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

authored by: Marco Behrendt, Matthias G.R. Faes, Marcos A. Valdebenito, Michael Beer
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.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): TU Dortmund University
University of Liverpool
Tongji University
Type: Article
Journal: Mechanical Systems and Signal Processing
Volume: 189
ISSN: 0888-3270
Publication date: 15.04.2023
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.2022.110072 (Access: Closed)