Stochastic Sensitivity Analysis for Robust Topology Optimization
Stochastic Sensitivity Analysis for Robust Topology Optimization
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DOI：
10.1007/978-3-319-67988-4_26
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Xuchun Ren;Xiaodong Zhang
中科院分区：
文献类型：
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作者：
Xuchun Ren;Xiaodong Zhang
不确定条件下的拓扑优化使本已具有挑战性的拓扑优化问题变得更加困难。本文提出了一种计算随机输入下高维复杂系统统计矩拓扑灵敏度的新方法。该方法集成了多元随机响应函数的多项式维数分解（PDD）和确定性拓扑导数，能够评估大规模鲁棒拓扑优化（RTO）问题的随机灵敏度。此外，统计矩和它们的拓扑灵敏度都是由单次随机分析同时确定的。当与基于梯度的优化算法协同应用时，该方法具有解决工业规模RTO设计问题的能力。数值算例表明，所提出的新方法具有较高的计算效率。
Topology optimization under uncertainty poses extreme difficulty to the already challenging topology optimization problem. This paper presents a new computational method for calculating topological sensitivities of statistical moments of high-dimensional complex systems subject to random inputs. The proposed method, capable of evaluating stochastic sensitivities for large-scale, robust topology optimization (RTO) problems, integrates a polynomial dimensional decomposition (PDD) of multivariate stochastic response functions and deterministic topology derivatives. In addition, the statistical moments and their topology sensitivities are both determined concurrently from a single stochastic analysis. When applied in collaboration with the gradient based optimization algorithm, the proposed method affords the ability of solving industrial-scale RTO design problems. Numerical examples indicate that the new method developed provides computationally efficient solutions.