Accurate prediction of the remaining useful life (RUL) of lithium ion batteries is critical for ensuring the safety, reliability, and optimal performance of electric vehicles (EVs). Lithium ion batteries dominate the EV market due to their high energy density, low self-discharge rate, and absence of memory effects. However, capacity degradation and internal resistance growth caused by electrochemical side reactions pose significant challenges to their long-term usability. Typically, a 20% capacity fade or 100% increase in internal resistance signals the end of life for lithium ion batteries in EVs. Early detection of aging trends and precise RUL estimation enable proactive maintenance, reduce operational risks, and extend battery service life. This paper proposes a hybrid deep learning framework integrating Empirical Mode Decomposition (EMD), Multilayer Long Short-Term Memory (MLSTM), and Elman neural networks to achieve high-precision RUL prediction for lithium ion batteries.
1. Lithium Ion Battery Aging Experiments and Data Collection
To analyze degradation characteristics, eight prismatic lithium ion batteries (rated capacity: 1.1 Ah) were divided into two groups for accelerated aging tests. Each test cycle comprised constant-current constant-voltage (CC-CV) charging, discharge, and rest intervals. Key experimental parameters are summarized in Table 1.
Table 1: Specifications of Tested Lithium Ion Batteries
| Parameter | Value |
|---|---|
| Rated Capacity | 1100 mAh |
| Chemistry | LiCoO₂ Cathode, Graphite Anode |
| Weight | 21.1 g |
| Dimensions | 5.4 mm × 33.6 mm × 50.6 mm |
| Charge Current (CC Phase) | 0.55 A |
| Cutoff Voltage (Charge) | 4.2 V |
| Discharge Rates | 0.5C, 1C |
Batteries CS2#33 and CS2#36 (discharged at 0.5C and 1C, respectively) provided training data, while CS2#34 and CS2#37 were reserved for testing. Capacity measurements were recorded over 360 charge-discharge cycles under controlled temperature (25°C).
2. Hybrid EMD-Elman-LSTM Prediction Framework
The proposed model leverages the complementary strengths of signal decomposition, recurrent neural networks, and feedforward architectures to capture multi-scale degradation patterns in lithium ion batteries.
2.1 Empirical Mode Decomposition (EMD)
EMD decomposes nonlinear, non-stationary battery capacity sequences Q(t) into intrinsic mode functions (IMFs) and a residual trend R(t):Q(t)=i=1∑nIMFi(t)+R(t),
where each IMF satisfies two conditions:
- The number of extrema and zero-crossings differs by at most one.
- The mean of upper and lower envelopes is zero.
The decomposition terminates when the residue R(t) becomes monotonic or exhibits negligible variability (standard deviation < 0.25). High-frequency IMFs reflect short-term capacity fluctuations, while low-frequency IMFs and R(t) represent gradual degradation trends.
2.2 Elman Neural Network for Trend Prediction
The Elman network processes low-frequency IMFs and R(t) using context-sensitive recurrent connections:ht=σh(Whxt+Uhht−1+bh),yt=σy(Wyht+by),
where ht is the hidden state, xt is the input vector, yt is the predicted trend, and σh, σy are sigmoid activation functions.
2.3 Multilayer LSTM for High-Frequency Feature Learning
A two-layer LSTM architecture extracts temporal dependencies from high-frequency IMFs. The LSTM cell updates its state St and hidden output ht through gating mechanisms:ft=σ(Wf⋅[ht−1,xt]+bf)(Forget Gate),it=σ(Wi⋅[ht−1,xt]+bi)(Input Gate),S~t=tanh(Wc⋅[ht−1,xt]+bc)(Candidate State),St=ft⊙St−1+it⊙S~t(State Update),ot=σ(Wo⋅[ht−1,xt]+bo)(Output Gate),ht=ot⊙tanh(St),
where ⊙ denotes element-wise multiplication.
2.4 Stacked Prediction Integration
Final RUL predictions combine outputs from Elman and LSTM modules:Q^(t)=i=1∑kIMF^iLSTM(t)+j=1∑mIMF^jElman(t)+R^(t).
3. Experimental Validation and Performance Analysis
3.1 Implementation Details
- Hardware: NVIDIA RTX 2080 Ti GPUs, Intel Core i9-9280X CPU.
- Software: PyTorch 1.9.0, Python 3.8.
- Hyperparameters:
- Learning rate: 10−3 (Adam optimizer).
- Batch size: 50.
- Training epochs: 15,000.
- Regularization: L2 penalty (λ=10−4).
3.2 Evaluation Metrics
- Mean Absolute Percentage Error (MAPE):
MAPE=N100%t=1∑NQ(t)Q(t)−Q^(t).
- Root Mean Squared Error (RMSE):
RMSE=N1t=1∑N(Q(t)−Q^(t))2.
- Mean Absolute Error (MAE):
MAE=N1t=1∑N∣Q(t)−Q^(t)∣.
3.3 Comparative Results
Table 2: Performance Comparison of RUL Prediction Models
| Model | MAPE (%) | MAE (Ah) | RMSE (Ah) |
|---|---|---|---|
| SVM | 4.85 | 0.045 | 0.988 |
| Logistic Regression | 5.66 | 0.056 | 1.163 |
| RNN | 4.15 | 0.037 | 1.281 |
| LSTM | 2.99 | 0.030 | 0.974 |
| Proposed Model | 1.44 | 0.012 | 0.101 |
The hybrid model reduced MAPE by 51.8% compared to standalone LSTM, demonstrating superior capacity to disentangle complex degradation patterns. Training and testing losses converged to 7.87% and 11.13%, respectively, indicating robust generalization.
4. Conclusion
This study presents a hybrid deep learning framework for RUL prediction in lithium ion batteries, addressing the limitations of conventional methods in handling non-stationary capacity data. By integrating EMD-based signal decomposition, LSTM networks, and Elman recurrent architectures, the model achieves state-of-the-art prediction accuracy (MAPE: 1.44%). Future work will explore online learning adaptations and multi-physics degradation modeling to enhance real-world applicability.