Quantitative Lithium Inventory Tracking via Differential Capacity Peak Fitting Algorithms
Differential capacity peak fitting deconvolutes cell voltage data into loss of lithium inventory and active material degradation for precise health tracking.
Spline Approximation
Meaning
Numerical interpolation methods construct smooth piecewise polynomial curves that fit experimental data points within a specified error tolerance. Engineers apply spline approximation to reconstruct continuous open circuit voltage curves from discrete experimental state of charge measurements. This method generates a continuous representation of electrochemical behavior across the full operating window of the battery.
Mathematical Principle
Dividing the data domain into subintervals allows the algorithm to fit low-degree polynomials that are joined at boundaries called knots. Continuity of the function and its first two derivatives is enforced at each knot, producing a curve that is globally smooth. By using cubic splines, the calculation avoids the oscillations that occur when using high-degree polynomials over the entire domain.
Data Preprocessing
Smooth derivatives are essential when evaluating electrochemical data because any discontinuity in the derivative will generate false peaks in the results. In differential capacity analysis, the derivative of capacity with respect to voltage requires a continuous function to avoid amplifying measurement noise. Applying the approximation to the raw charge curve stabilizes the subsequent derivative calculation, permitting reliable peak analysis.
Computational Benefit
Reduced data storage is achieved by storing polynomial coefficients rather than millions of raw voltage points in the memory of the battery management system. This optimization allows real-time state estimations to run on resource-constrained microcontrollers.