Relaxed power spectrum estimation from multiple data records utilising subjective probabilities

In structural dynamics, the consideration of statistical uncertainties is imperative to ensure a realistic modelling of loading and material parameters. It is well-known that any deterministic analysis only constitutes a single result for the given input parameters. Because of aleatoric or epistemic uncertainties, many factors must be considered either in certain intervals or with subjective probabilities. Especially for environmental processes, such as earthquakes or wind loads, a reliable prediction of future event characteristics is important for the design of safe structures. This work attends to the statistical procedure of simulating the response behaviour of a dynamic system under an excitation described by a stochastic process. A versatile option for this procedure is the estimation of the Power Spectral Density (PSD) function from real data records. The PSD function determines dominant frequencies and their magnitude of influence on the stochastic process. There are numerous methods for estimating the PSD function from source data, but usually these estimators do not account for uncertainties inherent in data records as they have a rigorous mathematical relationship between data and estimated PSD function. To address this issue, an approach for a stochastic load model that captures epistemic uncertainties by encompassing inherent statistical differences that exist across real data sets is proposed. Due to an increase in available data, reliable statistical information can be extracted from an ensemble of similar PSD functions that differ, for instance, only slightly in shape and peak frequency. Based on these statistics, a PSD function model is derived utilising subjective probabilities to capture the epistemic uncertainties and represent this information effectively. The spectral densities are characterised as random variables instead of employing discrete values, and thus the PSD function itself represents a non-stationary random process comprising a range of possible valid PSD functions for a given data set. This novel representation is useable for producing non-ergodic process realisations immediately applicable for Monte Carlo simulation analyses. The strengths and advantages are demonstrated by means of numerical examples