TY - JOUR

T1 - Data-driven and physics-based interval modelling of power spectral density functions from limited data

AU - Behrendt, Marco

AU - Dang, Chao

AU - Beer, Michael

N1 - Funding Information: Chao Dang would like to thank the support of the China Scholarship Council (CSC) .

PY - 2024/2/15

Y1 - 2024/2/15

N2 - 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.

AB - 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.

KW - Power spectral density function

KW - Random vibrations

KW - Stochastic dynamics

KW - Stochastic processes

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85182446818&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2023.111078

DO - 10.1016/j.ymssp.2023.111078

M3 - Article

AN - SCOPUS:85182446818

VL - 208

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 111078

ER -