Buildings are complex systems whose reliability and robustness depend not only on the components, but also on how they are organised, which dictates how damage propagates across spatial scales. In this paper, we develop a probabilistic building model based on network theory that abstracts redundant compartments as nodes and failure propagation between adjacent compartments as probabilistic edges, such that progressive collapse is represented as a stochastic contagion process equivalent to bond percolation. A percolation-based threshold is introduced to characterise the transition from a local to a systemic failure regime and provide a reference point for sensitivity to failure propagation. To move segmentation beyond qualitative provisions, a risk-equivalence criterion is formulated to determine a risk-neutral calibration point for the failure propagation probability, and an analytical approximation is derived for regular three-dimensional lattices to support early-stage evaluations without extensive numerical analyses. Application examples involving a three-dimensional lattice structure demonstrate how segmentation effectiveness is governed by topology and failure propagation and is approximately independent of the spontaneous compartment failure probability for small spontaneous compartment failure probabilities, implying that improving compartment reliability cannot compensate for insufficient segmentation. The examples further show that increasing continuity and the failure propagation probability can markedly increase the likelihood of progressive and disproportionate collapse, while a high likelihood of progressive collapse is not synonymous with complete system collapse. Overall, the framework provides a basis for defining explicit, topology-dependent performance objectives for segmentation and for supporting reliability-based and risk-informed approaches to mitigating progressive collapse in buildings.
Constructing accurate and computationally efficient surrogate models for predicting dynamical system responses is critical in many engineering domains, yet remains challenging due to the strongly nonlinear and high-dimensional mapping from external excitations and system parameters to system responses. This work introduces a novel Function-on-Function Nonlinear AutoRegressive model with eXogenous inputs (F2NARX), which reformulates the recently proposed F-NARX method from a function-on-function regression perspective. The proposed framework substantially improves predictive efficiency while maintaining high accuracy. By combining principal component analysis with Gaussian process regression, F2NARX further enables probabilistic predictions of dynamical responses via the unscented transform in an autoregressive manner. The effectiveness of the method is demonstrated through case studies of varying complexity. Results show that F2NARX outperforms state-of-the-art NARX model by orders of magnitude in efficiency while achieving higher accuracy in general. The probabilistic prediction capability of F2NARX is further demonstrated by combining it with active learning for first-passage probability estimation, showing its potential for reliability-oriented applications.
Reliability-based design optimization (RBDO) is often computationally intensive due to the coupling of two cumbersome ingredients, namely optimization and reliability analysis. By adhering to surrogate modeling in the augmented space with both global and local enrichment stages, this study endeavors to treat the RBDO task from a new perspective of Bayesian active learning. Then, three major contributions are made as follows. (i) Drawing on the component case, a composite look-ahead learning function is defined to quantify the potential reduction in the overall epistemic uncertainty of Kriging-based failure probability estimates for multiple constraints when a batch of k(≥1) new samples is added. (ii) The entry rule of local enrichment stage is developed based on the notation of “critical” constraints, which are identified according to an approximate 90% credible interval of failure probability estimate. (iii) The multi-point enrichment process is directly realized by maximizing this composite learning function in a stepwise manner, where the candidate pool is pruned and the number of new samples added per iteration is adaptively identified. Obviously, both multi-point enrichment and multiple constraints are handled in an unified way. The composite learning function and the entry rule jointly set the priority of active learning among multiple constraints along optimization. Five numerical examples are studied to test the performance of the proposed method, and comprehensive comparisons are made against several existing RBDO methods. Results indicate that the proposed method achieves high computational accuracy and efficiency, particularly with the adaptive batch-size selection strategy.
The spatial and temporal variability of corrosion affects the time-dependent performance of aging reinforced concrete (RC) members because the correlation structure influences the extent to which deterioration develops simultaneously across multiple reinforcing bars. Previous studies have simulated steel weight loss by incorporating anisotropic spatial correlation in the longitudinal and transverse directions. However, the evolution of spatial corrosion patterns over time, referred to here as spatiotemporal correlation, has received limited attention in simulations and experiments. This paper develops a three-dimensional univariate random field for time-dependent steel corrosion that accounts for correlation along and among multiple tensile rebars and over the investigated exposure period. The model combines the spectral representation method with a frequency-wavenumber spectrum to generate realizations with prescribed anisotropic spatiotemporal correlation. A procedure is proposed to estimate the model parameters through Fourier-transform analysis of time-sequenced steel weight loss data. The procedure is applied to data obtained from two RC slab specimens subjected to controlled wetting-drying cycles and measured at multiple times using X-ray imaging and digital image processing. As an illustrative example, the developed random field is applied to corroded RC slabs. The calibrated parameters are interpreted primarily within the experimental observation period, while results beyond the final inspection are treated only as a short illustrative extrapolation. The results show that the calibrated spatial and temporal correlations affect the persistence of localized corrosion patterns and the distribution of the minimum total residual cross-sectional area of multiple tensile rebars.
Estimating small failure probabilities remains a fundamental challenge in reliability analysis. Adaptive importance sampling (AIS) methods address this challenge by iteratively refining a proposal distribution, yet most existing approaches rely on explicit density estimation or surrogate modeling, which can scale poorly with the input dimension and/or the sample amount. This paper proposes an alternative AIS framework leveraging scalable neural network classification. At each intermediate stage, a neural classifier is trained to approximate the indicator function of the current failure event. The classifier output, combined with the known nominal distribution, defines an unnormalized importance sampling proposal from which samples are drawn using the Metropolis-adjusted Langevin algorithm (MALA), exploiting classifier gradient information while preserving the stationary distribution convergence. To address practical challenges inherent to rare events, we incorporate focal loss training to handle severe class imbalance and adopt a defensive importance sampling mixture to stabilize importance weights. Numerical experiments on various benchmarks up to 784-dimensions demonstrate the effectiveness of the proposed method.
