In this work, metamodel-based robust optimization is performed using measured scatter of noise variables. Principal component analysis is used to describe the input noise using linearly uncorrelated principal components. Some of these principal components follow a normal probability distribution, others however deviate from a normal probability distribution. In that case, for more accurate description of material scatter, a multimodal distribution is used. An analytical method is implemented to propagate the noise distribution via metamodel and to calculate the statistics of the response accurately and efficiently. The robust optimization criterion as well as the constraints evaluation are adjusted to properly deal with multimodal response. Two problems are presented to show the effectiveness of the proposed approach and to validate the method. A basketball free throw in windy weather condition and forming of B-pillar component are presented. The significance of accounting for non-normal distribution of input variables using multimodal distributions is investigated. Moreover, analytical calculation of response statistics, and adjustment of the robust optimization problem are presented and discussed.

在这项工作中，基于元模型的稳健优化是使用噪声变量的测量散射来执行的。主成分分析用于使用线性不相关的主成分来描述输入噪声。这些主成分中的一些遵循正态概率分布，而其他主成分则偏离正态概率分布。在这种情况下，为了更准确地描述材料散射，使用了多峰分布。实现了一种分析方法，通过元模型传播噪声分布，并准确有效地计算响应的统计数据。调整鲁棒优化标准以及约束评估以正确处理多模态响应。提出了两个问题来证明所提出方法的有效性并验证该方法。介绍了大风天气条件下的篮球罚球和B柱组件的形成。研究了使用多峰分布解释输入变量的非正态分布的重要性。此外，还介绍并讨论了响应统计的解析计算和鲁棒优化问题的调整。