Meaning
A numeric curve-fitting algorithm generates smooth, continuous mathematical curves between discrete battery test measurements. In battery testing, cubic spline interpolation constructs continuous open-circuit voltage profiles from sparse experimental data points. This technique fits third-degree polynomials between adjacent points to ensure first and second derivative continuity across the entire boundary.
It minimizes artificial oscillations that often arise from higher-order polynomial interpolation, giving battery engineers a reliable representation of cell behaviors.
Mathematical Formulation
Piecewise polynomials are constructed by solving a system of linear equations determined by boundary conditions. For cubic spline interpolation, the method secures a smooth transition from one interval to the next by matching both slope and curvature at every knot. This approach delivers a twice-differentiable curve across the entire data range.
It proves highly effective when tracking rapid voltage drops at low states of charge.
Operational Advantage
Accuracy gains are realized because the spline avoids the numerical instability known as Runge’s phenomenon. The algorithm allows researchers to reconstruct the state-of-charge curve using fewer measurements, reducing overall test cell occupancy. Accurate intermediate values are retrieved without running time-consuming low-current discharge tests.
It simplifies the extraction of differential capacity peaks.
Limitation Threshold
Extrapolation beyond the outermost data points represents the critical point of failure for this method. When input values fall outside the tested limits, the cubic polynomial can diverge to infinity. Therefore, the computation must be restricted strictly to the interpolating domain.
It requires dense points near the discharge limits to avoid non-physical curvature.
