基于含噪数据的平面固支-自由弹性杆逆设计
Inverse Design of Planar Clamped-Free Elastic Rods from Noisy Data
AI总结：
针对平面悬挂弹性杆的自然形状逆设计问题，构建静力学理论框架，分析噪声等不确定性的影响，结合伴随法提出鲁棒性更强的学习框架，经数值验证有效，可用于软体机器人等领域的软结构逆设计。
摘要：
细长结构（如杆）即便在中等外力（例如重力）作用下也常出现大幅非线性几何变形。这一特性会带来丰富多样的形态变化，使其在工程设计与应用中颇具吸引力，例如软体机器人、海底电缆、装饰绳结等领域。此前的研究已表明，杆的自然形状会显著影响其变形后的几何形态。因此，在制造和设计类杆结构时，应当考虑杆的自然形状。本文聚焦于一个逆问题：我们能否确定悬挂式二维平面杆的自然形状，使其变形后达到期望的目标形状？我们首先基于平面杆静力学平衡构建了一个理论框架，该框架可在给定目标形状的情况下计算平面杆的自然形状。此外，我们分析了不确定性（例如数据中的噪声）对该理论框架准确性的影响。结果揭示了该理论框架在处理逆问题中的不确定性时存在的缺陷，而这一点在以往的研究中常被忽视。为减轻不确定性的影响，我们将平面杆静力学与用于参数灵敏度分析的伴随法相结合，构建了一个学习框架，该框架能够高效探索待设计杆的自然形状，且鲁棒性更强。我们通过数值验证了该框架的准确性与鲁棒性，为软体结构的逆设计（涵盖软体机器人、变形结构动画等多种应用场景）提供了有价值的见解。
英文摘要：
Slender structures, such as rods, often exhibit large nonlinear geometrical deformations even under moderate external forces (e.g., gravity). This characteristic results in a rich variety of morphological changes, making them appealing for engineering design and applications, such as soft robots, submarine cables, decorative knots, and more. Prior studies have demonstrated that the natural shape of a rod significantly influences its deformed geometry. Consequently, the natural shape of the rod should be considered when manufacturing and designing rod-like structures. Here, we focus on an inverse problem: can we determine the natural shape of a suspended 2D planar rod so that it deforms into a desired target shape? We begin by formulating a theoretical framework based on the statics of planar rod equilibrium that can compute the natural shape of a planar rod given its target shape. Furthermore, we analyze the impact of uncertainties (e.g., noise in the data) on the accuracy of the theoretical framework. The results reveal the shortcomings of the theoretical framework in handling uncertainties in the inverse problem, a fact often overlooked in previous works. To mitigate the influence of the uncertainties, we combine the statics of the planar rod with the adjoint method for parameter sensitivity analysis, constructing a learning framework that can efficiently explore the natural shape of the designed rod with enhanced robustness. This framework is validated numerically for its accuracy and robustness, offering valuable insights into the inverse design of soft structures for various applications, including soft robotics and animation of morphing structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
