Optimal Sensor Placement for Response Reconstruction in Structural Dynamics

A framework for optimal sensor placement (OSP) for response reconstruction under uncertainty is presented based on information theory. The OSP is selected as the one that maximizes an expected utility function taken as the mutual information between data and response quantities of interest (QoI). The expected utility function is extended to make the OSP design robust to uncertainties in structural model parameter and modelling errors. The resulting utility function is a multidimensional integral of the information entropy for each possible value of the model parameters, weighted by the prior or posterior probability distribution of the model parameters. The formulation uses the Gaussian nature of the response QoI given the measurements to simplify the expected utility function in terms of the covariance matrix of the uncertainty in the response output QoI given the values of modeling parameters. Methods to compute the multidimensional integrals and to optimize the sensor placement are discussed. The implementation is presented for two cases used to predict response time histories from output-only measured data: modal expansion techniques and filter-based techniques.