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This paper introduces a ridge regression scheme to enhance the estimation of parameters in nonlinear phenomenological models, particularly for state of health (SoH) prediction in lithium-ion batteries. By optimizing the ridge regression hyper-parameter at each iteration using information theoretic measures, the method addresses the challenges posed by confounded parameters and improves numerical conditioning. The results from simulations demonstrate rapid convergence and efficacy in fitting both heteroscedastic and serially correlated data.
Optimizing hyper-parameters in ridge regression can significantly enhance the reliability of parameter estimation in complex nonlinear models.
In some fields currently dominated by empirical approaches, such as state of health (SoH) prediction for lithium-ion batteries, phenomenological models motivated by quasi-physical thinking contain parameters to be estimated from experimental data. Often the structure of such models yields fully or partially confounded parameters, which are difficult or even impossible to estimate reliably. To preserve the desired model formulation and simultaneously improve the numerical conditioning for the problem we introduce a ridge regression scheme. An automated method is provided, based on information theoretic measures of model performance, which optimises the ridge regression hyper-parameter at each iteration. The formulae presented require fixed point iteration to solve for the hyper-parameter. Given a suitable starting value, analysis demonstrates convergence is very rapid. The optimal hyper-parameter selection mechanism is incorporated within an efficient regularised iterative generalised least squares mechanism, capable of fitting both heteroscedastic and serially correlated data as required. Simulation confirms the efficacy of the overall method.
