9.20.16 Mulani

9.20.16 Mulani

Title: Polynomial Chaos Decomposition with Differentiation and Applications

Speaker: Sameer B. Mulani, Assistant Professor, University of Alabama

Date: September 20, 2016

Location: NIA, Room 137

Time: 10:00am

Introduction by: Carly Bosco, NIA

Presentation Link:

Abstract: A new non-intrusive polynomial chaos (PC) method is proposed where the response and input random variables are expanded in a similar way to the traditional PC that is then followed by differentiation of basis polynomials as well as sensitivity calculation of the response. Here, two analytical problems are studied with three different techniques for sensitivity calculation: 1) analytical differentiation, 2) higher order forward finite difference, and 3) first order forward finite difference with three different step-sizes. This “higher order finite difference” is also a new technique obtained by using Taylor series expansion and it has been observed that the results obtained by implementing this higher order finite difference have a higher order of accuracy than first order finite difference, which increases with increase in the order of chaos expansion. The number of samples required for finding expansion coefficients is equal to the number of polynomials used in the expansion and less than required for existing non-intrusive methods. In some cases, similar results to that of analytical differentiation for output are obtained by using higher order finite difference. The PCDD is applied to the modeling of an eight-layered fiber reinforced plastic (FRP) composite laminate with uncertainties in material and geometric properties. The PCDD was capable of providing similar results to 5e04 Latin Hypercube Sampling with similar accuracy and substantial computational savings.

Bio: Dr. Sameer B. Mulani graduated from Indian Institute of Technology Bombay (IIT Bombay), Mumbai, India, with Masters in Aerospace Engineering. During his Master’s, he was awarded DAAD fellowship to carry out Master’s thesis work at the Institut fur Statik und Dynamik der Luft- und Raumfahrtkonstruktionen (ISD), Universitat Stuttgart, Germany. He completed his Ph.D. in July 2006 from Aerospace and Ocean Engineering at Virginia Tech. He was Post-doctoral Associate and Research Scientist until the end of 2013 December in the Department of Aerospace and Ocean Engineering at Virginia Tech and carried research in the area of Multi-Disciplinary Optimization and Uncertainty Quantification. Currently, he is an Assistant Professor in the Department of Aerospace Engineering and Mechanics at the University of Alabama.



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