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

Abstract

In this study, we present two Bayesian frequency-domain methods for identifying the complex modal parameters of a linear dynamic system from ambient vibration data. The identification of complex modal parameters is applicable to both classically and non-classically damped systems, in contrast to the identification of real modal parameters, which is restricted to classically damped systems. This study investigates the statistical properties of the response spectral density estimator and the response Discrete Fourier Transform (DFT) to formulate Bayesian probabilistic approaches for modal identification. These approaches involve finding the optimal modal parameters and their associated uncertainties by calculating the joint posterior Probability Density Function (PDF) of the modal parameters for given measured data and modeling assumptions. Identification strategies for both closely-spaced and well-separated modes are provided and the respective mathematical analyses are presented. Derivation of analytical expressions for computing the gradient and Hessian of the objective function is included. The validation of the developed approach is done through simulated examples and an experimental study.