On-the-Fly Dual Reduction for Optimal Design of Transient Responses in Thermal Energy Storage

该项目的目标是开发一种计算设计方法，使定制的瞬时物理响应能够实现有效的拓扑优化(TO)。许多物理现象本质上是瞬变的，如非定常流动、瞬变换热、弹性动力和与时间相关的粘弹性蠕变响应。TO是一种计算设计方法，可以自动确定量身定制的物理响应的材料分布。虽然过去人们对含时问题进行了研究，但由于缺乏有效处理暂态问题中计算和存储障碍的计算机方法，使得设计优化主要局限于二维空间，从而限制了它的实际应用。本研究旨在通过开发一种新的降阶、基于模型的高效TO方法来解决三维时变问题，以填补这一知识空白，并有针对性地应用于基于潜热的热能储存装置的拓扑设计。这种新的基于模型简化的TO方法产生的设计将与数据驱动的设计协同互补，这些设计将由来自不同学科的本科生研究人员小组进行。该项目的成功完成将导致一系列产品的技术进步，在这些产品中，瞬时物理响应是至关重要的，例如储能应用。该项目将导致基于潜热的热能存储的优化设计，从而提高功率密度和充放电效率。该项目还将为不同学科的本科生拓宽研究机会。它将提高他们对STEM职业的兴趣，并增加他们攻读STEM学科高级学位的可能性。该项目填补了计算机方法方面的一个智力空白，可以在三维环境中实现高效的、依赖于时间的。这将导致一种新的基于降阶模型(ROM)的时间依赖的方法，即通过移动局部基来实现动态对偶约简。在该方法中，构造只读存储器所需的快照和基础在优化过程中被动态更新，而不需要对全阶解进行任何无关的计算。PI不是用全局基矢量来构造线性ROM，而是基于向后和向前的快照策略来构造移动局部基。PI不会对原始平衡方程的近似ROM发展伴随灵敏度，而是发展了一种对偶约化方法，其中原始方程和伴随方程的约化是独立进行的。为了克服时变偏微分方程强非线性带来的潜在降阶挑战，还计划通过深度神经网络应用深度学习方法进行模型降阶。这项研究的完成将导致一种新的基于只读存储器的优化方法，它克服了时间依赖的TO中的计算和存储障碍。此外，该项目将开发一种基于团队的体验式学习方法，以拓宽本科生的研究机会。来自不同学科的本科生团队将进行数据驱动设计研究，并将其应用于储能设备设计。从新的TO方法和数据驱动的设计方法的设计将进行比较，以提高这两种方法在储能设备设计中的效率。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The objective of this project is to develop a computational design method that enables efficient topology optimization (TO) for tailored transient physical responses. Many physical phenomena are transient in nature, such as unsteady flow, transient heat transfer, and elastodynamic and time-dependent viscoelastic creep responses. TO is a computational design method that can automatically determine material distribution for tailored physical responses. Although TO for time-dependent problems has been conducted in the past, lack of computer methods for effectively handling computational and storage obstacles in transient problems has restricted the design optimization to mostly two-dimensional space, thus limiting its practical use. This research aims to fill the knowledge gap by developing a novel reduced-order, model-based efficient TO method for three-dimensional time-dependent problems, with targeted applications in topological design of latent heat-based thermal energy storage devices. The resulting designs from this new model reduction-based TO method will be synergistically complemented with data-driven designs that will be undertaken by groups of undergraduate researchers from diverse disciplines. Successful completion of this project will lead to technological advances in a host of products where transient physical responses are critical, such as energy storage applications. This project will result in optimized designs for latent heat-based thermal energy storage with increased power density and improved charging/discharging efficiency. This project will also broaden research opportunities for undergraduates from diverse disciplines. It will enhance their interest in STEM careers and increase the likelihood for them to pursue advanced degrees in STEM disciplines.This project fills an intellectual gap in computer methods that can enable efficient time-dependent TO in three-dimensional settings. It will lead to a novel reduced-order model (ROM) based approach for time-dependent TO through on-the-fly dual reduction with moving local basis. In this approach, snapshots and basis required for constructing ROMs are dynamically updated during the optimization without any extraneous computing of full-order solutions. Instead of constructing linear ROMs with global basis vectors, the PI plans to construct moving local basis based on backward and forward snapshot strategies. Instead of developing adjoint sensitivity to approximated ROMs for primal equilibrium equations, the PI will develop a dual reduction method where reduction of primal and adjoint equations are conducted independently. In order to overcome potential reduction challenges due to strong non-linearity in time-dependent partial different equations, it is also planned to apply a deep learning approach through deep neural networks for model reduction. Completion of this research will lead to a new ROM-based optimization methodology that overcomes both computational and storage obstacles in time-dependent TO. Further, this project will develop a team-based experiential learning approach to broadening research opportunities for undergraduates. Teams of undergraduates from diverse disciplines will be conducting data-driven design research and applying it in energy storage device design. The designs from the new TO method and the data-driven design method will be compared to improve the efficacy of both methods in energy storage device design.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.