可靠性全局灵敏度指标的空间分割高效方法

发布时间：2018-06-08 01:02

  本文选题：可靠性全局灵敏度指标 + 连续无重叠区间上的全方差公式　； 参考：《北京航空航天大学学报》2017年06期

【摘要】：可靠性全局灵敏度指标能够有效地分析输入变量的不确定性对结构系统失效概率的影响程度,为提高该灵敏度指标求解数字模拟法的效率,提出了一种基于密度权重及连续无重叠区间全方差公式的空间分割高效方法。所提方法通过连续无重叠区间上的全方差公式来加快该指标计算的收敛速度,利用密度权重法在输入变量可能的取值区间内进行均匀抽样,并以均匀样本点的联合概率密度函数的权重来保证计算的等价性,这使得所构造的方法不需要寻找失效域的设计点,因此其可以有效解决非线性程度较高难以找到设计点及多设计点的问题。除此之外,应用空间分割技术,使得本文所提方法仅需重复利用一组样本点,就可同时得到各个输入变量的可靠性全局灵敏度指标,消除了计算量与输入变量维数的相关性,大大地提高了样本的利用率和计算效率。验证算例的计算结果,说明了本文方法对计算功能函数非线性程度较高及多设计点问题的高效性。
[Abstract]:The reliability global sensitivity index can effectively analyze the influence of the uncertainty of the input variables on the failure probability of the structural system. In order to improve the efficiency of the sensitivity index to solve the digital analog method, An efficient spatial segmentation method based on density weight and continuous nonoverlapping interval total variance formula is proposed. The proposed method accelerates the convergence rate of the index calculation by the formula of total variance on the continuous non-overlapping interval. The density weight method is used to carry out uniform sampling in the range of the possible values of the input variables. The weight of the joint probability density function of the uniform sample points is used to ensure the equivalence of the calculation, which makes it unnecessary to find the design point of the failure region. Therefore, it can effectively solve the problem that it is difficult to find design points and multiple design points with high degree of nonlinearity. In addition, by using spatial segmentation technique, the reliability global sensitivity index of each input variable can be obtained by using only one set of sample points repeatedly, which eliminates the correlation between the calculation amount and the dimension of input variable. The efficiency of sample utilization and calculation is greatly improved. The results of the examples show that the proposed method is highly nonlinear and efficient for the problem of multiple design points.
【作者单位】： 西北工业大学航空学院;中国飞行试验研究院飞机所;
【基金】：国家自然科学基金(51475370) 中央高校基本科研业务费专项资金(3102015BJ(Ⅱ)CG009) 西北工业大学博士论文创新基金(CX201708)~~
【分类号】：TB114.3
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本文编号：1993653