基于降维可视化技术的结构可靠性灵敏度分析

Analysis of Structural Reliability Sensitivity Based on Dimensionality Reduction and Visualization Technique

针对多维隐式结构可靠性问题,应用降维可视化技术进行可靠性灵敏度分析。基于i HLRF法求解设计点,根据模型计算精度确定有限差分步长。用一条直线将平面分为安全域和失效域两部分,通过计算直线初始位置附近数据点对应的响应量,来调整并确定直线的最终位置,根据直线上方数据点提供的信息计算可靠性灵敏度。提出的可靠性灵敏度分析方法的准确性不受维度以及非线性的影响,且效率较高。最后计算了两个结构系统的可靠度及各个变量的可靠性灵敏度,为结构设计提供了理论依据。算例表明了文中所给出的计算公式的正确性和有效性。

For the implicit reliability problem with multiple dimensions,the reliability sensitivity of structure is analyzed by applying the dimensionality reduction and visualization technique. The design point is found based on i HLRF method,and the step size of finite difference is determined according to the modeling computational precision. The plane is divided into two parts of safe domain and failure domain by a straight line,and the final position of the straight line is determined by calculating the responses corresponding to several data points nearby its initial position. The dimensionality and nonlinearity do not affect the accuracy of the proposed method,which also has relatively high efficiency. Finally,the reliabilities of two structural systems and the reliability sensitivities of various influencing factors are calculated,which provides a theoretical basis for designing the structural systems. The examples show that these theories and formulas are rational and efficient.