Capturing Epistemic Uncertainties in the Power Spectral Density for Limited Data Sets

In stochastic dynamics, it is indispensable to model environmental processes in order to design structures safely or to determine the reliability of existing structures. Wind loads or earthquakes are examples of these environmental processes and may be described by stochastic processes. Such a process can be characterised by means of the power spectral density (PSD) function in the frequency domain. Based on the PSD function, governing frequencies and their amplitudes can be determined. For the reliable generation of such a load model described by a PSD function, uncertainties that occur in time signals must be taken into account. In this paper, an approach is presented to derive an imprecise PSD model from a limited amount of data. The spectral densities at each frequency are described by reliable bounds instead of relying on discrete values. The advantages of the imprecise PSD model are illustrated and validated with numerical examples in the field of stochastic dynamics.