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A Bayesian experimental design approach to structural health monitoring with application to ultrasonic guided waves


The dissertation will present the application of a Bayesian experimental design framework to structural health monitoring (SHM). When applied to SHM, Bayesian experimental design (BED) is founded on the minimization of the expected loss, i.e., Bayes Risk, of the SHM process through the optimization of the detection algorithm and system hardware design parameters. This expected loss is a function of the detector and system design, the cost of decision/detection error, and the distribution of prior probabilities of damage. While the presented framework is general to all SHM applications, particular attention is paid to guided wave-based SHM (GWSHM). GWSHM is the process of exciting user-defined mechanical waves in plate or beam-like structures and sensing the response in order to identify damage, which manifests itself though scattering and attenuation of the traveling waves. Using the BED framework, both a detection-centric and a localization-centric optimal detector are derived for GWSHM based on likelihood tests. In order to objectively evaluate the performance in practical terms for the users of SHM systems, the dissertation will introduce three new statistics-based tools: the Bayesian combined receiver operating characteristic (BCROC) curve, the localization probability density (LPDF) estimate, and the localizer operating characteristic (LOC) curve. It will demonstrate the superior performance of the BED-based detectors over existing GWSHM algorithms through application to a geometrically complex test structure. Next, the BED framework is used to establish both a model-based and data -driven system design process for GWSHM to ascertain the optimal placement of both actuators and sensors according to application-specific decision error cost functions. This design process considers, among other things, non- uniform probabilities of damage, non-symmetric scatterers, the optimization of both sensor placement and sensor count, and robustness to sensor failure. The sensor placement design process is demonstrated and verified using several hypothetical and real-world design scenarios

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