Sequential Cascaded Multi-Stage RFR Machine Learning Models for Predicting Electrical and Thermal Behavior in High-Capacity Lithium-Ion Batteries

Figure A1 and the accompanying code present the results of systematically training, validating, and testing a cascaded multi-stage machine-learning framework on the battery dataset. The framework consists of three sequential models, each trained to predict key battery parameters based on discharge conditions.

1. Stage 1: Predicting Temperature Rise

   • Inputs: Discharge time, ambient temperature, and C-rate
   • Output: Predicted temperature rise

2. Stage 2: Predicting Depth of Discharge (DoD)

   • Inputs: Discharge time, ambient temperature, C-rate, and the predicted temperature rise from Stage 1
   • Output: Predicted Depth of Discharge (DoD)

3. Stage 3: Predicting Heat Generation

   • Inputs: Discharge time, ambient temperature, C-rate, predicted temperature rise (from Stage 1), and predicted DoD (from Stage 2)
   • Output: Predicted heat generation

During evaluation, user-defined values for discharge time, ambient temperature, and C-rate are supplied as inputs to initiate the prediction process. The model sequentially computes temperature rise, DoD, and heat generation, using predicted outputs from earlier stages as inputs for subsequent predictions.

The model performance is assessed using the R-squared metric:

• R² ≈ 1: Strong agreement with experimental data
• R² = 0: Performance equivalent to a constant model
• R² < 0: Worse performance than a naive model

After training and cross-validation, the models are tested on the complete dataset, generating predictive plots for temperature rise, DoD, and heat generation. These visualizations demonstrate the accuracy of the models across different operating conditions, validating their ability to predict battery behavior effectively.