An optimal sensor placement design framework for structural health monitoring using Bayes risk

Abstract This paper presents a novel generalized framework for optimal sensor placement design for structural health monitoring (SHM) applications using Bayes risk as the objective function. Bayes risk considers the costs of consequences associated with making decisions and design selection (extrinsic cost) in the monitoring process, as well as intrinsic costs (e.g., sensor deployment and maintenance costs), which suggests that it is a natural choice for an SHM design objective function. The framework is intended to be sufficiently generalized to be applicable to any optimal sensor placement design used for SHM. To demonstrate the effectiveness and comprehensiveness of the proposed framework, it is applied to an example problem concerning the state detection of the boundary of a beam modeled by springs. We discuss in-depth the specific formulation of Bayes risk for this demonstration problem and detail multiple approaches to evaluate it. This paper addresses the challenges encountered in optimal sensor design problem due to the computationally expensive physics-based model, and it considers various uncertainties through the investigation and integration of Bayesian inference methods, uncertainty quantification, and optimization strategies. The effect of the initial design assumption and the technique used to approximate the Bayes risk on the final optimal sensor design is discussed.