A two-stage model updating using complex modal data

The process of Finite Element (FE) modelling is often associated with uncertainties which necessitates its updating using measured data. Updating dynamical model has a considerable importance in Structural Health Monitoring (SHM), estimating the structural responses, and structural control applications. Among the various presently available approaches for performing model updating, the probabilistic updating approach such as Bayesian model updating has gained a great deal of attention in the last two decades. It can aggregate all the types of uncertainties, e.g., prediction errors, modelling errors, measurement errors, etc., and deal with them as epistemic uncertainties about the system. This paper introduces a two-stage Bayesian model updating procedure of FE dynamical model. The targeted systems encounter a non-classical damping yielding complex modes of vibration. The original FE model is reduced using the method of dynamic condensation, where the reduced FE model is related to the observed Degrees-of-Freedoms (DOFs). Due to the usual availability of a limited number of sensors during real-world applications, modal data used to update the FE model is obtained from multiple setups. Finally, to simulate samples that approximate the posterior Probability Density Function (PDF), a new MWG sampling algorithm is used and compared with Transitional Markov Chain Monte Carlo (TMCMC) algorithm. The proposed approach has been applied to a numerical dynamical system with synthetic modal data acquired from multiple setups. Results revealed that the proposed approach could update the system's uncertain parameters efficiently with a visible reduction in the uncertainty in both undamaged and damaged system.