The aim of this dissertation is to develop structural health monitoring (SHM) strategies specifically suited for application to structures of significant geometric or material complexity. To accomplish this aim, a statistical framework is developed that characterizes and idealizes such environments and then finds optimal approaches from a detection theory standpoint. An optimal detector for discriminating damaged and undamaged cases in complex structures is derived. A maximum-likelihood approach to estimating the first arrival point is presented as part of a larger framework for damage localization. Novel sensor fusion approaches are also developed to account for the varying uncertainties associated with each sensor pair in the array. Extensive empirical validation of the statistical framework is provided through experiments on multiple testbeds with diverse geometries, materials, and damage modes. The proposed approaches to damage detection and localization are proved to be effective through quantitative comparison with existing approaches from the literature. Characterizing the wave scattering properties (also called scattering matrices) from geometric features is an important topic for guided wave SHM, whether the features are damage modes or not. Two different sensing methodologies are presented for constructing empirical estimates of the scattering matrices. Additionally, other topics of critical importance to SHM system design are addressed--namely, uncertainty quantification, Bayesian experimental design, and optimal sensor placement. The result is a significant step forward in advancing SHM toward structures of realistic complexity

Bearing damage in composite bolted connections (such as those commonly used in aerospace applications) is investigated through the application of ultrasonic guided waves. Specifically, identical macro-fiber composite sensor arrays were bonded to each of two identical composite plates. One plate was then inspected ultrasonically in the unloaded condition with bearing damage being introduced through successive uniaxial tensile tests, while the other plate was assessed while under load in the tensile testing machine. A scattering matrix approach is employed to characterize the interaction of the guided waves with the target bolt hole. The effects of applied load and the bolt fixture on the ultrasonic results are explored. A parametric study is carried out to determine the optimal actuation frequency and interrogation angle for this application. The results demonstrate that the system is capable of detecting bolt bearing damage as well as monitoring of the applied load in the elastic region.