Efficient Multipoint Aerodynamic Design Optimization Via Cokriging

Abstract

Multipoint objective functions are often employed within aerodynamic optimizations to prevent a reduction in offdesign performance. However, this typically results in the need for a significant number of simulations at a variety of design conditions to calculate the objective function. The following paper attempts to address this problem through the application of a multilevel cokriging model within the optimization process. A large number of single-point design simulations are augmented by a smaller number of multipoint simulations. The technique is shown to result in surrogate models as effective as those produced using a traditional multipoint process when optimizing a transonic airfoil but with a reduction in the total number of simulations.between expensive and cheap data K = total number of design conditions n = total number of sample points p = hyperparameter governing smoothness R = correlation matrix r = correlations between known and unknown points w = design point weighting X = matrix of design points x = vector of design variables y = vector of objective function values Zx = Gaussian process = hyperparameter governing correlation = regression constant = mean = scaling parameter 2 = variance = concentrated log likelihood Subscripts c = cheap data d = difference between cheap and expensive data e = expensive data

Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models

“…Whilst this simple example illustrates the clear advantages that a multi-fidelity approach can bring, which has been mirrored by results presented within the literature [2,3,7,17,24], to date a number of important questions relating to the general application of such approaches have yet to be addressed:…”

“…Consider now the multipoint aerodynamic design optimization of a two-dimensional airfoil section taken from Toal and Keane [24]. In this case 2D CFD simulations, A weighted combination of the drag at these three points was then used as a metric of design quality.…”

“…As the performance of any surrogate based optimization is determined by the accuracy of the model a more accurate model can significantly reduce the total number of simulations required for an optimization. Such multi-fidelity approaches have been successfully employed throughout the literature in the design optimization of airfoils [17,24,26], wings [3], compressor rotors [2], combustors [25] and the creation of aerodynamic models [7,[9][10][11]26]. 1 An example of single and multi-fidelity Kriging [5] Figure 1 is a simple example, recreated from Forrester et al [5], of the advantages that multi-fidelity Kriging can offer if used to create a surrogate model.…”

Isothermal Combustor Prediffuser and Fuel Injector Feed Arm Design Optimization Using the prometheus Design System

“…The literature contains a number of examples of the effectiveness of this technique on problems including airfoil design [23][24][25], the creation of aerodynamic models [25][26][27][28][29], compressor blade design [3] and even whole engine optimization [10].…”

An Accelerated Medial Object Transformation for Whole Engine Optimisation

“…Although not considered within the presented work it should also be recognised that the generated medial mesh can also be used to help construct a high-quality volume mesh [15,16] for further analysis or as part of a multi-fidelity design optimisation [17][18][19]. The accelerated medial object transformation presented in this paper is a key component within a proposed whole engine optimisation work flow.…”