Structural reliability analysis via dimension reduction, adaptive sampling, and Monte Carlo simulation

Seismic Fragility Analysis of Structures Based on Adaptive Gaussian Process Regression Metamodel

“…GPR is a regression method that uses the Gaussian process model to fit the data. GPR can not only provide the approximation but also predict the error of the approximation, which is conducive to the realization of AL sampling [31].…”

“…As the training set is updated by AL sampling, only a small number of initial points are required. For example, the number of initial samples can be equal to the dimensions of the metamodel input vector [31].…”

An uncertainty propagation analysis method considering multimodal random distribution

“…播方法的研究已经取得了许多重要的成果, 大体上可 以分为四类: 抽样法、 最可能失效点法、 数值积分法和 代理模型法. 抽样法包括直接蒙特卡洛法 [9] 和重要抽 样法 [10] 等, 这类方法虽然容易实施, 但是计算精度取 决于样本的数量, 需要大量的样本以保证较高的精度, 因此往往难以适用于复杂工程问题, 例如 Fan 等 [11] 提 出了一种改进的冷负荷预测可靠性方法, 将输入变量 输入预测模型之前, 通过蒙特卡洛法和随机处理法离 线标定输入变量, 得到了较好的效果. 最大可能失效 点法包括一阶可靠度法 [12] 和二阶可靠度法 [13] 等, 这类 获取解, 因此首先需要将非正态变量转变成标准正态 变量来定位最大可能失效点, 例如袁 [14] 等提出了一种 融合 Kriging 与改进一次二阶矩方法的分析方法, 通 过解决隐式极限状态函数的求导来提高结构可靠性 分析的效率.…”

Active learning with generalized sliced inverse regression for high-dimensional reliability analysis

“…Machine learning and regression methods have recently been used in high dimensional reliability analysis. Several studies [29][30][31][32][33][34] combine meta-modeling and dimension reduction techniques. Two steps are typically involved.…”