Woodruff School of Mechanical Engineering

Guest Speaker

Title:

Reducing Data Requirements in Metamodeling by using Multiple Responses and Bound Information

Speaker:

Dr. David Romero

Affiliation:

Universidad del Zulia, in Maracaibo, Venezuela

When:

Monday, April 30, 2012 at 11:00:00 AM

Where:

MRDC Building, Room 4211

Host:

Dr. Chris Paredis
chris.paredis@me.gatech.edu
404.894.5613

Abstract

The optimal design of complex systems in engineering requires the availability of mathematical models of systemís behavior as a function of a set of design variables; such models allow the designer to search for the best solution to the design problem. However, system models (e.g. CFD analysis, physical experiments) are usually time-consuming and expensive to evaluate, and thus unsuited for systematic use during design. A solution proposed in the literature is the creation of approximate models of system behavior, also known as surrogate models, or metamodels, from limited data obtained in the context of computer experiments with a time-consuming model of the system. By reducing the number of model evaluations required to reach a solution to the design problem, significant cost and time savings are realized. In this seminar, we will visit two approaches to further improve the efficiency of the metamodeling process. First, we explore the use of multi-response metamodels (MRM) to approximate several aspects of system behavior jointly, instead of modeling each individually. By exploiting the correlation between the response variables of interest and other data that is already available at no extra cost, we expect to reduce the number of experiments required to meet a given accuracy target. Based on comparisons using a set of test functions with varying degrees of correlation, our results indicate that MRM outperform individual metamodels in 53% to 75% of the test cases, though the relative performance depends on the sample size, sampling scheme, and on the actual correlation among the observed response values. In addition, results indicate that realization of this performance improvement depends on an appropriate choice of covariance/correlation function, a task for which the modified Akaikeís Information Criterion (AICc) was observed to be inadequate. As a second approach to improve the efficiency of metamodeling, we explore a formulation in multiple stages with non-stationary covariance functions. After demonstrating the feasibility of the proposed formulation with an example, we move on to demonstrate its potential to take advantage of upper/lower bound information about the response variables. Results show that the use of bound information can improve metamodel accuracy without requiring additional experimental runs, although the significance of this improvement in more general cases is currently under study.


Biography

David A. Romero is a Profesor Asociado at the Universidad del Zulia, in Maracaibo, Venezuela. David holds M.Sc. (2003) and Ph.D. (2008) degrees in Mechanical Engineering from Carnegie Mellon University. Davidís research interests are in applied computing, statistics and mathematics in support of engineering design, modeling and optimization, particularly in the thermal sciences. His current interests are metamodeling and optimization based on multiple responses/objectives, and optimization applications in wind energy. Previous work experience includes surrogate-modeling based optimization of thermal systems and of enhanced oil recovery methods, dynamic simulation of thermal/fluid flow systems, and evaluation of wind energy resources. David is currently on leave from his faculty position, as a Postdoctoral Fellow at the Department of Mechanical & Industrial Engineering, University of Toronto, Canada