A modified robust design optimization approach is presented, which uses the first-order second-moment method to compute the mean value and the standard deviation for arbitrary objective functions. Existing approaches compute the gradient of the variance using the adjoint method, direct differentiation or finite differences, respectively. These approaches either access to the FE-code and/or have high computational cost. In this paper, a new approach for the computation of the gradient of the variance is provided. It can be easily implemented as a non-intrusive method, which behaves similar to finite differences with the cost of only one additional objective evaluation, independent of the number of variables. Here, a step-size has to be chosen carefully and therefore, a procedure to determine a problem-independent step-size is provided. As an alternative, the approach can be implemented as an analytic method with the same cost like the adjoint method, but providing wider applicability (e.g. eigenvalue problems). The provided approach is derived, analyzed and applied to several benchmark examples.

提出了一种改进的稳健设计优化方法，该方法使用一阶二阶矩法计算任意目标函数的均值和标准差。现有方法分别使用伴随方法、直接微分或有限差分来计算方差的梯度。这些方法要么访问 FE 代码和/或具有高计算成本。在本文中，提供了一种计算方差梯度的新方法。它可以很容易地实现为一种非侵入性方法，其行为类似于有限差分，只需一个额外的客观评估成本，与变量的数量无关。这里，必须仔细选择步长，因此，提供了确定与问题无关的步长的过程。作为替代方案，该方法可以作为分析方法来实施，其成本与伴随方法相同，但适用性更广（例如特征值问题）。所提供的方法被派生、分析并应用于几个基准示例。