Bayesian Updating for Safety-Critical Structures under Limited Data

Bayesian updating provides a rigorous probabilistic framework for reliability assessment of safety-critical structures by fusing prior knowledge with site-specific observations. However, in real-world engineering practice, monitoring data are often extremely sparse, resulting in several fundamental challenges (e.g., ill-posed likelihood functions, high prior sensitivity, the curse of dimensionality, and likelihood misspecification). This paper presents a state-of-the-art review of Bayesian updating strategies for overcoming these limited-data obstacles. Four advanced methodologies are systematically reviewed, including efficient sampling and approximation techniques, surrogate-model-assisted updating, multifidelity and multisource data fusion, and physics-informed Bayesian machine learning. Typical applications in bridge engineering, geotechnical engineering, and offshore platform foundations are summarized. Despite tremendous advances, critical research potentials persist, such as real-time updating for digital twins, integration of imprecise probability theories, time-varying degradation models, and consideration of hydraulic properties and structure-interaction effects. This paper aims to provide a comprehensive reference for researchers to perform robust Bayesian reliability updating in the inevitable presence of sparse data.