Quantifying Cell Degradation Using Thermally Corrected Differential Capacity Spectra
Thermally corrected differential capacity spectra isolate lithium loss from active material decay by subtracting entropic and kinetic overpotential shifts.
Spline Interpolation
Meaning
Mathematical construction technique uses piecewise polynomials to build smooth curves connecting discrete coordinate points in battery discharge and state of charge modeling. Spline interpolation calculates values between measured calibration points by fitting low degree polynomials across adjacent intervals while maintaining continuous second derivatives at the boundaries. Engineers apply the method to voltage curves and thermal decay profiles where abrupt changes in slope would introduce numerical instability in simulation software.
Boundary conditions dictate the specific shape of the terminal segments, requiring either zero curvature or a fixed slope depending on the physical constraints of the cell chemistry under test. The technique stops applying when data points are too sparse to capture high frequency electrochemical noise, which creates artificial oscillations between the nodes.
Curve Fitting
Polynomial selection determines the fidelity of the resulting approximation against empirical laboratory data. Cubic variants offer the optimal balance between computational speed and smoothness for real time battery management system algorithms. Higher degree polynomials introduce numerical instability through Runge phenomenon oscillations near the edges of the lookup table.
Practitioners establish knots at specific voltage plateaus where phase changes occur during lithium intercalation.
Boundary Control
Terminal conditions govern the behavior of the curve outside the measured data range. Clamped splines receive fixed derivative inputs from electrochemical impedance spectroscopy measurements to prevent erratic extrapolation behavior. Natural variants set the second derivative to zero at the endpoints, forcing a linear continuation that avoids artificial voltage spikes in open circuit voltage curves.
Selecting the wrong boundary condition distorts state of charge estimation accuracy during low current discharge phases.
Thermal Correction
Temperature compensation adjustments modify the coordinate nodes before curve construction proceeds. Heat generation rates alter internal resistance values across different operational regimes, requiring multidimensional interpolation routines to map voltage drop accurately. Ambient temperature shifts displace the position of voltage plateaus on the capacity curve.
Software routines execute tensor product expansions to evaluate both current and thermal dimensions simultaneously within the control unit lookup table.