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

本项目的目标是开发一种计算设计方法，使有效的拓扑优化（TO）定制的瞬态物理响应。许多物理现象在本质上是瞬态的，例如非稳态流动、瞬态热传递以及弹性动力学和时间相关的粘弹性蠕变响应。TO是一种计算设计方法，可以自动确定定制物理响应的材料分布。虽然在过去已经进行了时间相关问题的TO，缺乏有效处理瞬态问题中的计算和存储障碍的计算机方法，限制了设计优化主要是二维空间，从而限制了其实际应用。本研究的目的是通过开发一种新的降阶，基于模型的高效的三维时间依赖性问题的TO方法，有针对性地应用于基于潜热的热能存储设备的拓扑设计，以填补知识空白。这种新的基于模型简化的TO方法所产生的设计将与数据驱动的设计协同补充，这些设计将由来自不同学科的本科研究人员进行。该项目的成功完成将导致瞬态物理响应至关重要的许多产品的技术进步，例如储能应用。该项目将优化基于潜热的热能储存设计，提高功率密度和充电/放电效率。该项目还将为来自不同学科的本科生拓宽研究机会。这将提高他们对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的知识空白，可以在三维环境中实现有效的时间依赖性TO。这将导致一种新的降阶模型（ROM）为基础的方法，通过在飞行中的双重减少与移动的本地基础的时间相关的TO。在这种方法中，快照和构建ROM所需的基础在优化过程中动态更新，而无需任何额外的计算全阶解决方案。PI计划基于向后和向前快照策略构建移动局部基，而不是使用全局基向量构建线性ROM。PI将开发一种双重归约方法，独立进行原始和伴随方程的归约，而不是开发对原始平衡方程近似ROM的伴随灵敏度。为了克服由于时间相关偏微分方程的强非线性而带来的潜在简化挑战，还计划通过深度神经网络应用深度学习方法进行模型简化。这项研究的完成将导致一个新的ROM为基础的优化方法，克服了计算和存储的时间依赖TO的障碍。此外，该项目将开发一种以团队为基础的体验式学习方法，以扩大本科生的研究机会。来自不同学科的本科生团队将进行数据驱动的设计研究，并将其应用于储能设备设计。该奖项反映了NSF的法定使命，通过使用基金会的知识价值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.