Session: 12-03-02: Data-Enabled Predictive Modeling, Scientific Machine Learning, and Uncertainty Quantification in Computational Mechanics

Paper Number: 112401

112401 - Multi-Material Design Under Uncertainty of Building Envelopes Thermal Insulation 

This work presents a novel computational framework for the simulation-based optimal design of thermal insulation components of buildings to achieve target thermal performances while retaining sufficient mechanical strength. The framework is applied to the thermo-mechanical continuum model of mesoporous silica aerogel materials based on the continuum theory of mixture. The model parameters representing the elasticity and conductivity of solid and fluid phases are uncertain, obtained from the Bayesian model calibration using experimental data. The design scenarios are various building envelope thermal break components with desired insulation functionalities and mechanical strength under external loads. The design parameter is taken as the spatial distribution of porosity over the insulation components’ domain, which includes uncertainty due to material variability and errors in the additive manufacturing process. The design and uncertainty parameters are both space-dependent fields that, after finite element discretization, result in a high-dimensional design problem. To design the thermal breaks with desired properties, a risk-averse formulation of the design objective is employed to achieve both target performances and mitigation of uncertainty during the multi-objective design process. In addition, a second-order Taylor approximation of the design objective is employed to ensure the efficiency and scalability of the solution algorithm. To this end, the computational cost of solving the optimization problem becomes independent of the number of uncertain and design parameters. The scalability of this approach arises from solving a generalized eigenvalue problem using a randomized algorithm that only requires the action of the Hessian on a small number of random directions. Moreover, a scalable gradient-based optimization method is implemented using the Lagrangian formalism to derive expressions for the gradient and Hessian with respect to the uncertain and design parameters. Finally, approximated L0 functions and phase-field type regularization are utilized via a continuation numerical scheme to promote sparsity in the designed porosity. Additionally, the continuation scheme is blended with adaptive mesh refinement to obtain a near-sharp interface between materials with various porosity that are appropriate for high-volume manufacturing. The accuracy, efficiency, and scalability of the proposed design under uncertainty framework are demonstrated with examples of different building insulation scenarios. The numerical results indicate that using the approximated design objective directly or as a control variate leads to several orders of magnitude computational savings in the optimization solution compared to a plain Monte Carlo method. Additionally, the partial differential equation (PDE) constrained optimization under uncertainty framework enables mitigating the modeling uncertainty to increase reliance on the designed components. 

Presenting Author: Danial Faghihi University at Buffalo

Presenting Author Biography: Danial Faghihi is an assistant professor in the Department of Mechanical Engineering and holds an affiliated position at the Department of Civil, Structural and Environmental Engineering as well as the Institute for Computational and Data Sciences at the University at Buffalo (UB). Before joining UB in 2019, he was a research scientist in the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin. He obtained his Ph.D. in structural engineering and mechanics from Louisiana State University. Dr. Faghihi’s research interests focus on predictive multiscale modeling of complex materials and biological systems. In particular, he is interested in developing novel computational frameworks at the interface of physics-based models, scientific machine learning methods, and high-performance computing. Dr. Faghihi is the recipient of the National Science Foundation CAREER Award in 2022 and has published 34 journal articles in the area of computational mechanics.

Authors:

Danial Faghihi University at Buffalo
Jingye Tan University at Buffalo