arXiv subjects

Jianhua Xian

Publications and source records attributed to Jianhua Xian.

4 recordsLinked to original sources

arXiv2026

First-passage reliability sensitivity analysis of linear systems subjected to non-Gaussian wind excitations by surface decomposition method

This contribution develops a surface decomposition method for first-passage dynamic reliability sensitivity analysis of linear systems exposed to non-Gaussian wind excitations. The first-passage failure probability sensitivity is formulated as a system surface integral over a highly non-smooth and high-dimensional hypersurface. This complex integral is first decomposed into a collection of component surface integrals over the truncated smooth quadratic hypersurfaces. The dominant components are then identified based on the relative magnitudes of the first-order approximations of the component failure probabilities. A nested sampling algorithm is constructed to efficiently estimate the sum of these component surface integrals, in which the number of system limit-state function evaluations equals the number of outer-level samples while remaining independent of the inner-level sample size. A key advantage of the present approach is that the function evaluation results can be reused across different design parameters. Two numerical examples are explored to demonstrate the effectiveness of the proposed method. The results indicate that the number of function evaluations required is typically below 100 to achieve a target coefficient of variation of 0.1.

stat.ME↗

arXiv2026

Surface decomposition method for sensitivity analysis of first-passage dynamic reliability of linear systems

This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage failure probability into a sum of surface integrals over the constrained component limit-state hypersurfaces. The evaluation of these surface integrals can be accomplished, owing to the availability of closed-form linear expressions of both the component limit-state functions and their sensitivities for linear systems. An importance sampling strategy is introduced to further enhance the efficiency for estimating the sum of these surface integrals. The number of function evaluations required for the reliability sensitivity analysis is typically on the order of 10^2 to 10^3. The approach is particularly advantageous when a large number of design parameters are considered, as the results of function evaluations can be reused across different parameters. Three numerical examples are investigated to demonstrate the effectiveness of the proposed method.

stat.ME↗

arXiv2024

A physics and data co-driven surrogate modeling method for high-dimensional rare event simulation

This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical models with data-driven error corrections. The hypothesis is that a well-designed and well-trained simplified physical model can preserve salient features of the original model, while data-fitting techniques can fill the remaining gaps between the surrogate and original model predictions. The coupled physics-data-driven surrogate model is adaptively trained using active learning, aiming to achieve a high correlation and small bias between the surrogate and original model responses in the critical parametric region of a rare event. A final importance sampling step is introduced to correct the surrogate model-based probability estimations. Static and dynamic problems with input uncertainties modeled by random field and stochastic process are studied to demonstrate the proposed method.

stat.CO↗

arXiv2023

Relaxation-based importance sampling for structural reliability analysis

This study presents an importance sampling formulation based on adaptively relaxing parameters from the indicator function and/or the probability density function. The formulation embodies the prevalent mathematical concept of relaxing a complex problem into a sequence of progressively easier sub-problems. Due to the flexibility in constructing relaxation parameters, relaxation-based importance sampling provides a unified framework for various existing variance reduction techniques, such as subset simulation, sequential importance sampling, and annealed importance sampling. More crucially, the framework lays the foundation for creating new importance sampling strategies, tailoring to specific applications. To demonstrate this potential, two importance sampling strategies are proposed. The first strategy couples annealed importance sampling with subset simulation, focusing on low-dimensional problems. The second strategy aims to solve high-dimensional problems by leveraging spherical sampling and scaling techniques. Both methods are desirable for fragility analysis in performance-based engineering, as they can produce the entire fragility surface in a single run of the sampling algorithm. Three numerical examples, including a 1000-dimensional stochastic dynamic problem, are studied to demonstrate the proposed methods.

stat.AP↗