This study focuses on developing and examining the effectiveness of Transfer Learning (TL) for structural health monitoring (SHM) systems that transfer knowledge about damage states from one structure (i.e., the source domain) to another structure (i.e., the target domain). Transfer Learning (TL) is an efficient method for knowledge transfer and mapping from source to target domains. In addition, Proper Orthogonal Modes (POMs), which help classify behavior and health, provide a promising tool for damage identification in structural systems. Previous investigations show that damage intensity and location are highly correlated with POM variations for structures under unknown loads. To train damage identification algorithms based on POMs and ML, one generally needs to use multiple simulations to generate damage scenarios. The developed process is applied to a simply supported truss span in a multi-span railway bridge. TL is first used to obtain relationships between POMs for two modeled bridges: one being a source model (i.e., labeled) and the other being the target modeled bridge (i.e., unlabeled). This technique is then implemented to develop POMs for a damaged, unknown target using TL that links source and target POMs. It is shown that the trained knowledge from one bridge was effectively generalized to other, somewhat similar, bridges in the population.

Mathematical derivation and numerical verification of a wave transformation model in the frequency domain are discussed. The model is a fully dispersive nonlinear wave model and is derived based on the boundary value problem. Transforming the problem in the frequency domain and using multiple scale analysis in space and perturbation theory, the model is expanded up to second order in wave steepness. This fully dispersive nonlinear wave model is a set of evolution equations which explicitly contains quadratic near-resonant interactions. The comparison between the presented model, the existing fully dispersive model, and a nearshore model with different sets of laboratory and field data shows that the presented model provides significant improvements particularly at higher frequency.