Engineering design optimization often gives rise to problems in which expensive objective func-tions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate mod-els of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.

Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary design optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, where zero and first order information are required. In these methods, designers must generate and query a database of order O(n²) in order to compute the second order terms of the quadratic response surface approximation. As the number of design variables grows, the computational cost of generating the required database becomes a concern. In this paper, we present an new approach in which we require just O(n) parameters for constructing a second order approximation. This is accomplished by transforming the matrix of second order terms into the canonical form. The method periodically requires an order O(n²) update of the second order approximation to maintain accuracy. Results show

This report is intended to facilitate dialogue between engineers and optimizers about the efficiency of Taguchi methods for robust design, especially in the context of design by computer simulation. Three approaches to robust design are described: 1. Robust optimization, i.e. specifying an objective function f and then minimizing a smoothed (robust) version of f by the methods of numerical optimization. 2. Taguchi's method of specifying the objective function as a certain signal-to-noise ratio, to be optimized by designing, performing and analyzing a single massive experiment. 3. Specifying an expected loss function f and then minimizing a cheap-to-compute surrogate objective function f , to be obtained by designing and performing a single massive experiment. Some relations between these approaches are noted and it is emphasized that only the first approach is capable of iteratively progressing toward a solution. Adjunct Associate Professor, Department of Computational & Applied Mat...

Design and implementation of a digital feedback controller for a flow control experiment was performed. The experiment was conducted in a cryogenic pressurized wind tunnel on a generic separated configuration at a chord Reynolds number of 16 million and a Mach number of 0:25. The model simulates the upper surface of a 20% thick airfoil at zero angle-of-attack. A moderate favorable pressure gradient, up to 55% of the chord, is followed by a severe adverse pressure gradient which is relaxed towards the trailing edge. The turbulent separation bubble, behind the adverse pressure gradient, is then reduced by introducing oscillatory flow excitation just upstream of the point of flow separation. The degree of reduction in the separation region can be controlled by the amplitude of the oscillatory excitation. A feedback controller was designed to track a given trajectory for the desired degree of flow reattachment and to improve the transient behavior of the flow system. Closed-loop experiments demonstrated that the feedback controller was able to track step input commands and improve the transient behavior of the open-loop response.

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Abstract. In this report, we address aerodynamic shape optimization problems including uncertain operating conditions. After a review of robust control theory and the possible approaches to take into uncertainty, we propose to use Taguchi robust design methods in order to overcome single point design problems in Aerodynamics. The latter techniques produce solutions that perform well for the selected design point but have poor off-design performance. Under the conduct of Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are mean performance and its variance, so that the solutions are as less insensitive to the uncertainty of the input parameters as possible. Furthermore, the Multi-Criterion Evolutionary Algorithms (MCEAs) are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier-Stokes computation. In order to reduce the number of expensive evaluations of fitness function, Response Surface Modelling (RSM) is employed to estimate fitness value using the polynomial approximate model. The proposed approach is applied to the robust optimization of the 2D high lift devices of a business aircraft, by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free-stream angle of attack at landing and takeoff flight conditions respectively