Parameter uncertainty and design of optimal experiments for the estimation of elastic constants

Abstract

This paper investigates an inverse technique for the identification of orthotropic elastic constants from measured plate natural frequencies. In general, the accuracy of the identified parameters depends on the method of estimation, modelling errors and measurement errors. The paper addresses the parameter uncertainty due to errors in the measurements. Based on assumptions of the measurement errors, second-order statistics of parameters are approximated by linearization schemes. The main focus is on the possibility of designing the experiment to minimize the uncertainty of the estimated parameters. The uncertainty of each estimate as function of the experimental design variables is investigated. Also the overall optimality of the experimental design defined as the hypervolume of the confidence region is considered. The results show that not all parameters are estimated with a sufficient precision in the general case, but by carefully designing the experiment, the parameter uncertainties can be greatly reduced. Both thin and thick plates are considered with focus on single-layer plates, but the results for laminated plates are also discussed.