data.
| Model | MAPE (%) | MAE (Ah) | RMSE (Ah) |
|---|---|---|---|
| SVM | 4.52 | 0.042 | 0.915 |
| LR | 5.63 | 0.053 | 1.148 |
| RNN | 3.47 | 0.033 | 1.118 |
| LSTM | 1.615 | 0.014 | 0.202 |
| Proposed Model | 1.438 | 0.012 | 0.101 |
As shown in Table 2, the hybrid model outperformed all others, with a MAPE of only 1.438%, highlighting its efficacy for electric vehicle battery management in China. The use of EMD decomposition significantly improved performance across all models, underscoring its value in handling non-linear battery data. For instance, without EMD, the proposed model’s MAPE was 2.49%, but with EMD, it dropped to 1.438%, demonstrating the importance of data preprocessing for China’s EV applications.
In conclusion, the hybrid deep learning model I developed offers a reliable solution for predicting the RUL of lithium-ion batteries in China’s electric vehicles. By leveraging EMD decomposition and combining Elman and MLSTM networks, the model achieves high accuracy and robustness, addressing the limitations of existing methods. This approach not only enhances battery safety and longevity but also supports the sustainable growth of China’s electric vehicle industry. Future work could explore real-time implementation and adaptation to diverse battery chemistries, further solidifying China’s position in the global EV market.