Data-driven and physics-based interval modelling of power spectral density functions from limited data

authored by: Marco Behrendt, Chao Dang, Michael Beer
Abstract: In stochastic dynamics, ensuring the structural reliability of buildings and structures is of paramount importance, especially when subjected to environmental loads such as wind or earthquakes. To adequately address these loads and the uncertainties associated with them, it is often necessary to utilise advanced load models, frequently expressed using a power spectral density (PSD) function. The construction of these load models becomes challenging when only limited data is available and meaningful statistics cannot be reliably derived. To address this issue, safety bounds are commonly used in load models to account for uncertainties. Many PSD functions, such as the Clough–Penzien model, are described by parameters with a physical background and can therefore reflect the real case. The aim of this work is to expand these physical parameters in order to account for uncertainties. For this purpose, bootstrapping is used to derive more reliable statistics. By introducing a scaling parameter that allows for flexibility, bounds of the data set can be derived. Consequently, suitable PSD models are fitted to the derived bounds. The PSD function is thus represented by intervals for its physical properties instead of relying on discrete values. When applying such a bounded load model to a structure, advanced interval propagation schemes can be utilised to bound the failure probability.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): University of Liverpool
Tongji University
Type: Article
Journal: Mechanical Systems and Signal Processing
Volume: 208
No. of pages: 15
ISSN: 0888-3270
Publication date: 15.02.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.ymssp.2023.111078 (Access: Closed)

BibTeX

@article{b057226a9f414f0782f6ee9908ff6083,
title = "Data-driven and physics-based interval modelling of power spectral density functions from limited data",
abstract = "In stochastic dynamics, ensuring the structural reliability of buildings and structures is of paramount importance, especially when subjected to environmental loads such as wind or earthquakes. To adequately address these loads and the uncertainties associated with them, it is often necessary to utilise advanced load models, frequently expressed using a power spectral density (PSD) function. The construction of these load models becomes challenging when only limited data is available and meaningful statistics cannot be reliably derived. To address this issue, safety bounds are commonly used in load models to account for uncertainties. Many PSD functions, such as the Clough–Penzien model, are described by parameters with a physical background and can therefore reflect the real case. The aim of this work is to expand these physical parameters in order to account for uncertainties. For this purpose, bootstrapping is used to derive more reliable statistics. By introducing a scaling parameter that allows for flexibility, bounds of the data set can be derived. Consequently, suitable PSD models are fitted to the derived bounds. The PSD function is thus represented by intervals for its physical properties instead of relying on discrete values. When applying such a bounded load model to a structure, advanced interval propagation schemes can be utilised to bound the failure probability.",
keywords = "Power spectral density function, Random vibrations, Stochastic dynamics, Stochastic processes, Uncertainty quantification",
author = "Marco Behrendt and Chao Dang and Michael Beer",
note = "Funding Information: Chao Dang would like to thank the support of the China Scholarship Council (CSC) . ",
year = "2024",
month = feb,
day = "15",
doi = "10.1016/j.ymssp.2023.111078",
language = "English",
volume = "208",
journal = "Mechanical Systems and Signal Processing",
issn = "0888-3270",
publisher = "Academic Press Inc.",
}