Data Optimization for Parameter Estimation under System Uncertainties with Application to Li-ion Battery

For the practice of system identification/parameter estimation, the quality of data has significant impact on the accuracy of results. Therefore, data optimization, or optimal experiment design, plays a critical role. Traditionally, the common practice is to design input excitation by maximizing the Fisher information, which is related to the variance of the estimation error. However, this approach suffers from fundamental limitations, including the assumption of no estimation bias and negligence of system uncertainties in measurement, model, and parameter, which severely affect the effectiveness of the method. In this paper, we establish new criteria and a novel framework for data optimization and uncertainty quantification to overcome the fundamental limitations. First, we derive a formula for quantifying the estimation error induced by sensor, model, and parameter uncertainties for the commonly used least-squares algorithm. Based on the formula, we identify desirable data structures, which could minimize the errors caused by each uncertainty. These structures are then adopted as new criteria to formulate the novel data optimization framework. The proposed methodology is applied to parameter estimation of a lithium-ion battery electrochemical model, showing up to one order of magnitude improvement in accuracy compared with the traditional Fisher-information-based approach.