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摘要:
在同时包含随机不确定性和模糊不确定性结构系统中，为了分别度量随机输入变量和模糊输入变量对输出响应的统计特征的影响，提出了随机输入变量和模糊输入变量的全局灵敏度新指标。在模糊变量可能性矩定义的基础上，分析了混合不确定性下输出响应的特征。从输出响应可能性矩的角度出发，以输出响应的可能性期望为例，通过比较输出响应有条件和无条件可能性期望的概率密度函数（PDF）的平均差异，分别建立了随机输入变量和模糊输入变量关于输出响应的可能性期望的灵敏度指标。讨论了所提指标的性质，并采用Kriging代理模型来提高混合不确定性全局灵敏度指标的计算效率。最后通过算例验证了本文所提方法的准确性和高效性。
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关键词:
- 模糊变量 /
- 随机变量 /
- 灵敏度分析 /
- 可能性矩 /
- Kriging代理模型
Abstract:For the structures with fuzzy uncertainty and random uncertainty simultaneously, to measure the influence of fuzzy and random input variables on the statistical characteristic of output response, a new global sensitivity index is proposed. Based on the definition of possibilistic moments of the fuzzy variable, the characteristic of the output response under mixed uncertainty is analyzed. With respect to the possibilistic moments of the output response, the possibilistic expectation of output response is taken as an example, and the average difference between the unconditional probability density function (PDF) and the conditional PDF of the model output possibilistic expectation is used to establish the global sensitivity indices for both the fuzzy input and the random input. The properties of the proposed global sensitivity indices are discussed, and the Kriging surrogate model is applied to solving the proposed index efficiently. Finally, some examples are used to verify the rationality and effectiveness of the proposed method.
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表 1 算例1各输入变量的灵敏度指标值
Table 1. Sensitivity index values of input variables in Example 1
随机变量 灵敏度指标值 一般方法 Kriging法 x1 0.211 3 0.211 3 x2 0.408 7 0.408 7 x3 0.048 2 0.048 2 x4 0.094 7 0.094 8 
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表 2 算例2各模糊变量参数值
Table 2. Parameter values of fuzzy variables in Example 2
随机变量 模糊变量 c σ x1 C1 0.825 0.070 x2 C2 0.825 0.070 x3 C3 0.900 0.050
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表 3 算例2各输入变量的灵敏度指标值
Table 3. Sensitivity index values of input variables in Example 2
参数 灵敏度指标值 一般方法 Kriging法 C1 0.004 9 0.004 9 C2 0.004 9 0.004 9 C3 0.004 3 0.004 3 Y 0.764 2 0.764 2 W 0.053 7 0.053 7
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表 4 屋架结构随机变量的数值特征
Table 4. Numerical characteristics of random variables in roof truss structure
随机变量 分布类型 均值 标准差 q/(N·m-1) 正态 20 000 1 400 l/m 正态 12 0.12 As/m2 正态 9.82×10-4 5.982×10-5 Ac/ m2 正态 0.04 0.004 8
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表 5 算例3各输入变量基于输出可能性期望的灵敏度指标值
Table 5. Sensitivity index values of input variables based on output possibilistic expectation in Example 3
参数 灵敏度指标值 一般方法 Kriging法 q 0.339 4 0.339 1 l 0.673 9 0.673 6 Ac 0.144 4 0.144 3 Ec 0.012 0 0.011 9 As 0.158 5 0.158 4 Es 0.029 1 0.029 0
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