Estimation of an imprecise power spectral density function with optimised bounds from scarce data for epistemic uncertainty quantification

Behrendt, Marco, Faes, Matthias GR, Valdebenito, Marcos A and Beer, Michael ORCID: 0000-0002-0611-0345 (2023) Estimation of an imprecise power spectral density function with optimised bounds from scarce data for epistemic uncertainty quantification. Mechanical Systems and Signal Processing, 189. p. 110072.

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Official URL: http://dx.doi.org/10.1016/j.ymssp.2022.110072

Abstract

In engineering and especially in stochastic dynamics, the modelling of environmental processes is indispensable in order to design structures safely or to determine the reliability of existing structures. Earthquakes or wind loads are examples of such environmental processes and can be described by stochastic processes. Such a process can be characterised by the power spectral density (PSD) function in the frequency domain. The PSD function determines the relevant frequencies and their amplitudes of a given time signal. For the reliable generation of a load model described by a PSD function, uncertainties that occur in time signals must be taken into account. This work mainly deals with the case where data is limited and it is infeasible to derive reliable statistics from the data. In such a case, it may be useful to identify bounds that characterise the data set. The proposed approach is to employ a radial basis function network to generate basis functions whose weights are optimised to obtain data-enclosing bounds. This results in an interval-based PSD function. No assumptions are required about the distribution of the data within those bounds. Thus, the spectral densities at each frequency are described by optimised bounds instead of relying on discrete values. The applicability of the imprecise PSD model is illustrated with recorded earthquake ground motions, demonstrating that it can be utilised for real world problems.

Item Type:	Article
Uncontrolled Keywords:	Power spectral density function, Random vibrations, Stochastic processes, Stochastic dynamics, Imprecise probabilities, Uncertainty quantification
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	23 Jan 2023 16:05
Last Modified:	06 Jan 2024 02:30
DOI:	10.1016/j.ymssp.2022.110072
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3167807