Empirical Similitude

University Of Texas At Austin, Austin TX

Investigators

Abstract

The goal of this project is to advance the fundamental understanding of mathematical predication through Empirical Similitude Method (ESM), a novel approach that takes non-linearities and property variations into account to estimate the performance of an actual product. The Traditional Similitude Method (TSM) or Dimensional Analysis incorporates the Buckingham's Pi theorem to predict the behavior of a system by analyzing and testing its corresponding scaled prototype. The constraints and limitations in using this method lie in the assumption that the system follows a power law, the scaling parameters obtained after analysis are unique and constant through the entire range of application, and the parameters are indicative of the actual system only. The TSM analysis is primarily confined to prediction in focused domains. Preliminary work in ESM has been achieved by implementing systematic numerical manipulations in the algebraic domain by using tools including Conformal Mapping, Linear Algebra, Vector Calculus and Statistics to address the concerns of various forms of distortion comprising model distortion like isotropic and orthotropic properties, geometric distortion including shape and orientation, parametric distortion like size and dimensions and feature distortion like square holes vs. round holes. This project aims to develop a comprehensive mathematical derivation that gives insights into the existing methods of ESM and further extends this process for complex systems. Research tasks include extending the Conformal Mapping, evaluating the system in the Z-space or the imaginary domain, developing a pragmatic definition for Lumped Empirical Similitude Method and using the Circulant Matrix approach to establish the practical reasoning of ESM. Collaboration with industry on such applications as scaled automotive crash testing will demonstrate the significant impact this approach can have to numerous complex systems problems. The researchers will also explore a collaborative research activity with a group of faculty at Texas A & M University (TAMU). This collaboration will investigate possible connections between this work and research into probability modeling of design spaces with the characterization of uncertainties being conducted at TAMU.