A mode shape assembly algorithm by using two stage Bayesian Fast Fourier Transform Approach

Abstract

Abstract Operational modal analysis may require identifying global modal shapes by using multiple setup measurements. For this purpose, various algorithms have been developed which make use of the Bayesian approach to estimate the global mode shapes. The main motivation of the available Bayesian approaches is based on the estimation of the optimal global mode shape vector directly from Fast Fourier Transform data or assembling the local mode shapes that are identified in the individual setups by using Gaussian approximation. In this study, the two-stage Bayesian Fast Fourier Transform Approach which is originally applied to single setups is implemented to multiple setup problems for well separated modes. Analytically it is shown that the resulting formulation is the same for the mode shape assembly by using the Gaussian approximation. In addition, the weights of individual setups in the global mode shape vector is analytically calculated which depend on the Hessian matrix for local mode shapes. To validate the proposed methodology, a numerical example that considers setup-to-setup variability of modal signal-noise ratios is presented. For comparison purposes a ten-story shear frame model is experimentally investigated, and the measurements of a benchmark bridge structure are considered in the verification of the current procedure.