Lithium-ion batteries have become the primary energy storage solution for electric vehicles due to their high energy density, low self-discharge rate, and long cycle life. However, capacity degradation caused by irreversible electrochemical reactions significantly impacts their remaining useful life (RUL). This paper proposes a hybrid deep learning framework integrating Empirical Mode Decomposition (EMD), Multilayer Long Short-Term Memory (MLSTM), and Elman neural networks to address RUL prediction challenges.
Methodology
1. Data Decomposition via EMD:
The original lithium-ion battery capacity sequence $x(t)$ is decomposed into intrinsic mode functions (IMFs) and residual components through sifting process:
$$x(t) = \sum_{i=1}^{n}c_i(t) + r_n(t)$$
where $c_i(t)$ represents IMFs and $r_n(t)$ denotes the residual trend. The decomposition process employs cubic spline interpolation for envelope construction and stopping criterion:
$$SD = \sum_{t=0}^{N} \frac{|c_{i-1}(t) – c_i(t)|^2}{c_{i-1}(t)^2} < 0.3$$
| Component | Frequency | Variance Contribution |
|---|---|---|
| IMF1 | High | 28.5% |
| IMF2 | Medium | 19.2% |
| Residual | Low | 52.3% |
2. Hybrid Prediction Architecture:
The decomposed components are processed through specialized networks:
$$h_t^{LSTM} = \sigma(W_f[h_{t-1},x_t] + b_f) \odot \tanh(W_c[h_{t-1},x_t] + b_c)$$
$$y_t^{Elman} = \sigma(W_y \cdot \sigma_h(W_hx_t + U_hh_{t-1} + b_h) + b_y)$$
where LSTM handles high-frequency IMFs and Elman network processes low-frequency components.
Experimental Validation
Testing with 1.1Ah lithium-ion batteries under 0.5C-1C discharge rates demonstrates superior performance:
| Model | Raw Data | EMD Processed |
|---|---|---|
| SVM | 4.85 | 4.52 |
| LSTM | 2.99 | 1.62 |
| Proposed | 2.49 | 1.44 |
The final prediction combines component forecasts through superposition:
$$y_{total} = \sum_{i=1}^k y_{LSTM}^i + \sum_{j=1}^m y_{Elman}^j + y_{Residual}$$
Key Innovations
- Multi-scale decomposition of lithium-ion battery degradation patterns
- Dual-network architecture for frequency-adaptive prediction
- Dynamic weighting mechanism for component integration
This hybrid approach demonstrates 39.6% lower MAPE than conventional LSTM models in lithium-ion battery RUL prediction, particularly effective for capturing nonlinear capacity regeneration phenomena. The framework provides critical insights for battery management systems in electric vehicles, enabling proactive maintenance strategies and optimized charging protocols.