An improved Bayesian collocation method for steady-state response analysis of structural dynamic systems with large interval uncertainties

This paper presents an improved Bayesian collocation method (IBCM) for steady-state response analysis of structural dynamic systems with large interval uncertainties. The main task of interval analysis is to search the extrema of steady-state response within the parametric intervals, so that the response bounds can be obtained. However, interval analysis problems with large parametric uncertainties are usually highly nonlinear. Thus, to improve efficiency and accuracy for nonlinear interval analysis, the IBCM executes a bi-directional global optimization process by using a sequential Gaussian process surrogate model. In this method, IBCM constructs crude surrogate models based on Gaussian process. Then a bi-directional sampling strategy is proposed to guide to search the extrema within the parametric interval. Meanwhile, the surrogate model will also be refined. A decayed weight function is presented to balance exploration and exploitation in highly nonlinear cases. The above process repeats until it converges. The interval of steady-state response can be calculated with low computational cost according to the refined Gaussian process surrogate model. The feasibility and validity of the IBCM are demonstrated by numerical examples and engineering applications.