1,721,015 research outputs found
A study into the potential of GPUs for the efficient construction & evaluation of kriging models
No full textThe surrogate modelling technique known as Kriging, and its various derivatives, requires an optimization process to effectively determine the model’s defining parameters. This optimization typically involves the maximisation of a likelihood function which requires the construction and inversion of a correlation matrix dependent on the selected modelling parameters. The construction of such models in high dimensions and with a large numbers of sample points can, therefore, be considerably expensive. Similarly, once such a model has been constructed the evaluation of the predictor, error and other related design and model improvement criteria can also be costly. The following paper investigates the potential for graphical processing units to be used to accelerate the evaluation of the Kriging likelihood, predictor and error functions. Five different Kriging formulations are considered including, ordinary, universal, non-stationary, gradient-enhanced and multi-fidelity Kriging. Other key contributions include the derivation of the adjoint of the likelihood function for a fully and partially gradient-enhanced Kriging model as well as the presentation of novel schemes to accelerate the likelihood optimization via a mixture of single and double precision calculations and by automatically selecting the best hardware to perform the evaluations on
Applications of multi-fidelity multi-output Kriging to engineering design optimization
No full textSurrogate modelling is a popular approach for reducing the number of high fidelity simulations required within an engineering design optimization. Multi-fidelity surrogate modelling can further reduce this effort by exploiting low fidelity simulation data. Multi-output surrogate modelling techniques offer a way for categorical variables e.g. the choice of material, to be included within such models. While multi-fidelity multi-output surrogate modelling strategies have been proposed, to date only their predictive performance rather than optimization performance has been assessed. This paper considers three different multi-fidelity multi-output Kriging based surrogate modelling approaches and compares them to ordinary Kriging and multi-fidelity Kriging. The first approach modifies multi-fidelity Kriging to include multiple outputs whereas the second and third approaches model the different levels of simulation fidelity as different outputs within a multi-output Kriging model. Each of these techniques is assessed using three engineering design problems including the optimization of a gas turbine combustor in the presence of a topological variation, the optimization of a vibrating truss where the material can vary and finally, the parallel optimization of a family of airfoils
Proper orthogonal decomposition & kriging strategies for design
No full textThe proliferation of surrogate modelling techniques have facilitated the application of expensive, high fidelity simulations within design optimisation. Taking considerably fewer function evaluations than direct global optimisation techniques, such as genetic algorithms, surrogate models attempt to construct a surrogate of an objective function from an initial sampling of the design space. These surrogates can then be explored andupdated in regions of interest.Kriging is a particularly popular method of constructing a surrogate model due to its ability to accurately represent complicated responses whilst providing an error estimate of the predictor. However, it can be prohibitively expensive to construct a kriging model at high dimensions with a large number of sample points due to the cost associated withthe maximum likelihood optimisation.The following thesis aims to address this by reducing the total likelihood optimisationcost through the application of an adjoint of the likelihood function within a hybridised optimisation algorithm and the development of a novel optimisation strategy employinga reparameterisation of the original design problem through proper orthogonal decomposition
Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models
No full textSurrogate models or metamodels are commonly used to exploit expensive computational simulations within a design optimization framework. The application of multi-fidelity surrogate modeling approaches has recently been gaining ground due to the potential for further reductions in simulation effort over single fidelity approaches. However, given a black box problem when exactly should a designer select a multi-fidelity approach over a single fidelity approach and vice versa? Using a series of analytical test functions and engineering design examples from the literature, the following paper illustrates the potential pitfalls of choosing one technique over the other without a careful consideration of the optimization problem at hand. These examples are then used to define and validate a set of guidelines for the creation of a multi-fidelity Kriging model. The resulting guidelines state that the different fidelity functions should be well correlated, that the amount of low fidelity data in the model should be greater than the amount of high fidelity data and that more than 10\% and less than 80\% of the total simulation budget should be spent on low fidelity simulations in order for the resulting multi-fidelity model to perform better than the equivalent costing high fidelity model
On the potential of a multi-fidelity G-POD based approach for optimization & uncertainty quantification
No full textTraditional multi-fidelity surrogate models require that the output of the low fidelity model be reasonably well correlated with the high fidelity model and will only predict scalar responses. The following paper explores the potential of a novel multi-fidelity surrogate modelling scheme employing Gappy Proper Orthogonal Decomposition (G-POD) which is demonstrated to accurately predict the response of the entire computational domain thus improving optimization and uncertainty quantification performance over both traditional single and multi-fidelity surrogate modelling scheme
Performance of an ensemble of ordinary, universal, non-stationary and limit kriging predictors
No full textThe selection of stationary or non-stationary Kriging to create a surrogate model of a black box function requires a priori knowledge of the nature of response of the function as these techniques are better at representing some types of responses than others. While an adaptive technique has been previously proposed to adjust the level of stationarity within the surrogate model such a model can be prohibitively expensive to construct for high dimensional problems. An alternative approach is to employ a surrogate model constructed from an ensemble of stationary and non-stationary Kriging models. The following paper assesses the accuracy and optimization performance of such a modelling strategy using a number of analytical functions and engineering design problems
Non-stationary kriging prediction of turbomachinery time variant responses
No full textSurrogate models are usually employed in the representation of scalar values with little emphasis given to the modelling of time variant responses of scalar or vector quantities. The following paper aims to address this by presenting two non-stationary kriging based techniques which can be used to represent such quantities. These surrogate modelling strategies are demonstrated to accurately model the variation in turbomachinery component cycle performance with design changes thereby permitting future cross partner optimisations and trade-off studies
SDF-GAN: aerofoil shape parameterisation via an adversarial auto-encoder
No full textCurrent aerodynamic design processes suffer from expensive optimisation procedures, in part due to the requirement to search large design spaces. Recent advances in deep learning, and more precisely the development of high quality generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs), have opened up new possibilities for shape parameterisation and aerodynamic design. As the focus of work in this area so far has primarily been on generative aerofoil design via coordinate-based shape representations,aerofoil generation via image-based shape representation is yet to receive much attention. This study aims to rectify this by investigating aerofoil shape generation using signed distance field geometry representations. A key issue with direct geometry representation is the potential lack of smoothness in the output design. Two features are proposed to mitigate this: the first is an auto-encoding architecture, which was found to help drive the output designs to smoother geometries; the second is a Hanning filter provided by XFOIL, which acts to smooth the surface speed distribution and return the corresponding geometry. Network hyper-parameters are set through an optimisation procedure using an LP-tau design of experiments. The approach is compared to alternative state-of-the-art parameterisation techniques
Multiresolution surface blending for detail reconstruction
No full textWhile performing mechanical reverse engineering, 3D reconstruction processes often encounter difficulties capturing small, highly localised surface information. This can be the case if a physical part is 3D scanned for life-cycle management or robust design purposes, with interest in corroded areas or scratched coatings. The limitation partly is due to insufficient automated frameworks for handling -localised - surface information during the reverse engineering pipeline. We have developed a tool for blending surface patches with arbitrary irregularities, into a base body that can resemble a CAD design. The resulting routine preserves the shape of the transferred features and relies on the user only to set some positional references and parameter adjustments for partitioning the surface features
Efficient multipoint aerodynamic design optimization via cokriging
No full textMultipoint 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 simulation
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