This paper deals with an efficient and multi-fidelity design strategy for high dimensional industrial problems. The most significant factors have been determined based on the Muschelknautz method of modeling (MM) using the screening approach. For cyclone separator, only four (from seven) geometrical parameters are significant. An optimized sampling plan based on random Latin hypercube (LHS) has been used to fit Co-Kriging based on CFD data and an analytical model for estimation of pressure drop. Co-Kriging exhibits better accuracy than ordinary Kriging and blind Kriging if only the high fidelity data is used. For global optimization, the Co-Kriging surrogate in conjunction with genetic algorithms (GA) is used. CFD simulations based on the Reynolds stress turbulence model are also used in this study. A new set of geometrical ratios (design) has been obtained (optimized) to achieve minimum pressure drop. A comparison of numerical simulation of the new design and the Stairmand design confirms the superior performance of the new design compared to the Stairmand design.Recently, the meta-models have been used as tool to calibrate the less accurate (simplified) codes. Such multi-fidelity or multi-level approaches can also deal with experimental data and CFD simulations data or for CFD simulation on different grid levels, or fully developed flow results and developing flow results. Co-Kriging is a typical example of surrogate models which can handle multi-fidelity data. To filter the noise of the experimental data or the computational noise stems from the used schemes [1], meta-models can help the engineer as well. A typical example is the Regression Kriging. The surrogate models have been used as a data-mining tool several decades ago, when the polynomial regression was the cheap tool for data-mining.
Constructing The Surrogate ModelThe application of met-model instead of the experimental or computational approach is not an easy task. The following difficulties (rocks) should be overcome (passed). The following summary is inspired by the book of Forrester et al. [1].Many parameters affecting this selection; number of independent variables, the expected input-output relationship (linear, second order, etc.), the possible interaction between independent variables. These factors need some prior knowledge of the problem and the surrogate modeling.Generally speaking, not all the independent variables are significant, some are negligible. To efficiently decide that, a screening study is needed, one common approach is via first order polynomial regression after creating a design of experiment, then from the analysis of variance, one could decide the most significant parameters. A better and more accurate (but expensive) is by using Morris algorithm [2], where a surrogate model is fitted with limited number of points and then the distribution of the elementary effects is plotted (mean against standard deviation) [1]. Moreover, the dimensionless number is also helpful in reducing the number of design parameters.