A New Bayesian Method for Dynamic System Identification Using FFT Data

Dynamic system identification is an important field of research focused on identifying accurate system models of structures for predicting dynamic behaviors. This field finds widespread application in downstream research such as response prediction, structural failure and reliability analysis, and related areas of structural health monitoring. Conventional methods update structural finite element models (FEMs) using experimental modal parameters, because excitations are difficult to measure for full-scale structures and measured responses cannot be used as data in model updating. One challenge of conventional methods is thus that additional time is required for modal analysis, and by packing response data into modal parameters, original information in response data may be lost and cannot be used for model updating. Concerning this issue, this paper develops a dynamical system identification method to directly update an FEM using experimental fast Fourier transform (FFT) data following a Bayesian approach. The modeling of FFTs combing FEM and an efficient algorithm for processing the large amount of FFTs are not available for conventional methods. In this paper, the posterior probability density function (PDF) of the model parameters is derived assuming that FFTs at different frequency. instances follow independent and identically distributed complex Gaussian distributions under the long-data condition. One contribution of this work is that the sub-structure FEM analysis is integrated into the formulation of the posterior PDF to make the direct use of FFT data possible, and increase computational efficiency. The most probable values (MPVs) of the model parameters are obtained by maximizing the posterior PDF. By making use of the special mathematical structure of the posterior PDF, a novel algorithm that iterates among the model parameters is developed to efficiently search parameter space for the maximization. A numerical case has demonstrated that the proposed method can accurately identify the FEM of the target structure together with the unmeasured excitation parameters and damping ratios.