Stochastic Processes Identification from Data Ensembles via Power Spectrum Classification

Abstract

Modern approaches to solve dynamic problems where random vibration is of significance will in most of cases rely upon the fundamental concept of the power spectrum as a core model for excitation and response process representation. This is partly due to the practicality of spectral models for frequency domain analysis, as well as their ease of use for generating compatible time domain samples. Such samples may be utilised for numerical performance evaluation of structures, those represented by complex non-linear models. Utilisation of ensemble statistics will be considered first for stationary processes only. For a stationary stochastic process, its power spectrum can be estimated statistically across all time or for a single window in time across an ensemble of records. In this work, it is first shown that ensemble characteristics can be utilised to improve the resulting power spectra by using estimations of the median instead of the mean of multiple data records. The improved power spectrum will be more robust in the presence of spectral outliers. The median spectrum will result in more reliable response statistics, particularly when source ensemble records contain low power spectra that are significantly below the mean. A weighted median spectrum will also be utilised, based upon the spectral distance of each record from the median, which will shift the estimated spectrum in the direction of the closest samples. In some cases, the data records exhibit high spectral variance so such an extent that a single power spectrum estimate is insufficient to adequately model the process statistics. In such cases, a more realistic representation of the spectral range of the process is captured by estimating two or more power spectra. This is done by classifying individual process records based upon their individual spectral estimates distance from each other, and therefore the only parameterisation required is to choose the number of spectrum models to be defined.