TY - JOUR

T1 - Estimation of an imprecise power spectral density function with optimised bounds from scarce data for epistemic uncertainty quantification

AU - Behrendt, Marco

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Beer, Michael

PY - 2023/4/15

Y1 - 2023/4/15

N2 - 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.

AB - 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.

KW - Imprecise probabilities

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=85145967701&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2022.110072

DO - 10.1016/j.ymssp.2022.110072

M3 - Article

AN - SCOPUS:85145967701

VL - 189

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 110072

ER -