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Incremental Capacity Analysis (ICA)

This document explains Incremental Capacity Analysis and its use in battery degradation modeling.

Overview

Incremental Capacity Analysis (ICA) is a powerful technique for analyzing battery degradation by examining the derivative of capacity with respect to voltage (dQ/dV).

Theory

dQ/dV Curve

The Incremental Capacity (\(dQ/dV\)) is the numerical derivative of battery capacity with respect to the terminal voltage:

\[ \text{IC}(V) = \frac{dQ}{dV} \approx \frac{Q_{i+1} - Q_i}{V_{i+1} - V_i} \]

Since raw voltage data is often noisy, numerical differentiation can amplify noise. BatteryML uses high-order Savitzky-Golay filters to smooth the signal:

\[ Y_j = \frac{\sum_{i=-k}^k C_i y_{j+i}}{N} \]

Where \(C_i\) are the filter coefficients and \(2k+1\) is the window size.

Physical Interpretation

  • Peaks: Correspond to phase transition plateaus in the \(V-Q\) curve (Gibbs Phase Rule).
  • Peak positions: Indicate the state of equilibrium potentials where phase transitions occur.
  • Peak heights: Proportional to the amount of active material undergoing phase transformation.

Degradation Indicators

Loss of Lithium Inventory (LLI)

Indicator: Peak shifts in the voltage domain.

If the amount of cyclable lithium decreases due to SEI growth, the corresponding phase transitions occur at different stoichiometry points, leading to a shift:

\[ \Delta V_{peak} \propto \Delta \text{Li}_{\text{inv}} \]

Loss of Active Material (LAM)

Indicator: Peak height decreases

Explanation: Less active material reduces peak magnitude

Example: Peak height decreases from 100 to 80

Impedance Rise

Indicator: Peak width increases

Explanation: Higher resistance broadens peaks

Example: Peak FWHM increases from 0.1V to 0.15V

ICA Feature Extraction

Peak Detection

  1. Smoothing: Apply Savitzky-Golay filter to reduce noise
  2. Peak Finding: Use peak detection algorithms
  3. Peak Characterization: Extract position, height, width, area

Features

For each peak:

  • Voltage: Peak position (V)
  • Height: Peak magnitude (dQ/dV)
  • Width: Full-width at half-maximum (FWHM)
  • Area: Integrated area under peak

Additional Features

  • Total area: Total integrated dQ/dV curve
  • Number of peaks: Count of detected peaks
  • Voltage at max dQ/dV: Voltage at maximum dQ/dV value

Implementation in BatteryML

ICAPeaksPipeline

The ICAPeaksPipeline extracts ICA features:

from src.pipelines.ica_peaks import ICAPeaksPipeline

pipeline = ICAPeaksPipeline(
    sg_window=51,      # Smoothing window
    sg_order=3,        # Polynomial order
    num_peaks=3,       # Number of peaks to extract
    voltage_range=(3.0, 4.2)
)

samples = pipeline.fit_transform({'curves': voltage_curves, 'targets': targets})

Processing Steps

  1. Load voltage curve: 0.1C discharge curve
  2. Compute dQ/dV: Numerical differentiation
  3. Smooth: Savitzky-Golay filtering
  4. Find peaks: Peak detection algorithm
  5. Extract features: Position, height, width, area
  6. Normalize: StandardScaler normalization

Interpretation

Peak Shifts

  • To higher voltage: LLI (less lithium)
  • To lower voltage: Unusual, may indicate other mechanisms

Peak Height Changes

  • Decrease: LAM (less active material)
  • Increase: Unusual, may indicate measurement issues

Peak Width Changes

  • Increase: Impedance rise (higher resistance)
  • Decrease: Unusual, may indicate improved kinetics

Best Practices

  1. Smoothing: Use appropriate smoothing to reduce noise
  2. Voltage Range: Focus on relevant voltage range (e.g., 3.0-4.2V)
  3. Peak Selection: Extract consistent number of peaks
  4. Validation: Verify peaks correspond to known transitions
  5. Caching: Cache expensive ICA computations

Limitations

  1. Noise: Sensitive to measurement noise
  2. Smoothing: May obscure fine details
  3. Peak Detection: May miss peaks or detect false peaks
  4. Interpretation: Requires domain knowledge

Applications

  1. Degradation Diagnosis: Identify degradation mechanisms
  2. Feature Engineering: Extract features for ML models
  3. Quality Control: Detect manufacturing defects
  4. Research: Understand battery behavior

References

  • Battery electrochemistry literature
  • ICA analysis papers
  • Oxford Battery Intelligence Lab documentation

Next Steps