Bayesian probabilistic structural modeling for optimal sensor placement in ultrasonic guided wave-based structural health monitoring

Abstract

Many optimal sensor placement methods for structural health monitoring establish performance metrics based on the detection of a limited set of damage states and locations. In guided wave-based inspection, however, monitoring is carried out over a continuous region with a continuous distribution of possible damage locations, types, sizes, and orientations. Here, traveling waves are excited and then received by a set of transducers with the intent of detecting and localizing previously unobserved scattering sources that are associated with damage. To measure sensor network performance in this application, we implement a Bayesian experimental design approach by computing the total posterior expected cost of detection over the entire monitoring region. Since the optimization usually must be carried out using a computationally expensive meta-heuristic such as a genetic algorithm, efficient modeling of the interrogation process is key to solving this distributed sensor placement problem. In this work, we implement a previously developed semi-analytical modeling approach for wave scattering within our Bayesian probabilistic framework in order to optimally place active sensors for detecting cracks of unknown location, size, and orientation. This involves assuming a set of a priori probability distributions on the three unknowns and defining spatial distributions of cost associated with type I and type II detection error. These parameters are driven by the geometry, material, in-service structural loading, and performance requirements of the structure. Through a set of sensor placement examples, we demonstrate how changes in the probability and cost distributions will dramatically alter the optimal layout of the transducer network.