Operational Modal Analysis in Frequency Domain using Gaussian Mixture Models

Abstract

Operational Modal Analysis is widely gaining popularity as a means to perform system identification of a structure. Instead of using a detailed experimental setup Operational Modal Analysis relies on measurement of ambient displacements to identify the system. Due to the random nature of ambient excitations and their output responses, various statistical methods have been developed throughout the literature both in the time-domain and the frequency-domain. The most popular of these algorithms rely on the assumption that the structure can be modelled as a multi degree of freedom second order differential system. In this paper we drop the second order differential assumption and treat the identification problem as a curve-fitting problem, by fitting a Gaussian Mixture Model in the frequency domain. We further derive equivalent models for the covariance-driven and the data-driven algorithms. Moreover, we introduce a model comparison criterion to automatically choose the optimum number of Gaussian’s. Later the algorithm is used to predict modal frequencies on a simulated problem.