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State of Health Estimation using Convolutional and Bidirectional LSTM Neural Networks tuned by Bayesian Optimization
Panagiotis Eleftheriadis, Foivos Georgios Kyrgios, Sonia Leva
TL;DR
Accurate battery SOH estimation is important for battery management, but available SOH datasets are limited and often omit dynamic aging conditions. The paper combines CNN and RNN architectures with Bayesian hyperparameter optimization, feature-combination analysis, and multi-dataset validation; CNN-FC-BiLSTM performs best on Oxford and PoliMi, while CNN-BiGRU performs best on NASA.
Problem
SOH estimation is important for battery management, while publicly accessible SOH datasets are limited and often lack aging under dynamic driving cycles.
Method
The study combines cascaded CNN and RNN layers, Bayesian hyperparameter optimization, systematic feature-combination analysis, and validation across three battery datasets.
Results
CNN-FC-BiLSTM achieved the best performance on the Oxford and PoliMi datasets, whereas CNN-BiGRU achieved superior results on the NASA dataset.
Takeaways & Limitations
The framework captures battery degradation dynamics across multiple datasets and has practical value for battery management systems requiring accurate SOH assessment.
Takeaways & Limitations
The best-performing solution requires substantial computational resources because of its high FLOP count, making cloud-based implementation advantageous under computational constraints.
Abstract
from arXiv · showhide
In this research, a novel framework is proposed for the SOH estimation, which employs a hybrid deep learning architecture of a concatenation of a Convolution Neural Network (CNN) and a Bidirectional Long Short-Term Memory (BiLSTM) Neural Network (NN) with the integration of Bayesian Optimization-based hyperparameter tuning for the network. Three different deep learning architectures are being evaluated: standalone recurrent models, CNN-RNN architectures and CNN-RNN combinations enhanced with intermediate Fully Connected (FC) layers. Among the three, the model with the intermediate FC layers demonstrated the highest predictive accuracy. A comprehensive feature engineering approach combines capacity (Q), voltage (V), Incremental Capacity Analysis (ICA), and Differential Voltage Analysis (DVA), with systematic evaluation of multiple combinations to identify the optimal input representation. To validate the proposed method, three publicly available datasets were utilized, ensuring reproducibility of the results, two from external sources and one developed by the author of this study using a unique experimental setup. The comparison study was performed using the Mean Absolute Error (MAE), the Root Mean Squared Error (RMSE) and the FLoating-point OPerations (FLOPs) as evaluation metrics.
1 Introduction
The paper addresses accurate battery SOH estimation through hybrid deep learning, Bayesian hyperparameter optimization, and systematic feature analysis. It validates the proposed approach across three datasets.
- Accurate SOH estimation is central to battery management because it provides insight into battery capacity and supports system scheduling, planning, and optimization.
- The proposed architecture combines CNN-based spatial feature extraction with an RNN that captures temporal variations in battery dynamics.
- Bayesian optimization is integrated to efficiently explore hyperparameters and identify settings intended to improve model performance.
- The study validates the proposed model using three battery datasets.
- An exhaustive analysis evaluates five input-feature combinations to identify the most promising representation.
2 Datasets
The study uses three battery datasets and constructs time-series inputs from voltage, capacity, ICA, and DVA features. Dataset-specific voltage windows, sampling choices, and discharge-cycle data support SOH estimation.
- Datasets: Three datasets comprise the PoliMi private dataset and the publicly available Oxford and NASA datasets.The datasets provide voltage, capacity, ICA, and DVA information for SOH estimation.
- Feature engineering: ICA is defined as dQ/dV, while DVA is calculated as dV/dQ and plotted against voltage.The resulting curves are filtered with Savitzky-Golay processing to reduce noise before feature extraction.
- Oxford dataset: The Oxford dataset contains eight NMC cells cycled at 40 °C between 2.7 V and 4.2 V, with a nominal capacity of 740 mAh.Only discharge-phase data are used for the study.
- Dataset processing: Oxford and NASA partial-discharge inputs use the 3.4–4.1 V window, while the TUB dataset uses 3.1–3.7 V to capture ICA peaks.Sampling intervals were manually adjusted to 10 seconds for the Oxford and PoliMi datasets.
- NASA dataset: The NASA dataset contains four lithium-ion cells whose voltage profiles vary more across cycles, while discharge capacity shows consistent degradation.The Oxford dataset includes disconnected cells 4 and 6 during testing.
- Input representation: The network receives time-series representations of ICA, DVA, voltage, and capacity from partial-discharge cycles.At each time step, SOH is estimated until cell end of life, defined at 70% SOH.
3 Proposed Method
The proposed method combines CNN and recurrent processing with Bayesian optimization of hyperparameters. Stacked CNN, RNN, and fully connected layers form the final architecture for sequential SOH estimation.
- CNN architecture: CNNs extract features using convolution, local connections, weight sharing, and pooling-based dimension reduction.Conv1D is suited to time-series and sequential data.
- Recurrent architecture: LSTMs use input, output, and forget gates to control information flow and capture long-term dependencies.BiLSTMs process information in both forward and backward temporal directions.
- Bayesian optimization: Bayesian optimization searches the CNN-RNN hyperparameter space using a probabilistic strategy that focuses exploration on promising regions.The approach is presented as more efficient and accurate than exhaustive grid or random search in high-dimensional spaces.
- Proposed network: The final algorithm stacks multiple CNN, RNN, and FC layers to process sequential input x and produce SOH output y_t.The paper states that stacked intermediate stages substantially improve performance.
4 Results
Across PoliMi, Oxford, and NASA, the best predictive architecture and input features varied by dataset. The highest-accuracy models generally required more computation, while compact alternatives offered lower FLOPs with acceptable errors for BMS deployment.
- Evaluation criteria: RMSE and MAE evaluate SOH prediction error, while FLOPs quantify the floating-point operations required for one model instance.SOH errors are reported as percentages.
- PoliMi dataset: 0.12% MAE and 0.14% RMSE were achieved on PoliMi by the CNN-FC-BiLSTM using ICA and voltage inputs.This last-category architecture produced the highest predictive performance on PoliMi.
- PoliMi dataset: 2176 FLOPs, 0.17% MAE, and 0.20% RMSE characterized PoliMi’s most favorable compact GRU configuration.Its low computational cost supports implementation in a BMS microcontroller for online applications.
- Oxford dataset: 0.16% MAE and 0.19% RMSE were achieved on Oxford by the CNN-FC-BiLSTM using ICA, DVA, and voltage inputs.The last-category architecture again delivered the best predictive performance.
- Oxford dataset: 2305 FLOPs, 0.22% MAE, and 0.26% RMSE defined Oxford’s most favorable compact LSTM configuration.The reduced computational burden was presented as feasible for BMS microcontroller implementation.
- NASA dataset: 0.45% MAE and 0.71% RMSE were achieved on NASA by the CNN-BiGRU using ICA alone.Unlike PoliMi and Oxford, NASA’s highest-accuracy model came from the CNN-RNN category without intermediate FC layers.
- NASA dataset: 4096 FLOPs, 0.53% MAE, and 0.72% RMSE characterized NASA’s most advantageous compact BiGRU configuration.This compact option was described as viable for real-time operation in a BMS microcontroller.
5 Discussion
The hybrid CNN–RNN framework achieved accurate SOH estimation across three datasets, with the best architecture depending on dataset conditions. CNN-FC-BiLSTM performed best on Oxford and Polimi, whereas CNN-BiGRU was superior on NASA.
- CNN-FC-BiLSTM yielded the best performance on the Oxford and Polimi datasets.It combines convolutional spatial-feature extraction, fully connected nonlinear transformation, and bidirectional temporal modeling.
- CNN-BiGRU achieved superior results on the NASA dataset.The NASA data had higher noise and more aggressive degradation than the other datasets.
- The proposed CNN–RNN framework estimated SOH accurately across three publicly available datasets.
- Performance across battery cells demonstrated generalization under relatively stable and homogeneous operating conditions.
6 Conclusions
The study combines cascaded CNN and RNN layers with Bayesian hyperparameter tuning for battery SOH estimation. CNN-FC-BiLSTM was strongest on PoliMi and Oxford, while CNN-BiGRU was strongest on NASA, supporting dataset-specific architecture selection.
- The proposed approach combines cascaded CNN and RNN layers for battery SOH estimation.
- BiLSTM layers with intermediate FC connections performed best on the PoliMi and Oxford datasets.
- BiGRU layers without FC layers performed best on the NASA dataset.
- Bayesian Optimization systematically tuned hyperparameters, reducing prediction errors and improving generalization.
- Architecture selection should account for dataset-specific degradation patterns.
A Tables
The tables organize error and computational-cost comparisons across feedforward, recurrent, CNN–RNN, and CNN–FC–RNN model categories.
- Table 9 reports errors and FLOPS for the first FFNN category.
- Table 10 reports errors and FLOPS for the second RNN category.
- Table 11 reports errors and FLOPS for the third CNN–RNN combination category.
- Table 12 reports errors and FLOPS for the fourth CNN–FC–RNN combination category.