Quantification of Aleatory Uncertainty in Blast Wave Problem
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摘要: 复杂工程建模与模拟中始终存在不确定度，分析与辨识不确定度的来源及量化不确定度对建模与模拟可信度评估具有重要意义。为此，给出了建模与模拟中误差与不确定度的概念以及不确定度量化的过程，并以爆炸波问题为例说明量化偶然不确定度的过程，得到了爆炸波问题的期望和标准差以及激波位置的概率密度函数，验证了非嵌入多项式混沌方法在复杂非线性系统不确定度量化中的有效性。Abstract: As uncertainty always exists in the modeling and simulation of complex engineering problems, the identification and analysis of its source and the quantification of its degrees play an important role in assessing the credibility of the modeling and simulation results.In this paper, the concept of uncertainty as well as uncertainty quantification process was presented in the modeling and simulation, with the blast wave problem used as a typical example to illustrate the detailed process for the quantification of the aleatory uncertainty.The expectations and variances of density, pressure, velocity and internal energy were calculated and, moreover, the probability density function of the shock wave position was obtained using the Monte-Carlo and the non-intrusive polynomial chaos (NIPC).The results were consistent with each other, which verified that the NIPC method is an efficient approach in the uncertainty quantification of a complex nonlinear system.
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图 3 1 000组抽样下爆炸波问题的计算结果
Figure 3. Results of blast wave problem solved with 1 000 times sampling by NIPC method
图 4 T=0.10时刻爆炸波问题中密度、压强、速度和能量的期望与标准差
Figure 4. Expectations and standard variances of density, pressure, velocity and internal energyin blast wave problem at T=0.10
图 5 激波位置的概率密度分布函数
Figure 5. Probability density funtion of shockwave position by NIPC at T=0.10
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