论文标题
基于动量的加速镜下降随机近似在随机载荷下优化可靠的拓扑结构
Momentum-based Accelerated Mirror Descent Stochastic Approximation for Robust Topology Optimization under Stochastic Loads
论文作者
论文摘要
稳健的拓扑优化（RTO）改善了现实世界中随机来源的鲁棒性，但是准确的灵敏度分析需要在每个优化步骤中对许多方程式进行解决方案，从而导致高计算成本。为了在各种随机来源下打开RTO的全部潜力，本文提出了一种基于动量的加速镜下降随机近似（AC-MDSA）方法，以有效解决涉及各种类型的负载不确定性的RTO问题。提出的框架可以使用高度嘈杂的随机梯度执行高质量的设计更新。我们将样本量减少到两个（无偏方差估计的最小值），并且仅显示两个样本足以评估随机梯度以获得强大的设计，从而大大降低了计算成本。我们基于$ \ ell_1 $ norm的熵功能来得出AC-MDSA更新公式，该公式是根据可行域的几何形状量身定制的。为了加速和稳定算法，我们整合了基于动量的加速度方案，这也减轻了步骤尺寸的灵敏度。提出了几个具有各种尺寸的2D和3D示例，以证明所提出的AC-MDSA框架的有效性和效率处理涉及各种载荷不确定性的RTO。
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.
