A scalable framework for multi-objective PDE-constrained design of building insulation under uncertainty
A scalable framework for multi-objective PDE-constrained design of building insulation under uncertainty
复制标题
不确定性下建筑保温多目标 PDE 约束设计的可扩展框架
DOI：
10.1016/j.cma.2023.116628
复制
发表时间：
2024
影响因子：
7.2
通讯作者：
Faghihi, Danial
中科院分区：
文献类型：
--
作者：
Tan, Jingye;Faghihi, Danial
本文介绍了一个可扩展的计算框架下的高维不确定性的优化设计，应用于隔热部件。多孔材料的热、力学行为由偏微分方程（PDE）控制的连续多相模型描述，材料孔隙率是一个不确定的空间相关场。有限元离散化后，这些因素导致一个高维的偏微分方程约束优化问题。该框架采用了一个风险厌恶的配方，占的均值和方差的设计目标。它结合了两个正则化技术，100-范数和相场泛函，使用连续的数值方案，以促进空间稀疏的设计参数。为了确保效率，该框架利用二阶泰勒近似的均值和方差，并利用低秩结构的预处理海森的设计目标。这导致计算成本由预处理Hessian的秩确定，与不确定参数的数量无关。的准确性，可扩展性的参数尺寸，和稀疏促进能力的框架进行评估，通过涉及各种建筑保温组件的数值例子。
This paper introduces a scalable computational framework for optimal design under high-dimensional uncertainty, with application to thermal insulation components. The thermal and mechanical behaviors are described by continuum multi-phase models of porous materials governed by partial differential equations (PDEs), and the design parameter, material porosity, is an uncertain and spatially correlated field. After finite element discretization, these factors lead to a high-dimensional PDE-constrained optimization problem. The framework employs a risk-averse formulation that accounts for both the mean and variance of the design objectives. It incorporates two regularization techniques, the ℓ 0-norm and phase field functionals, implemented using continuation numerical schemes to promote spatial sparsity in the design parameters. To ensure efficiency, the framework utilizes a second-order Taylor approximation for the mean and variance and exploits the low-rank structure of the preconditioned Hessian of the design objective. This results in computational costs that are determined by the rank of preconditioned Hessian, remaining independent of the number of uncertain parameters. The accuracy, scalability with respect to the parameter dimension, and sparsity-promoting abilities of the framework are assessed through numerical examples involving various building insulation components.
登录
查看更多内容
影响因子：
4.1
作者：
J. Tan;Pedram Maleki;Lu An;M. Di Luigi;Umberto Villa;Chi Zhou;Shenqiang Ren;D. Faghihi
通讯作者：
J. Tan;Pedram Maleki;Lu An;M. Di Luigi;Umberto Villa;Chi Zhou;Shenqiang Ren;D. Faghihi
使用任意响应函数的一阶二阶矩方法进行鲁棒拓扑优化的通用方法
影响因子：
3.9
作者：
M. Kranz;J. K. Lüdeker;B. Kriegesmann
通讯作者：
B. Kriegesmann
用于热管理的柔性渗滤纤维隔热复合膜
影响因子：
5
作者：
Lu An;M. Di Luigi;J. Tan;D. Faghihi;Shenqiang Ren
通讯作者：
Shenqiang Ren
DOI：
10.1016/j.cma.2004.04.004
发表时间：
2004-11
影响因子：
7.2
作者：
S. Ganapathysubramanian;N. Zabaras
通讯作者：
S. Ganapathysubramanian;N. Zabaras
影响因子：
4.1
作者：
Chen, Peng;Haberman, Michael R.;Ghattas, Omar
通讯作者：
Ghattas, Omar