Probability distributions for dynamic and extreme responses of linear elastic structures under quasi-stationary harmonizable loads

verfasst von: Zifeng Huang, Michael Beer
Abstract: The non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to ambiguous structural responses. Quasi-stationary harmonizable processes with non-negative Wigner-Ville spectra are suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, random environmental loads are modeled as quasi-stationary harmonizable processes. The Loève spectrum of a harmonizable load process contains several random physical parameters. An explicit approach to calculate the probability distributions for the dynamic and extreme responses of a linear elastic structure subjected to a quasi-stationary harmonizable load is proposed. Conditioned on the specific values of the load spectral parameters, the harmonizable load process is assumed to be Gaussian. The conditional joint probability density function (PDF) of structural dynamic responses at any finite time instants and the conditional cumulative distribution function (CDF) of the structural extreme response are provided. By multiplying these two conditional probability distributions with the joint PDF of the load spectral parameters, and then integrating these two products over the parameter sample space, the joint PDF of structural dynamic responses at any finite time instants and the CDF of the structural extreme response can be calculated. The efficacy of the proposed approach is numerically validated using two linear elastic systems, which are subjected to non-stationary and non-Gaussian wind and seismic loads, respectively. The merit of the harmonizable load process model is highlighted through a comparative analysis with the EPSD load model.
Organisationseinheit(en): Institut für Risiko und Zuverlässigkeit
Externe Organisation(en): The University of Liverpool
Tongji University
Typ: Artikel
Journal: Probabilistic Engineering Mechanics
Band: 75
Anzahl der Seiten: 14
ISSN: 0266-8920
Publikationsdatum: 01.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Statistische und nichtlineare Physik, Tief- und Ingenieurbau, Kernenergie und Kernkraftwerkstechnik, Physik der kondensierten Materie, Luft- und Raumfahrttechnik, Meerestechnik, Maschinenbau
Elektronische Version(en): https://doi.org/10.1016/j.probengmech.2024.103590 (Zugang: Offen)

BibTeX

@article{c221f6bfba3848949f4fbec80aa1817f,
title = "Probability distributions for dynamic and extreme responses of linear elastic structures under quasi-stationary harmonizable loads",
abstract = "The non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to ambiguous structural responses. Quasi-stationary harmonizable processes with non-negative Wigner-Ville spectra are suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, random environmental loads are modeled as quasi-stationary harmonizable processes. The Lo{\`e}ve spectrum of a harmonizable load process contains several random physical parameters. An explicit approach to calculate the probability distributions for the dynamic and extreme responses of a linear elastic structure subjected to a quasi-stationary harmonizable load is proposed. Conditioned on the specific values of the load spectral parameters, the harmonizable load process is assumed to be Gaussian. The conditional joint probability density function (PDF) of structural dynamic responses at any finite time instants and the conditional cumulative distribution function (CDF) of the structural extreme response are provided. By multiplying these two conditional probability distributions with the joint PDF of the load spectral parameters, and then integrating these two products over the parameter sample space, the joint PDF of structural dynamic responses at any finite time instants and the CDF of the structural extreme response can be calculated. The efficacy of the proposed approach is numerically validated using two linear elastic systems, which are subjected to non-stationary and non-Gaussian wind and seismic loads, respectively. The merit of the harmonizable load process model is highlighted through a comparative analysis with the EPSD load model.",
keywords = "Extreme value distribution, Joint probability density function, Linear elastic structure, Quasi-stationary harmonizable load process",
author = "Zifeng Huang and Michael Beer",
note = "Funding Information: The works described in this paper are financially supported by the Alexander von Humboldt Foundation , to which the authors are most grateful. Any opinions and conclusions presented in this paper are entirely those of the authors. ",
year = "2024",
month = jan,
doi = "10.1016/j.probengmech.2024.103590",
language = "English",
volume = "75",
journal = "Probabilistic Engineering Mechanics",
issn = "0266-8920",
publisher = "Elsevier Ltd.",
}