Abstract Failure probability estimation is a core problem in risk and reliability analysis, made particularly demanding when forward simulations are computationally expensive and failure events are rare. Typically, costly high-fidelity forward models are complemented by lower-fidelity, inexpensive alternatives—e.g., simplified physics models or finite-element or finite-difference discretizations on coarser or sparse meshes. The multilevel Monte Carlo (MLMC) technique partially mitigates the fidelity–efficiency trade-off, but its Monte Carlo nature still entails large numbers of runs across parameter settings and fidelity levels. We propose an adaptive importance sampling framework that markedly reduces computational cost for rare-event estimation by constructing locally accurate surrogate models of the expensive simulator. By explicitly accounting for fidelity in surrogate modeling, failure boundary inference, and experimental design, the proposed method outperforms conventional approaches that treat fidelity merely as a scalar parameter. Numerical experiments on three representative problems demonstrate that the proposed approach delivers superior accuracy and substantially lower computational cost.
Abstract The spatial variability of soil can be characterized using random field theory. A widely adopted method for discretizing random fields is the orthogonal series expansion (OSE), which implements the Karhunen–Loève (KL) expansion. Accurately estimating the discretization error and determining the optimal number of expansion terms ( M 0 ) are very important, as M 0 governs both the accuracy and efficiency of random field discretization and the subsequent reliability analysis of geostructures in spatially variable soils. This paper systematically investigates the influencing factors on the discretization error and develops a framework for determining M 0 that accounts for multiple influencing factors. Representative examples of one- and two-dimensional (1D and 2D) random field discretization using the OSE shows that the discretization error exhibits an inverse relationship with the autocorrelation distance (ACD) and a direct relationship with the domain size of the random field. By defining a dimensionless R ratio as the product of ACDs (along each coordinate direction) divided by the domain size, the combined effects of ACD and domain size can be quantified conveniently in a unified manner. For random field simulations where both the single-exponential (SNX) and square-exponential (SQX) autocorrelation functions are applicable, the latter is preferable as it requires lower M 0 than the former.
Abstract To address the limitations of traditional single-perspective risk analysis in tackling the complex safety governance challenges of urban underground space, this study analyzes core safety risks based on 128 accident cases and constructs an integrated analytical framework incorporating static structural analysis, dynamic propagation analysis, and risk chains assessment. The research was conducted by applying association rule mining, complex network analysis, and temporal propagation models. Firstly, 36 standardized risks were extracted from four dimensions: human, machine, environment, and management. The effective strong association rules were mined using the Apriori algorithm, and the confidence values of the rules were used as the corresponding edge weights to construct a directed weighted risk network. Then, the network centrality metrics integrated through principal component analysis determined the static core risks. At the same time, based on the small-world network theory, a temporal propagation model was established to depict the dynamic propagation characteristics and extract the dynamic core risks. Through the comparative analysis from two perspectives, the core safety risks were finally determined. Then, the risk propagation paths were analyzed using depth-first search, the risk chains were evaluated through multi-index quantification, and the high-risk chains were identified. The results show that adverse geotechnical conditions, inaccurate geological surveys, safety leadership and duty deficiencies, insufficient or malfunctioning emergency equipment, internal water accumulation, and extreme rainfall and flooding are the key risks with high structural importance and propagation criticality. High-risk chains are primarily triggered by geological hazards, propagating through environmental and equipment nodes before converging on management defects; management risks act as critical convergent nodes in most risk chains. Based on these findings, this study proposes a targeted intervention strategy that integrates source control and chain interruption, providing methodological support and decision-making references for the safety governance of urban underground space.
Abstract 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.
Abstract Tall steel structures located in multihazard-prone regions should possess the ability to withstand the coupled effects of long-term wind-induced fatigue and intermittent seismic events throughout their service life. This study proposes a lifetime seismic fragility assessment framework for tall steel structures incorporating the wind vibration–seismic double control technique. The proposed framework explicitly incorporates wind-induced fatigue deterioration and epistemic uncertainty in seismic demand modeling, thereby establishing a closed-loop analytical procedure capable of capturing multihazard coupling effects. Within this framework, wind hazard is probabilistically characterized based on measured wind speed data and a Poisson process model, while cumulative wind-induced fatigue damage is quantified using probability-weighted analysis combined with a material degradation model. Taking buckling-restrained braces (BRBs) as the core components of the vibration-seismic double control system, nonlinear time-history analyses are conducted on a 30-story concentrically braced steel frame structure. Subsequently, a Bayesian updating approach is introduced to establish a time-dependent seismic fragility model. The results indicate that BRBs exhibit excellent double control performance under both wind and seismic excitations, particularly in mitigating the accumulation of wind-induced fatigue damage. The proposed analytical framework can effectively capture the progressive evolution of structural risk, while the Bayesian updating approach significantly constrains epistemic uncertainty associated with model parameters and provides seismic fragility estimates with confidence intervals. These findings provide a systematic method and theoretical support for the lifetime seismic resilience assessment and performance-based design of tall steel structures under multihazard coupling effects.
