Optimal Sensor Placement for Bayesian Parametric Identification of Structures

Abstract

There exists a choice in where to place sensors to collect data for Bayesian model updating and system identification of structures. It is desirable to use an available deterministic predictive model, such as a finite-element model, along with prior information on the uncertain model parameters and the uncertain accuracy of the predictive model, to determine which optimal sensor locations should be instrumented in the structure. In this thesis, an information-theoretic framework for optimality is considered. The mutual information between the uncertain model predictions for the data and the uncertain model parameters is presented as a natural measure of reduction in uncertainty to maximize over sensor configurations. A combinatorial search over all sensor configurations is usually prohibitively expensive. A convex optimization method is developed to provide a fast sub-optimal, but possibly optimal, sensor configuration when certain simplifying assumptions can be made about the chosen stochastic model class for the structure. The optimization method is demonstrated to work for a 50-story uniform shear building, with 20 sensors to be installed. The stability of optimal sensor configurations under refinement of the mesh of the underlying finite-element model is investigated and related to the choice of prediction-error correlations in the model. An example problem of placement of a single sensor on the continuum of an elastic axial bar is solved analytically. In order to solve the optimal sensor placement problem in the more general case, numerical estimation of mutual information between the model predictions for the data and the model parameters becomes necessary. To this end, a thermodynamic integration scheme based on path sampling is developed with the aim of estimating the entropy of the data prediction distribution. The scheme is demonstrated to work for an example that uses synthetic data for model class comparison between linear and Duffing oscillator model classes. The thermodynamic integration method is then used to determine the optimal location of a single sensor for a two degree-of-freedom oscillator model.