Optimal Experimental Design Methodology for Parameter Estimation of Nonlinear Models

Abstract

Experimental data are used to improve structural models and model-based predictions of output quantities of interest (QoI), that are crucial in making decisions regarding structural health, safety and performance. The objective in optimal experimental design (OED) is to optimize the design of the experiment such that the most informative data are obtained to reduce the uncertainties in the parameters of the models and the uncertainty in the model-based predictions of output QoI. Here we propose a Bayesian OED framework for model parameter estimation, based on maximizing a utility function built from appropriate measures of information in the data. Asymptotic approximations for the multidimensional integrals arising in the formulation are proposed. The design variables include the location of sensors/actuators and/or the characteristics (amplitude variation and frequency content) of the excitation. Heuristic algorithms are used to solve the optimization problem. The proposed framework is applicable to linear and nonlinear systems encountered in structural health monitoring (SHM) applications. The effectiveness of the method is demonstrated for a multi degree of freedom (DOF) spring-mass chain system with elements that exhibit hysteretic nonlinearities. © 2021 International Conference on Structural Health Monitoring of Intelligent Infrastructure: Transferring Research into Practice, SHMII. All rights reserved.