Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 150158

150158 - Stress Constrained Optimal Design of Building Insulations Under Spatially Correlated Uncertainty 

This study aims to develop a computational framework for designing thermal insulation components in net-zero buildings, leveraging silica aerogel superinsulation materials. The thermomechanical response of the component is governed by a multi-phase model-based continuum theory of mixture. This model does not only consider the uncertainty associated with the physical parameters like elastic modulus and thermal conductivity for the solid and fluid phases but also with the design parameter, which is the spatial distribution of the materials porosity over the domain of the component. The design is space-dependent fields, which after their finite element discretization, results in an optimal design problem under high dimensional and spatially correlated uncertainty. A mean-variance cost functional is employed to achieve target insulation performance along with uncertainty reduction during the design process. To avoid stress concentration, chance constraints are applied to the function that gives the difference between the allowable critical stress and the maximum von Mises stress occurring in the domain. A gradient-based optimization method is used built on Lagrangian formalism, which is utilized to derive expression for the design gradient and Hessian with respect to uncertainty parameter. In order to handle the nondifferentiability of the inequality in chance constraint, a smooth approximation of the discontinuous indicator function is implemented using a continuation scheme. Also, a penalty method is applied to approximate the chance-constrained problem to an unconstrained one. There are two efficient and dimension-independent approaches for the resulting optimization under uncertainty.  The first approach is based on a second-order Taylor (quadratic) approximation of the design objective that solves a generalized eigenvalue problem using a randomized algorithm that only requires the action of Hessian on a small number of random directions. The computational cost does not depend on the actual dimension of the uncertainty parameter, but depends only on the effective dimension, which is determined by the rank of the Hessian, and hence it provides a scalable algorithm to solve the problem. The reduction of variance through correction of the moments of second-order Taylor approximation through Monte Carlo samples is also studied. The second approach is based on approximating the PDE solution using a neural operator surrogate model. The neural operator exploits Principal Component Analysis (PCA) and Proper Orthogonal Decomposition (POD) for dimension reduction to achieve discretization-invariant property. The accuracy, efficiency, and scalability of the proposed design under uncertainty frameworks are demonstrated with examples of various building insulation scenarios. We demonstrate through numerical results that the proposed algorithms lead to a reduction of computational cost by up to several orders of magnitude in the optimization solution.

Acknowledgments: the financial support received from the U.S. National Science Foundation (NSF) CAREER Award CMMI-2143662 is acknowledged.

Presenting Author: Pratyush Kumar Singh University at Buffalo

Presenting Author Biography: Pratyush Kumar Singh is a dedicated researcher currently pursuing his Ph.D. in Mechanical Engineering at University at Buffalo. He obtained his Master of Science degree in Mechanical Engineering with highest honors(summa cum laude) from University at Buffalo. Pratyush's research interests span a wide range of topics within mechanical engineering, including uncertainty quantification, self assembly, surrogate modeling, bayesian neural networks, etc. He has been actively involved in cutting-edge research, focusing on a nonlocal theory of heat transfer and micro-phase separation of nano-structured copolymers, as evidenced by his publication in the International Journal of Heat and Mass Transfer. As an emerging scholar in the field of mechanical engineering, Pratyush Kumar Singh continues to push the boundaries of knowledge, bringing innovative solutions to the forefront of research and contributing significantly to the scientific community.

Authors:

Pratyush Kumar Singh University at Buffalo
Danial Faghihi University at Buffalo