Treatment and effect of noise modelling in Bayesian operational modal analysis

Abstract

Operational modal analysis (OMA) identifies the modal properties, e.g., natural frequencies, damping ratios and mode shapes, of a structure using ‘output-only’ ambient vibration data. Instrument noise need not be negligible in ambient vibration data, and it is often modelled statistically. Simple noise models, e.g., independent and identically distributed (i.i.d.) among data channels, are often used and are found to give reasonable results in typical applications, although there may be concerns for data with, e.g., low signal-to-noise (S/N) ratio, large difference in noise intensities or significant correlation among data channels. This work aims at investigating the effect of noise models on OMA performed with a Bayesian approach in the frequency domain. In addition to modal identification results, noise models are also assessed from a Bayesian evidence perspective. To enable the study, algorithms for efficient calculation of Bayesian statistics (most probable value and covariance matrix) are developed to account for general noise models that have not been considered in existing algorithms. As a further contribution to OMA theory, it is shown that, by a suitable transformation of data, an OMA problem with general noise model can be converted to one with i.i.d. noise model. Based on this analogy, asymptotic formulae for identification uncertainty of modal parameters, i.e., ‘uncertainty law’, have been developed. The theory reveals a definition for the modal S/N ratio that is an intuitive yet nontrivial generalisation of the existing formula for i.i.d. noise. The proposed objectives and methodology are investigated in a comprehensive study through synthetic, laboratory and field data.