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Article

Optimal Latinized Partially Stratified Sampling for High-Efficiency Nonstationary Stochastic Seismic Excitation and Response Analysis

1
College of Water Resources & Civil Engineering, Hunan Agricultural University, 1 Nongda Road, Changsha 410128, China
2
Hunan Provincial Engineering Research Center for Irrigation District Technology, Changsha 410128, China
3
Key Laboratory of Efficient Agricultural Water Conservation and Digital Water Resources Construction for Universities in Hunan Province, Changsha 410128, China
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(1), 140; https://doi.org/10.3390/math14010140 (registering DOI)
Submission received: 8 September 2025 / Revised: 21 December 2025 / Accepted: 27 December 2025 / Published: 29 December 2025
(This article belongs to the Special Issue Advances in High-Dimensional Scientific Computing)

Abstract

This paper proposes a computationally efficient framework for estimating first-passage probabilities of nonlinear structures under stochastic seismic excitations. The methodology integrates Optimal Latinized Partially Stratified Sampling (OLPSS) with the Random Function Spectral Representation Method (RFSRM) to generate a minimal yet optimal set of samples in the low-dimensional input space. Each sample corresponds to a representative nonstationary ground motion time history, which is then used to drive nonlinear dynamic analyses. The extreme values of the structural responses are extracted, and their distribution tails are accurately modeled using the Shifted Generalized Lognormal Distribution (SGLD), whose parameters are efficiently estimated via an extrapolation method. This allows for the construction of the probability density function (PDF) and cumulative distribution function (CDF) of the extreme responses, from which the failure probabilities and reliability indices are calculated. The proposed framework is rigorously validated against the Monte Carlo simulation (MCS) benchmarks using two illustrative examples, including a nonlinear single-degree-of-freedom (SDOF) system and a three-story shear building model. The results demonstrate that the proposed method achieves excellent accuracy in estimating failure probabilities and reliability indices, while significantly reducing the number of required simulations and thereby confirming its high efficiency and accuracy for rapid performance-based seismic assessment.
Keywords: first passage probabilities; dynamic reliability; seismic excitation; probability distributions; extreme value first passage probabilities; dynamic reliability; seismic excitation; probability distributions; extreme value

Share and Cite

MDPI and ACS Style

Liu, B.-H.; Cao, Y.; Zhang, L.-W. Optimal Latinized Partially Stratified Sampling for High-Efficiency Nonstationary Stochastic Seismic Excitation and Response Analysis. Mathematics 2026, 14, 140. https://doi.org/10.3390/math14010140

AMA Style

Liu B-H, Cao Y, Zhang L-W. Optimal Latinized Partially Stratified Sampling for High-Efficiency Nonstationary Stochastic Seismic Excitation and Response Analysis. Mathematics. 2026; 14(1):140. https://doi.org/10.3390/math14010140

Chicago/Turabian Style

Liu, Bao-Hua, Yan Cao, and Long-Wen Zhang. 2026. "Optimal Latinized Partially Stratified Sampling for High-Efficiency Nonstationary Stochastic Seismic Excitation and Response Analysis" Mathematics 14, no. 1: 140. https://doi.org/10.3390/math14010140

APA Style

Liu, B.-H., Cao, Y., & Zhang, L.-W. (2026). Optimal Latinized Partially Stratified Sampling for High-Efficiency Nonstationary Stochastic Seismic Excitation and Response Analysis. Mathematics, 14(1), 140. https://doi.org/10.3390/math14010140

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