Bayesian modal identification of non-classically damped systems using time-domain data

Abstract

In this work, we present a Bayesian time–domain method for identifying the complex modal parameters of a linear dynamic system from ambient vibration data. Complex modal parameter identification is valid for both classically and non-classically damped systems, in contrast to real modal parameter identification, which is exclusively applicable to classically damped systems. A Bayesian method is adopted here which makes it possible to determine the joint posterior Probability Density Function (PDF) of the modal parameters for given measured data and modeling assumptions. For sufficient data, it is seen that the modal parameters are globally identifiable, and the posterior PDF is approximated by a Gaussian distribution with mean at the optimal parameters that maximize the posterior PDF. The uncertainty in the identified modal parameters is given by the covariance matrix of the posterior PDF. Analytical expressions are derived for computing the gradient for efficient optimization and the Hessian for determining the covariance matrix. Further, it is shown that the assumption of classical damping during analysis results in poor prediction of damping ratios in the case of non-classically damped systems. The application of the proposed approach is illustrated by means of simulated examples and an experimental study.