Parameter Individual Optimal Experimental Design and Calibration of Parametric Models

Abstract

Parametric models allow to reflect system behavior in general and characterize individual system instances by specific parameter values. For a variety of scientific disciplines, model calibration by parameter quantification is therefore of central importance. As the time and cost of calibration experiments increases, the question of how to determine parameter values of required quality with a minimum number of experiments comes to the fore. In this paper, a methodology is introduced allowing to quantify and optimize achievable parameter extraction quality based on an experimental plan including a process and methods how to adapt the experimental plan for improved estimation of individually selectable parameters. The resulting parameter-individual optimal design of experiments (pi-OED) enables experimenters to extract a maximum of parameter-specific information from a given number of experiments. We demonstrate how to minimize variance or covariances of individually selectable parameter estimators by model-based calculation of the experimental designs. Using the Fisher Information Matrix in combination with the Cramer-Raó inequality, the pi-OED plan is reduced to a global optimization problem. The pi-OED workflow is demonstrated using computer experiments to calibrate a model describing calendrical aging of lithium-ion battery cells. Applying bootstrapping methods allows to also quantify parameter estimation distributions for further benchmarking. Comparing pi-OED based computer experimental results with those based on state-of-the-art designs of experiments, reveals its efficiency improvement. All computer experimental results are gained in Python and may be reproduced using a provided Jupyter Notebook along with the source code. Both are available under https://github.com/nicolaipalm/oed.INDEX TERMS Parametric models, parameter estimation, design of experiments, optimal experimental design, battery aging, computer experiment. I. DESIGN OF COST INTENSIVE EXPERIMENTS

A Method to Improve Parameter Estimation Success

“…In these studies, the methodologies have been handled to create a new method to improve parameter estimation qualities in each parametric model in each research field in each situation under some assumptions. Some of these studies are; improving Bayes estimation via sparse sum of squares relaxations [43], improving maximum likelihood estimation via sparse sum of squares relaxations [44], improving parameter estimation of change point models via using Poisson distribution as discrete in the exponential changes as continuous sampler [45] and improving parameter estimation quality via an Experimental Design methodology [46].…”