Pranav Shah

Electrochemical impedance spectroscopy (EIS) is an established technique for characterizing degradation in lithium-ion batteries. Compared with laboratory EIS, online EIS (OEIS) is constrained by a limited frequency window and measurement error, which challenge reliable state-of-health (SoH) estimation. This work proposes a low-complexity framework for SoH estimation using health indicators (HIs) derived from an impedance triangle within the OEIS frequency window down to 1 Hz. The impedance triangle is constructed from three characteristic points: the ohmic, peak, and transition points. The characteristic frequency HIs and geometry-based HIs derived from the impedance triangle are compared with a normalized impedance ratio and a model-based charge transfer resistance as reference HIs. Among these HIs, the peak frequency and the ohmic-to-transition distance exhibit complementary sensitivity over different state-of-charge (SoC) and SoH ranges and are fused recursively. Validation is performed with an open-source aging dataset of 21 cells with diverse aging trajectories under three conditions: noise-free data, proportional Gaussian noise, and a measured OEIS noise profile derived from an Analog Devices CN0510 system. Under matched SoC conditions over the range of 20%–80%, the framework achieves a median SoH root mean square error (RMSE) of 1.05% under Gaussian noise and 0.97% under OEIS noise, with higher accuracy than SoH estimation based on charge transfer resistance and substantially lower computational cost. Under SoC mismatch, the median RMSE stays below 2% over the SoC range from 20% to 65%. These results show the potential of the framework for embedded deployment in battery management systems.

This study presents a novel state estimation approach integrating Deep Neural Networks (DNNs) into Moving Horizon Estimation (MHE). This is a shift from using traditional physics-based models within MHE towards data-driven techniques. Specifically, a Long Short-Term Memory (LSTM)-based DNN is trained using synthetic data derived from a high-fidelity thermal model of a Permanent Magnet Synchronous Machine (PMSM), applied within a thermal derating torque control strategy for battery electric vehicles. The trained DNN is directly embedded within an MHE formulation, forming a discrete-time nonlinear optimal control problem (OCP) solved via the acados optimization framework. Model-in-the-Loop simulations demonstrate accurate temperature estimation even under noisy sensor conditions and simulated sensor failures. Real-time implementation on embedded hardware confirms practical feasibility, achieving computational performance exceeding real-time requirements threefold. By integrating the learned LSTM-based dynamics directly into MHE, this work achieves state estimation accuracy, robustness, and adaptability while reducing modeling efforts and complexity. Overall, the results highlight the effectiveness of combining model-based and data-driven methods in safety-critical automotive control systems.

This study introduces a novel state estimation framework that incorporates Deep Neural Networks (DNNs) into Moving Horizon Estimation (MHE), shifting from traditional physics-based models to rapidly developed data-driven techniques. A DNN model with Long Short-Term Memory (LSTM) nodes is trained on synthetic data generated by a high-fidelity thermal model of a Permanent Magnet Synchronous Machine (PMSM), which undergoes thermal derating as part of the torque control strategy in a battery electric vehicle. The MHE is constructed by integrating the trained DNN with a simplified driving dynamics model in a discrete-time formulation, incorporating the LSTM hidden and cell states in the state vector to retain system dynamics. The resulting optimal control problem (OCP) is formulated as a nonlinear program (NLP) and implemented using the \texttt{acados} framework. Model-in-the-loop (MiL) simulations demonstrate accurate temperature estimation, even under noisy sensor conditions or failures. Achieving threefold real-time capability on embedded hardware confirms the feasibility of the approach for practical deployment. The primary focus of this study is to assess the feasibility of the MHE framework using a DNN-based plant model instead of focusing on quantitative comparisons of vehicle performance. Overall, this research highlights the potential of DNN-based MHE for real-time, safety-critical applications by combining the strengths of model-based and data-driven methods.