The effect of prediction error correlation on optimal sensor placement in structural dynamics

Abstract

The problem of estimating the optimal sensor locations for parameter estimation in structural dynamics is re-visited. The effect of spatially correlated prediction errors on the optimal sensor placement is investigated. The information entropy is used as a performance measure of the sensor configuration. The optimal sensor location is formulated as an optimization problem involving discrete-valued variables, which is solved using computationally efficient sequential sensor placement algorithms. Asymptotic estimates for the information entropy are used to develop useful properties that provide insight into the dependence of the information entropy on the number and location of sensors. A theoretical analysis shows that the spatial correlation length of the prediction errors controls the minimum distance between the sensors and should be taken into account when designing optimal sensor locations with potential sensor distances up to the order of the characteristic length of the dynamic problem considered. Implementation issues for modal identification and structural-related model parameter estimation are addressed. Theoretical and computational developments are illustrated by designing the optimal sensor configurations for a continuous beam model, a discrete chain-like stiffness–mass model and a finite element model of a footbridge in Wetteren (Belgium). Results point out the crucial effect the spatial correlation of the prediction errors have on the design of optimal sensor locations for structural dynamics applications, revealing simultaneously potential inadequacies of spatially uncorrelated prediction errors models.