用于高性能设计优化的可微分结构分析框架

Keith J. Lee, Yijiang Huang, Caitlin T. Mueller
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引用次数: 0

摘要

长期以来,基于梯度的快速结构优化一直局限于高度受限的问题子集,即基于密度的符合性最小化问题,对于这些问题,梯度可以通过分析得出。对于其他目标函数、约束条件和设计参数化问题,梯度的计算仍然无法实现,需要使用无导数算法,而这种算法的规模与问题规模的关系不大。这限制了优化在抽象和学术问题上的应用,也限制了这些具有潜在影响力的方法在实践中的应用。在本文中,我们通过一个专为一般结构优化设计的可微分分析框架,弥合了计算效率与问题表述自由度之间的差距。为此,我们利用自动微分(AutomaticDifferentiation,AD)来管理结构分析程序的复杂计算图,并沿此图为性能关键函数实施特定的推导规则。本文全面概述了针对任意结构设计目标的梯度计算,指出了其实际应用的障碍,并推导出解决这些瓶颈的关键中间衍生操作。然后,我们用一系列复杂度不断增加的结构设计问题对我们的框架进行了测试:两个高度受限的最小体积问题、一个多阶段形状和截面设计问题以及一个体现碳最小化问题。我们将我们的框架与其他常见的优化方法进行了比较,结果表明我们的方法在速度、稳定性和解决方案质量方面都优于其他方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A differentiable structural analysis framework for high-performance design optimization
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions, constraints, and design parameterizations, computing gradients has remained inaccessible, requiring the use of derivative-free algorithms that scale poorly with problem size. This has restricted the applicability of optimization to abstracted and academic problems, and has limited the uptake of these potentially impactful methods in practice. In this paper, we bridge the gap between computational efficiency and the freedom of problem formulation through a differentiable analysis framework designed for general structural optimization. We achieve this through leveraging Automatic Differentiation (AD) to manage the complex computational graph of structural analysis programs, and implementing specific derivation rules for performance critical functions along this graph. This paper provides a complete overview of gradient computation for arbitrary structural design objectives, identifies the barriers to their practical use, and derives key intermediate derivative operations that resolves these bottlenecks. Our framework is then tested against a series of structural design problems of increasing complexity: two highly constrained minimum volume problem, a multi-stage shape and section design problem, and an embodied carbon minimization problem. We benchmark our framework against other common optimization approaches, and show that our method outperforms others in terms of speed, stability, and solution quality.
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