Battery RUL Predictor β€” Two-Stage Physics-Informed ML Model

A machine learning system for predicting the Remaining Useful Life (RUL) of Li-ion batteries using Battery Management System (BMS) signals.

Architecture

β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
β”‚  BMS Signals (11 features)              β”‚
β”‚  V, I, T, R, Q_charge, Q_discharge,    β”‚
β”‚  charge_time, Ξ·_energy, Ξ·_coulombic,   β”‚
β”‚  dQ/dV, dV/dQ                           β”‚
β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜
               β”‚
β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β–Όβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
β”‚  STAGE 1: Physics-Informed Degradation  β”‚
β”‚  Estimator (Deep Neural Network)        β”‚
β”‚  β”œβ”€ Arrhenius temperature gating        β”‚
β”‚  β”œβ”€ Cycle positional embedding          β”‚
β”‚  β”œβ”€ Monotonicity constraint loss        β”‚
β”‚  └─ Outputs: 7 degradation features     β”‚
β”‚     β€’ SEI layer thickness               β”‚
β”‚     β€’ Lithium inventory loss             β”‚
β”‚     β€’ Active material loss (an/ca)       β”‚
β”‚     β€’ Resistance growth                  β”‚
β”‚     β€’ Electrolyte decomposition          β”‚
β”‚     β€’ Lithium plating                    β”‚
β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜
               β”‚
β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β–Όβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
β”‚  STAGE 2: RUL Predictor Ensemble        β”‚
β”‚  β”œβ”€ Gradient Boosted Trees (GBT)        β”‚
β”‚  β”œβ”€ Neural Network                       β”‚
β”‚  └─ Weighted ensemble                    β”‚
β”‚  Input: BMS + Predicted Degradation      β”‚
β”‚  Output: Remaining Useful Life (cycles)  β”‚
β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜

Results

Metric Value
MAE 111.72 cycles
RMSE 140.22 cycles
RΒ² 0.9215
MAPE 50.41%

Physics-Informed Design

Stage 1: Degradation Estimator

Based on electrochemical battery degradation models from the literature:

  • SEI Growth: Arrhenius kinetics with diffusion-limited square-root scaling (Wang et al.)
  • Lithium Inventory Loss: Proportional to SEI thickness + power-law cycling
  • Active Material Loss: Stress-based fatigue model with temperature dependence
  • Electrolyte Decomposition: First-order reaction kinetics
  • Lithium Plating: Temperature and C-rate dependent nucleation

Key physics constraints in the loss function:

  • Monotonicity: Degradation features must increase with cycling
  • Arrhenius Gating: Temperature modulates hidden layer activations
  • Softplus Output: Ensures non-negative degradation predictions

Stage 2: RUL Predictor

Combines BMS signals with predicted degradation features using an ensemble:

  • Gradient Boosted Trees for robust non-linear feature interactions
  • Neural Network for pattern recognition
  • Optimized ensemble weights via validation-set grid search

Input Features

BMS Observable Signals

Feature Description Unit
voltage Terminal voltage V
current Charge/discharge current A
temperature_measured Cell temperature Β°C
internal_resistance Measured via pulse test mΞ©
charge_capacity Charge capacity Ah
discharge_capacity Discharge capacity Ah
charge_time Time to full charge s
energy_efficiency Round-trip energy efficiency -
coulombic_efficiency Charge/discharge ratio -
dqdv_peak_height Differential capacity peak Ah/V
dvdq_peak_height Incremental capacity peak V/Ah

Operating Conditions

Feature Description Unit
cycle Cycle number -
c_rate Charging C-rate C
depth_of_discharge Depth of discharge -

Based on Research

  • Hassanaly et al. (2023) β€” PINN surrogate of Li-ion battery models (arXiv:2312.17329)
  • Nicolae et al. (2024) β€” Physics-informed cycle life prediction (arXiv:2404.17174)
  • Wang et al. β€” Arrhenius-based capacity fade model for SEI formation
  • Microsoft BatteryML β€” Open-source battery degradation platform

Usage

import torch
import numpy as np
import joblib
import json

# Load model components
config = json.load(open('config.json'))
# ... (see repository for full loading code)
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