This paper implements a novel integration of the polynomial dimensional decomposition (PDD), topology derivative, and level-set method for robust topology optimization subject to a large number of random inputs. With this method, the influence of a large number of random inputs can be easily captured in an accurate manner. In addition, the stochastic moments and their sensitivities can be obtained from analytical expressions based on the PDD approximation of response functions and the deterministic topology derivative. Only a single stochastic analysis is required for evaluating the moments and their sensitivities in each iteration. The topology is described by the level-set function and its evolution is driven by solving the reaction-diffusion equation of the level-set function. An augmented Lagrange penalty formulation dovetails the stochastic topology derivatives of objective and constraints into the reaction term in the reaction-diffusion equation, which generates a new topology during the iteration process. The practical examples illustrate that the proposed method can render meaningful optimal designs for structures subject to several or a large number of random inputs.

本文实现了多项式维数分解 (PDD)、拓扑导数和水平集方法的新颖集成，用于在大量随机输入下进行稳健的拓扑优化。使用这种方法，可以轻松准确地捕获大量随机输入的影响。此外，随机矩及其灵敏度可以从基于响应函数的 PDD 近似和确定性拓扑导数的解析表达式中获得。只需要一次随机分析来评估每次迭代中的矩及其敏感性。拓扑由水平集函数描述，其演化由求解水平集函数的反应扩散方程驱动。增广拉格朗日惩罚公式将目标和约束的随机拓扑导数与反应扩散方程中的反应项相吻合，从而在迭代过程中生成新的拓扑。实际例子表明，所提出的方法可以为受多个或大量随机输入的结构提供有意义的优化设计。