Entropy-Based Optimal Sensor Location for Structural Model Updating

Abstract

A statistical methodology is presented for optimally locating the sensors in a structure for the purpose of extracting from the measured data the most information about the parameters of the model used to represent structural behavior. The methodology can be used in model updating and in damage detection and localization applications. It properly handles the unavoidable uncertainties in the measured data as well as the model uncertainties. The optimality criterion for the sensor locations is based on information entropy, which is a unique measure of the uncertainty in the model parameters. The uncertainty in these parameters is computed by a Bayesian statistical methodology, and then the entropy measure is minimized over the set of possible sensor configurations using a genetic algorithm. The information entropy measure is also extended to handle large uncertainties expected in the pretest nominal model of a structure. In experimental design, the proposed entropy-based measure of uncertainty is also well-suited for making quantitative evaluations and comparisons of the quality of the parameter estimates that can be achieved using sensor configurations with different numbers of sensors in each configuration. Simplified models for a shear building and a truss structure are used to illustrate the methodology.