Date of Award

2025

Degree Type

Thesis

Degree Name

Master of Science in Electrical Engineering (MSEE)

Department

Electrical, Computer, and Biomedical Engineering

First Advisor

Yeonho Jeong

Abstract

This work introduces an ensemble method for State of Health (SOH) estimation for Lithium-ion batteries that integrates three Machine Learning Models: a Symbolic Regression (SR) model using PySR, a Gaussian Process Regression (GPR) model using GPytorch, and a Neural Network (NN) model using PyTorch. The method utilizes the Two Pulse Load Test (TPLT) to extract a compact set of features, including voltage metrics, load current, and testing temperature. The ensemble method employs the Machine Learning Models in the following sequence: SR is used to derive a mathematical equation for fast inference on the Aged Charge/Discharge Rate (Crate,aged), and the GPR module corrects the predictive errors and provides uncertainty quantification. Crate,aged can be used to calculate SOH, and the GPR Predicted Crate,aged and uncertainty values from the GPR are used as inputs to the NN along with other features.

Because the TPLT produces a single-row feature vector for each test, the ensemble can make predictions without relying on full time-series input, significantly reducing the computational cost compared to more complex NNs that process sequential data. In addition, the GPR model can be updated without re-training, allowing for incremental updates as new data becomes available. The result is a robust, lightweight SOH estimation method that is suitable for real-time applications, particularly in resource constrained embedded Battery Management System (BMS) environments.

Real data is collected by performing TPLTs on LG Chem MH1 18650 and Panasonic NCR18650PF cells at varying load currents, State of Charge (SOC) levels, and temperatures. A public repo for the Panasonic NCR18650PF cell is used to enhance the basic table-based battery model found in Simulink for the Panasonic NCR18650PF cell to improve its accuracy. A comparison between the enhanced simulated model and real data from a real Panasonic NCR18650PF cell confirms that the accuracy is high enough to validate its use in generating a large set of simulated data for TPLTs. Using a combination of real and simulated data, the ensemble method is trained and validated.

The results show that the ensemble method is able to accurately estimate SOH with an average Root Mean Square Error (RMSE) of 1.06%. Using a Leave One Cell Out (LOCO) policy, the GPR model is trained with a dataset that has a single cell removed completely from the training and validation data sets. The combination of the PySR and GPR models performs well on the unseen cell data, with an average RMSE of 0.31% on all available data for that cell, and an average RMSE of 0.57% on the whole combined dataset comprised of the training data and the “new cell data”. An efficient update to the GPR model is employed using GPytorch’s fantasy update method, which is shown to drop the average RMSE on the Panasonic NCR18650PF down to 0.01% while the GPR model improved slightly in average RMSE. The NN model remains stable in its performance after the update, which means the model is able to adapt to new data without losing accuracy on the training data.

Finally, the full ensemble - including symbolic inference, GPR correction, and final NN prediction - was evaluated on a Raspberry Pi 4 Model B to test deployability. End to-end inference completed in 4.47 seconds using only CPU resources, with GPR fantasy updates taking 2.3 seconds, confirming that the system is suitable for real-time applications on constrained embedded platforms.

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Available for download on Tuesday, September 07, 2027

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