Past Event: Oden Institute Seminar

Inverse Problems and Hybrid Optimization Algorithms

George S. Dulikravich, Department of Mechanical and Materials Engineering, Florida International University, dulikrav@fiu.edu, http://maidroc.fiu.edu

Abstract

This lecture will demonstrate computational algorithms for the solution of several classes of inverse problems as applied to elasticity, thermoelasticity and materials engineering: 1. Inverse determination of unknown steady and unsteady boundary conditions 2. Inverse determination of 2D and 3D shapes in aerodynamics, heat transfer and elasticity 3. Inverse determination of unknown non-constant physical properties of solid materials Solution methods for these two classes of inverse problems involve applications of a non-iterative boundary-element method (utilizing SVD algorithm) and an iterative finite element method (utilizing a sparse matrix solver and regularization). 4. Inverse determination of concentrations of aloying elements that will produce specified multiple macroscopic properties. This computational/experimental alloy design method was verified during the past decade for H-type steels, Ni based steel superalloys, Ti based alloys, Hf based bulk metallic glasses, and Al based stress corrosion resistant alloys. This method combines: a. Experimentally obtained multiple properties and thermal treatment parameters of alloys, b. Robust multi-dimensional response surface generation algorithms, and c. Constrained, multi-objective, evolutionary optimization algorithms accounting for uncertainties in the alloy manufacturing and testing. Each optimization algorithm performs with a different speed and a different degree of reliability when applied to minimization of functions having varying degrees of convexity, smoothness, and constraints. Consequently, it is logical to suggest that several optimization algorithms should be made available to an intelligent selection algorithm that automatically decides when each constituent optimizer should be used and for how many iterations in order to avoid local minima and accelerate the convergence towards global minimum. Constraints are reformulated as additional objectives in a multi-objective optimization. Invited lecturer’s biosketch: Professor Dulikravich has a diverse educational background including private (Ph.D.-Cornell’79), public (M.Sc.-Minnesota’75) and international (Dipl.Ing.- Belgrade’73) schooling, three years of visiting research and teaching experience both domestic (NASA) and international (DFVLR), thirty years of teaching and research experience at four universities (UT-Austin, Penn State, UT-Arlington, FIU). Professor Dulikravich is the founder and Editor-in- Chief of the international journal on Inverse Problems in Science and Engineering and an Associate Editor of several other journals. He is a Fellow of the American Academy of Mechanics, a Fellow of the American Society of Mechanical Engineers, a Fellow of the Royal Aeronautical Society, and an Associate Fellow of the American Institute of Aeronautics and Astronautics. His research is highly multi-disciplinary spanning the fields of aerospace, mechanical, industrial, engineering mechanics, materials and biomedical engineering resulting in over 400 publications. Some of his research topics include: the development of a variety of inverse design algorithms; multi- objective hybrid constrained evolutionary design optimization algorithms; acceleration of iterative algorithms; turbomachinery aero-thermodynamics and heat transfer; conjugate heat transfer analysis, optimized topology of branching 3D micro-channels for high heat flux electronics and gas turbine blade cooling; brain cooling of stroked patients; optimized freezing of organs for tissue banking; optimally controlled solidification using electric, magnetic and thermal fields; multi-objective optimization and inverse design of chemical compositions of nickel superalloys, titanium alloys, aluminum alloys and bulk metallic glasses; thermo-elasticity analysis and inverse problems; design optimization of kinetic energy projectiles for maximum penetration; inverse design and optimization of transonic and hypersonic flight vehicle shapes; and constrained design optimization of chemical formulas for functional molecules such as new en