An investigation of optimal sensor locations for multi-type sensors considering modeling uncertainties by Bayesian system identification

Abstract

This study investigates optimal sensor locations using multi-type sensors for strain recovery. Weighted least squares estimation is used for strain recovery, and the optimal sensor locations are evaluated by minimizing the sum of the covariance of modal displacement coordinates. Here, modeling uncertainty is taken into account by using Bayesian system identification. The present study evaluates multiple optimal sensor locations considering modeling uncertainties and quantifying their plausibility using multi-type sensors. First, a 2-D truss is studied by using an exhaustive search. It has been observed that when strain and acceleration data are fused, the sum of the variances of the modal displacement coordinate estimates is not sensitive to the locations of the acceleration sensors and that multiple optimal solutions exist. In order to obtain a unique solution and extract maximum information from acceleration data too, the sum of the variances of the estimates of a quantity defined as the pseudo-modal acceleration coordinates is also used as a performance measure. Further investigation using Bayesian system identification has revealed that the optimal sensor location with maximum plausibility is the same as the one obtained from the nominal model. Next, the methodology is studied using the 3-D truss model of a bridge in Jhansi, India, and a genetic algorithm is used for optimization. It has been observed that the variance of the estimates is a better measure for selecting the optimal sensor locations than the Fisher information because it can detect ill-conditioning. Finally, the methodology is applied to the experimental data obtained from a four-story shear building to gain further insights. Here also, it has been observed that the variance of the estimates rightly predicts the order of the optimal sensor locations, unlike the Fisher information. When the experimental data are used for Bayesian system identification, it has been noticed that all the predicted OSLs correspond to the one predicted by the nominal model.