Optimization Or Bayesian Strategy? Performance of the Bhattacharyya Distance in Different Algorithms of Stochastic Model Updating

The Bhattacharyya distance has been developed as a comprehensive uncertainty quantification metric by capturing multiple uncertainty sources from both numerical predictions and experimental measurements. This work pursues a further investigation of the performance of the Bhattacharyya distance in different methodologies for stochastic model updating. The first procedure is the Bayesian model updating where the Bhattacharyya distance is utilized to define an approximate likelihood function and the transitional Markov chain Monte Carlo algorithm is employed to obtain the posterior distribution of the parameters. In the second model updating procedure, the Bhattacharyya distance is utilized to construct the objective function of an optimization problem. The objective function is defined as the Bhattacharyya distance between the samples of numerical prediction and the samples of the target data. The comparison study is performed on a four degree-of-freedoms mass-spring system. A challenging task is raised in this example by assigning different distributions to the parameters with imprecise distribution coefficients. This requires the stochastic updating procedure to calibrate not the parameters themselves, but their distribution properties. The performance of the Bhattacharyya distance in both Bayesian updating and optimization-based updating procedures are presented and compared. The results demonstrate the Bhattacharyya distance as a comprehensive and universal uncertainty quantification metric in stochastic model updating.