Bayesian learning has emerged as a compelling and vital research direction in the field of structural dynamics, offering a probabilistic lens to understand and refine the analysis of complex dynamical systems. This review meticulously traces the three-decade evolution of Bayesian learning in structural dynamics, illuminating core principles, groundbreaking methodologies, and diverse applications that have significantly influenced the field. The narrative commences by delving into the basics of Bayesian theory, clarifying essential concepts, and introducing primary methods for deriving posterior distributions, with an in-depth exploration of three types: Laplace approximation, stochastic sampling, and variational inference. Subsequently, the text explores the implementation of two types of Bayesian learning in structural dynamics: physical model learning and data-centric statistical model learning. Physical model learning emphasizes inferring physical model parameters within a Bayesian framework for system identification and prediction, while statistical model learning integrates Bayesian learning methodologies into data-centric statistical modeling within probabilistic machine learning. Both types resonate across various applications, such as modal analysis, model updating, damage detection, and reliability updating, highlighting their pivotal role in enhancing comprehension of dynamical systems and decision-making. The paper also navigates obstacles by proposing ways to enhance existing Bayesian inference strategies. Distinguished from previous research, this study offers a thorough examination of both traditional and cutting-edge Bayesian methods. It not only underscores the transformative influence of Bayesian approaches but also serves as a beacon, guiding researchers in the judicious selection and refinement of suitable methods for various challenges in structural dynamics.
Comment: 151 pages, 9 figures