基于数据降维理论的随机结构高维抗震可靠度研究

The problem of calculating the seismic reliability of structures with high-dimensional random variables is a problem to be solved imperatively, especially when the randomness of system parameters and external excitation are both considered. This program aims at solving the “curse of dimensionality” problem in high-dimensional reliability analysis. By combining the supervised dimension reduction theory and surrogate model based probability density evolution method, the reliability analysis of structures with high-dimensional random variables is studied. Firstly, by combining the high-dimensional sample selection method based on point set discrepancy theory and the active subspace analysis method, a supervised data dimension reduction method is proposed. Then, by reducing the dimension of the original high-dimensional data to establish a low-dimensional surrogate model in the active subspace and introducing the equivalent extreme value method in probability density evolution method, a new structural seismic reliability analysis method is developed. The proposed method can effectively discover the approximate low-dimensional structure hidden in the high-dimensional random function. Next, the probability density function of the structural response and the corresponding structural reliability can be calculated by employing the dimension reduced surrogate model and probability density evolution method, which provides the theoretical and engineering experience for the seismic reliability analysis of practical engineering structures.

当同时考虑系统参数随机性和外部激励随机性时，如何准确高效地计算含高维随机变量的结构抗震可靠度是目前需要解决的重要问题之一。本研究拟针对高维随机函数可靠度计算的“维数灾难”问题，结合有监督数据降维理论和基于响应面模型的概率密度演化方法，研究含高维随机变量的结构抗震可靠度计算问题：首先，通过结合基于点集偏差理论的高维点集选取方法和有效子空间分解，提出了一类有监督的数据降维方法；随后，通过对高维原始数据降维并在有效子空间中建立低维的响应面模型，结合概率密度演化理论的等价极值方法，发展适用于含高维随机变量的结构抗震可靠度计算方法。采用所建立的基于数据降维理论的高维可靠度计算方法，能够有效挖掘高维随机函数中潜藏的低维等效结构，进而结合降维后的响应面模型和概率密度演化方法计算含高维随机变量的结构响应的概率密度函数，为结构的抗震可靠性评估提供理论基础和技术依据。

当同时考虑系统参数随机性和外部激励随机性时，如何准确高效地计算含高维随机变量的.结构抗震可靠度是目前需要解决的重要问题之一。本研究拟针对高维随机函数可靠度计算的“.维数灾难”问题，结合有监督数据降维理论和基于响应面模型的概率密度演化方法，研究含高.维随机变量的结构抗震可靠度计算问题：首先，通过结合基于点集偏差理论的高维点集选取方.法和有效子空间分解，提出了一类有监督的数据降维方法；随后，通过对高维原始数据降维并.在有效子空间中建立低维的响应面模型，结合概率密度演化理论的等价极值方法，发展适用于.含高维随机变量的结构抗震可靠度计算方法。采用所建立的基于数据降维理论的高维可靠度计.算方法，能够有效挖掘高维随机函数中潜藏的低维等效结构，进而结合降维后的响应面模型和.概率密度演化方法计算含高维随机变量的结构响应的概率密度函数，为结构的抗震可靠性评估.提供理论基础和技术依据.