The objective of robust design optimization is to improve the quality ofa product or process by minimizing the deteriorating effects of variableor uncertain parameters. In addition to this original formulation of robustparameter design by G. TAGUCHI several other approaches based on decisiontheoretic formulations have been introduced to attain a robust design,e.g. the minimax principle which minimizes the worst case effected by variabilityand the BAYES principle to optimize the expectation of the objective. Bothapproaches require a lot of function evaluations either to find the worstcase or to calculate numerically the integral of the expectation. In caseswhere a large number of function evaluations is prohibitive, e.g. extensiveand timeconsuming computer simulations, an optimization method using metamodelsis suggested. Within this framework a surrogate model of the objectivefunction is constructed using the results of a finite element analysisat selected sampling points. On such a metamodel evaluations which representestimates for the true function are very cheap to get and thus the abovementioned criteria can easily be evaluated. In this paper a review of commonmetamodelling techniques is given with a focus on spatial correlation andresponse surface methods. The so called kriging has emerged as well suitedfor the analysis of computer experiments as it is able to interpolate theoutput of the simulations. This is an important feature regarding the factthat deterministic computer simulations are not subject to random error:equal input parameters yield equal responses up to floating-point precision.Hence we expect our metamodel to represent the output data exactly at thesampled points. On the other hand response surface methods are often andsuccessfully used in engineering applications due to their easy implementationand application. However, response surfaces usually only approximate thevalues at the sampled points. The selection of the sampling points usedto build the surrogate model can be implemented via classical design ofexperiments (DOE) including the crossed or combined array. In the contextof kriging models Latin hypercube designs have been widely used for instancebecause of their space filling property. This assures a balanced predictiveperformance of the kriging model throughout the investigated design space.Using the procedure presented above results in an estimate for the robustdesign. Verifying this design via the underlying computer simulation willshow whether the claimed accuracy of the metamodel compared to the computercode is met or further improvements of the surrogate model are necessary.Regarding the latter case an approach for the selection of additional samplingpoints to sequentially augment the significance of the metamodel is needed.In the literature various update algorithms are available related to thedifferent metamodelling techniques. Depending on objective and the formulationof the error estimate several alternatives are presented in this paper.Using the updated metamodels a new optimization can be run yielding animproved estimate of the robust optimum. This sequence will be continueduntil the stopping criterion is met.
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The objective of robust design optimization is to improve the quality ofa product or process by minimizing the deteriorating effects of variableor uncertain parameters. In addition to this original formulation of robustparameter design by G. TAGUCHI several other approaches based on decisiontheoretic formulations have been introduced to attain a robust design,e.g. the minimax principle which minimizes the worst case effected by variabilityand the BAYES principle to optimize the expectation of th...
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