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.

本文提出了一种改进的贝叶斯搭配方法 (IBCM)，用于具有大区间不确定性的结构动力系统的稳态响应分析。区间分析的主要任务是在参数区间内搜索稳态响应的极值，从而得到响应边界。然而，具有大参数不确定性的区间分析问题通常是高度非线性的。因此，为了提高非线性区间分析的效率和准确性，IBCM 通过使用顺序高斯过程代理模型执行双向全局优化过程。在这种方法中，IBCM 构建了基于高斯过程的粗略代理模型。然后提出了一种双向采样策略来指导在参数区间内搜索极值。同时，代理模型也将得到完善。提出了一个衰减的权重函数来平衡高度非线性情况下的探索和开发。重复上述过程直到收敛。根据精细的高斯过程代理模型，可以以较低的计算成本计算稳态响应区间。通过数值例子和工程应用证明了IBCM的可行性和有效性。