Optimal experimental design in structural dynamics.

Theoretical and computational issues arising in experimental design for model identification and parameter estimation in structural dynamics are addressed. The objective is to optimally locate sensors in a structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling. The information entropy, measuring the uncertainty in the parameters of a structural model class, is used as a performance measure of a sensor configuration. For a single model class, the optimal sensor location problem is formulated as an information entropy minimization problem. For model class selection and/or damage detection applications, the problem is formulated as a multi-objective optimization problem of finding the Pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices related to multiple model classes and/or probable damage scenarios. Asymptotic estimates for the information entropy, valid for large number of measured data, are presented that rigorously justify that the selection of the optimal experimental design can be based solely on the nominal structural model from a class, ignoring the details of the measured data that are not available in the experimental design stage. The effect of the measurement and model prediction error variances on the optimal sensor location design is examined. Finally, heuristic algorithms are proposed for constructing effective sensor configurations that are superior, in terms of accuracy and computational efficiency, to the sensor configurations provided by genetic algorithms.