Optimal Experimental Design for Large-Scale Inverse Problems via Multi-PDE-constrained Optimization

TL;DR

This paper develops and compares two optimal experimental design algorithms for parameter estimation in lithium-ion battery models, balancing accuracy and experimental duration, with potential applications to complex systems.

Contribution

It introduces two novel input design algorithms for large-scale inverse problems in battery modeling, emphasizing efficiency and applicability to complex models.

Findings

Longer experiments improve accuracy but are time-consuming.

Shorter, optimized experiments can achieve comparable accuracy in simulations.

Real data experiments show potential for reduced accuracy with shorter designs.

Abstract

Accurate parameter dependent electro-chemical numerical models for lithium-ion batteries are essential in industrial application. The exact parameters of each battery cell are unknown and a process of estimation is necessary to infer them. The parameter estimation generates an accurate model able to reproduce real cell data. The field of optimal input/experimental design deals with creating the experimental settings facilitating the estimation problem. Here we apply two different input design algorithms that aim at maximizing the observability of the true, unknown parameters: in the first algorithm, we design the applied current and the starting voltage. This lets the algorithm collect information on different states of charge, but requires long experimental times (60 000 s). In the second algorithm, we generate a continuous current, composed of concatenated optimal intervals. In this case, the experimental time is shorter (7000 s) and numerical experiments with virtual data give an even better accuracy results, but experiments with real battery data reveal that the accuracy could decrease hundredfold. As the design algorithms are built independent of the model, the same results and motivation are applicable to more complex battery cell models and, moreover, to other applications.