Efficient Bayesian model updating for dynamic systems

Bayesian updating has been a successful tool for model calibration in uncertainty analysis, especially in reliability analysis. However, Bayesian updating of dynamic systems with high-dimensional output remains challenging work due to the heavy computational burden associated with evaluating a high-dimensional likelihood function. In this case, even the efficient surrogate model methods can fall short of their expected potential. To solve this problem, this paper develops a novel Bayesian updating framework for dynamic systems based on principal component analysis (PCA), which can significantly reduce the output dimension and overcome the "curse of dimension". In the proposed framework, a new likelihood function is constructed based on the lowdimensional output principal components (PCs), and it is analytically proved that the new likelihood function can provide the equivalent likelihood measures to the original one. In this way, any common Bayesian updating method can be applied in the low dimensional PC space by using the new likelihood function. To further improve the efficiency, an efficient Bayesian updating algorithm is proposed in the PCA-based framework, which adopts adaptive Bayesian updating with structural reliability methods (aBUS) and the Kriging model. Finally, four examples are investigated to test the validity of the proposed method.