基于高斯过程模型的桥梁结构动力不确定性研究的解析方法

Structural parameter uncertainty inherent in real-world bridges will inevitably lead to the uncertainty in structural dynamic behavior of bridges. Uncertainty quantification analysis and sensitivity analysis are the key issues related to study on uncertainty in structural dynamics of bridges. Uncertainty quantification analysis refers to the quantification of the uncertainty in structural dynamics propagated from uncertain parameters, while uncertainty sensitivity analysis refers to evaluating the contributions of individual uncertain parameters to the overall uncertainty in structural dynamics. Due to the large-scale, complex feature of bridges, the traditional approaches that carry out the task of study on uncertainty in structural dynamics of bridges directly based on the computationally-expensive finite element model (FEM) will not be impractical because of the resulting unbearable high computational cost. This project uses analytical method to perform study on uncertainty in structural dynamics of bridges based on Gaussian process model (GPM). The Sobol sequence-based space-filling design of experiment (DOE) is adopted to construct GPM to replace the time-consuming FEM of bridge structures; Gaussian quadrature technique is applied to derive the closed-form expressions of the analytical method for uncertainty quantification analysis of uncertainty in structural dynamics; global sensitivity analysis (GSA) is utilized for uncertainty analysis of sensitivity in structural dynamics and analytical GSA method is derived. The project aims at efficiently and effectively conducting uncertainty analysis and sensitivity analysis in structural dynamics of bridges, thus having a significant theoretical value and an engineering application value as well.

实际桥梁结构的参数存在不确定性，参数不确定性会导致桥梁结构动力行为的不确定性。不确定性量化分析和灵敏度分析是桥梁结构动力不确定性研究的关键问题，前者是量化参数不确定性对结构动力特性的影响大小，后者是定量各单个不确定参数对结构动力特性的影响的贡献大小。桥梁结构通常结构形式复杂、尺寸大，直接基于有限元模型的常规方法用于桥梁结构动力不确定性研究因计算成本过高而难以实际应用。项目基于高斯过程替代模型，采用解析方法研究桥梁结构动力不确定性量化分析和灵敏度分析。Sobol序列空间充满采样方法用来建立桥梁结构有限元模型的高斯过程模型；高斯积分法用来推导基于高斯过程模型的结构动力不确定性量化分析解析方法的闭合解；全局灵敏度分析用来结构动力不确定性灵敏度分析，推导基于高斯过程模型的全局灵敏度分析解析方法的闭合解。项目旨在快速有效地完成桥梁结构动力不确定性量化分析和灵敏度分析，研究具有理论意义和工程实用价值。

实际桥梁结构的参数不可避免存在不确定性，参数不确定性会导致桥梁结构动力特性不确定性。准确量化结构参数不确定性传递给动力特性的不确定性有利于精确刻画桥梁结构的动力行为，研究具有理论意义和工程实用价值。桥梁结构通常结构形式复杂、尺寸大，直接基于有限元模型的常规方法用于桥梁结构动力特性不确定性量化因计算成本过高而难以实际应用。本项目采用高斯过程模型来取代耗时的有限元模型，然后在替代模型框架下进行结构动力不确定性分析。本项目解析而又高效地完成了结构动力不确定性量化和全局敏感性分析，前者是量化参数不确定性对结构动力特性的影响大小，后者是定量各单个不确定参数对结构动力特性的影响的贡献大小。本项目为解决大型桥梁结构动力不确定性量化和全局敏感性分析问题提供一种高效的解析方法。