Robust topology optimization (RTO) improves the robustness of designs with respect to random sources in real-world structures, yet an accurate sensitivity analysis requires the solution of many systems of equations at each optimization step, leading to a high computational cost. To open up the full potential of RTO under a variety of random sources, this paper presents a momentum-based accelerated mirror descent stochastic approximation (AC-MDSA) approach to efficiently solve RTO problems involving various types of load uncertainties. The proposed framework can perform high-quality design updates with highly noisy stochastic gradients. We reduce the sample size to two (minimum for unbiased variance estimation) and show only two samples are sufficient for evaluating stochastic gradients to obtain robust designs, thus drastically reducing the computational cost. We derive the AC-MDSA update formula based on $\ell_1$-norm with entropy function, which is tailored to the geometry of the feasible domain. To accelerate and stabilize the algorithm, we integrate a momentum-based acceleration scheme, which also alleviates the step size sensitivity. Several 2D and 3D examples with various sizes are presented to demonstrate the effectiveness and efficiency of the proposed AC-MDSA framework to handle RTO involving various types of loading uncertainties.

中文翻译：

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基于动量的加速镜像下降随机逼近，用于随机载荷下的稳健拓扑优化

鲁棒拓扑优化 (RTO) 提高了设计相对于现实世界结构中随机源的鲁棒性，但准确的灵敏度分析需要在每个优化步骤中求解许多方程组，从而导致高计算成本。为了在各种随机源下充分发挥 RTO 的潜力，本文提出了一种基于动量的加速镜像下降随机近似 (AC-MDSA) 方法，以有效解决涉及各种负载不确定性的 RTO 问题。所提出的框架可以执行具有高噪声随机梯度的高质量设计更新。我们将样本大小减少到两个（无偏方差估计的最小值）并表明只有两个样本足以评估随机梯度以获得稳健的设计，从而大大降低了计算成本。我们基于具有熵函数的 $\ell_1$-norm 推导出 AC-MDSA 更新公式，该公式针对可行域的几何形状量身定制。为了加速和稳定算法，我们集成了基于动量的加速方案，这也减轻了步长敏感性。提供了几个不同大小的 2D 和 3D 示例，以证明所提出的 AC-MDSA 框架在处理涉及各种类型负载不确定性的 RTO 方面的有效性和效率。