A probabilistic optimal sensor design approach for structural health monitoring using risk-weighted f-divergence

Abstract This paper presents a new approach to optimal sensor design for structural health monitoring (SHM) applications using a modified f-divergence objective functional. One of the primary goals of SHM is to infer the unknown and uncertain damage state parameter(s) from the acquired data or features derived from the data. In this work, we consider the loss of boundary contact (a “gap”) between a navigation lock miter gate and the supporting wall quoin block at the bottom of the gate to be the damage state parameter of concern. The design problem requires the optimal sensor placement of strain gages to obtain the best possible inference of the probability distribution of the gap length using the data from the multi-dimensional strain-gauge array. Using the notion of f-divergences (measures of difference between probability distributions), a risk-adjustment is made by using functions that weigh the importance of acquiring useful information for a given true value of the state-parameter and using Bayesian optimization. For this case study of miter gate monitoring, a computationally expensive high-fidelity finite element model and its digital surrogate is employed to provide efficient, previously-validated data.