Computer-Aided Civil and Infrastructure Engineering 30 (2015) 602–619 A Hybrid Optimization Algorithm with Bayesian Inference for Probabilistic Model Updating Hao Sun ∗ & Raimondo Betti Department of Civil Engineering & Engineering Mechanics, Columbia University, New York, NY, USA Abstract: A hybrid optimization methodology is presented for the probabilistic finite element model up- dating of structural systems. The model updating pro- cess is formulated as an inverse problem, analyzed by Bayesian inference, and solved using a hybrid optimiza- tion algorithm. The proposed hybrid approach is a com- bination of a modified artificial bee colony (MABC) algorithm and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The MABC includes four modifica- tions compared to the standard ABC algorithm, which basically improve the global convergence of ABC in the solution phases of initialization, updating, selection, and rebirth. The BFGS is inserted to improve the finer solu- tion search ability aiming at a higher solution accuracy. In brief, a probabilistic framework based on Bayesian in- ference is first derived so to get a regularized objective function for optimization. Then the proposed MABC- BFGS algorithm is applied to determine the unknown system parameters by minimizing the newly defined objective function. System parameters as well as the pre- diction error covariance are updated iteratively in the optimization process. Posterior distributions of the iden- tified system parameters are determined using a weighted sum of Gaussian distributions. Finally, the effectiveness of the proposed approach is illustrated by the numer- ical data sets of the Phase I IASC-ASCE benchmark model and the experimental data sets of a three-storey frame structure (from the Los Alamos National Labo- ratory (LANL), New Mexico, United States). 1 INTRODUCTION 1.1 Background Structural finite element (FE) model updating, based on input-output or output-only measurements, has been ∗ To whom correspondence should be addressed. Email: hs2595@ columbia.edu. widely used in structural health monitoring (SHM), damage and risk evaluation, structural control, etc. As modeling errors between the theoretical FE model and the real structure (e.g., due to uncertainties caused by distributed material properties, variation of construc- tion process, complicated component joint behavior, complex boundary conditions, etc.) are always present, updating (correcting) the initial/prior FE model, char- acterized by a set of system parameters, is often nec- essary. Because of the pressing need in the industry area, this topic has gained increasing interest in vari- ous disciplines such as civil and mechanical engineer- ing (see Levin and Lieven, 1998; Palmonella et al., 2005; Ching et al., 2006; Cheung and Beck, 2010; Jafarkhani and Masri, 2011; Gul and Catbas, 2011; Yuen, 2010; Zhou et al., 2013; Sun, 2014; Bursi et al., 2014; Yang and Nagarajaiah, 2014a, b). In the process of model updating, one’s objective is to find the optimal system parameters, expressed as either specific values (deterministic) or probability distributions (probabilistic). The difference between these two methods is that deterministic methods aim to obtain a single set of optimal parameters while probabilistic methods estimate statistical distributions of the structural parameters providing a family of possible models (Beck and Au, 2002). The parameters to be identified can be either physical quantities (e.g., structural mass, damping, stiffness, etc.) or modal quan- tities (e.g., natural frequency, mode shape, transfer function, etc.) of a structural system. The data used in the updating operation is usually the time histories of the structural response (e.g., dynamic strains, displace- ments, accelerations, etc.) recorded at various locations and, when possible, the time history of the input exci- tation. There have been many attempts to study system identification for model updating in recent years (e.g., see Koh and See, 1994; Lus ¸ et al., 1999; Franco et al., 2004; Jiang and Adeli, 2005; Lin et al., 2005; Adeli and C  2015 Computer-Aided Civil and Infrastructure Engineering. DOI: 10.1111/mice.12142