An efficient approach for topology optimization under uncertainty is presented. Stochastic reduced order models (SROMs) are leveraged for the modeling and propagation of uncertainties within a robust topology optimization (RTO) formulation. The SROM approach provides an alternative to existing uncertainty quantification methods and yields a substantial improvement in efficiency over a classical Monte Carlo based approach while retaining similar accuracy when representing the uncertainty in system parameters. In particular, random input parameters can be discrete or continuous and specified either analytically (standard distributions) or numerically (dataset samples). Furthermore, multiple random quantities need not be treated as uncorrelated; an SROM can seamlessly model random vectors with arbitrary correlation structure. The nonintrusive nature of the SROM method yields an implementation that can be seen as a drop-in replacement for a simple RTO approach that leverages Monte Carlo simulation and is therefore straightforward to implement in existing topology optimization software. The proposed approach is demonstrated in the context of structural topology optimization with uncertainty in applied loads. Several numerical results are presented, covering a range of uncertainty distributions that illustrate the flexibility afforded by the general SROM method, while highlighting the efficiency and accuracy achieved in uncertainty propagation.

中文翻译：

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基于随机降阶模型的负载不确定性下的稳健拓扑优化

提出了一种在不确定性下进行拓扑优化的有效方法。随机降阶模型 (SROM) 用于在稳健的拓扑优化 (RTO) 公式中对不确定性进行建模和传播。SROM 方法提供了现有不确定性量化方法的替代方法，与基于经典蒙特卡洛的方法相比，效率有了显着提高，同时在表示系统参数的不确定性时保持相似的准确性。特别是，随机输入参数可以是离散的或连续的，并且可以通过分析（标准分布）或数值（数据集样本）指定。此外，不需要将多个随机量视为不相关；SROM 可以无缝模拟具有任意相关结构的随机向量。SROM 方法的非侵入性产生的实现可以被视为简单 RTO 方法的直接替代，该方法利用 Monte Carlo 模拟，因此可以直接在现有拓扑优化软件中实现。所提出的方法在具有应用载荷不确定性的结构拓扑优化的背景下进行了演示。给出了几个数值结果，涵盖了一系列不确定性分布，说明了一般 SROM 方法提供的灵活性，同时突出了在不确定性传播中实现的效率和准确性。