• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.277-283
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• 2005

Kriging model is widely used as design analysis and computer experiment (DACE) model in the field of engineering design to accomplish computationally feasible design optimization. In general, kriging model has been applied to many engineering applications as an interpolation model because it is usually constructed from deterministic simulation responses. However, when the responses include not only global nonlinearity but also numerical error, it is not suitable to use Kriging model that can distort global behavior. In this research, generalized kriging model that can represent both interpolation and regression is proposed. The performances of generalized kriging model are compared with those of interpolating kriging model for numerical function with error of normal distribution type and trigonometric function type. As an application of the proposed approach, the response of a simple dynamic model with numerical integration error is predicted based on sampling data. It is verified that the generalized kriging model can predict a noisy response without distortion of its global behavior. In addition, the influences of maximum likelihood estimation to prediction performance are discussed for the dynamic model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.8
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• pp.813-818
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• 2009

Design analysis and computer experiments (DACE) model is widely used to express efficiently nonlinear responses in the field of engineering design. As a DACE model, kriging model can approximately replace a simulation model that is very expensive or highly nonlinear. The kriging model is composed of the summation of a global model and a local model representing deviation from the global model. The local model is determined by correlation coefficient with the pre-sampled points, where the accuracy and robustness of the kriging model depends on the selection of proper correlation coefficients. Therefore, to achieve the robust kriging model, the range of the correlation coefficients is explored with respect to the degrees of the global model. Based on this study we propose the proper orders of the global model and range of parameters to make accurate and robust kriging model.

• Journal of computational fluids engineering
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• v.17 no.4
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• pp.32-40
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• 2012

Efficient Global Optimization (EGO) method is a global optimization technique which can select the next sample point automatically by infill sampling criteria (ISC) and search for the global minimum with less samples than what the conventional global optimization method needs. ISC function consists of the predictor and mean square error (MSE) provided from the kriging model which is a stochastic metamodel. Also the constrained EGO method can minimize the objective function dealing with the constraints under EGO concept. In this study the constrained EGO method applied to the RAE2822 airfoil shape design formulated with the constraint. But the noisy CFD data caused the kriging model to fail to depict the true function. The distorted kriging model would make the EGO deviate from the correct search. This distortion of kriging model can be handled with the interpolation(p=free) kriging model. With the interpolation(p=free) kriging model, however, the search of EGO solution was stalled in the narrow feasible region without the chance to update the objective and constraint functions. Then the accuracy of EGO solution was not good enough. So the three-step search method was proposed to obtain the accurate global minimum as well as prevent from the distortion of kriging model for the noisy constrained CFD problem.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.701-705
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• 2008

Design analysis and computer experiments (DACE) model is widely used to express efficiently the nonlinear responses in the field of engineering design. Kriging model, a DACE model, can approximately replace a simulation model that is very expensive or highly nonlinear. The kriging model is composed of the summation of a global model and a local model representing deviation from global model. The local model is determined by correlation coefficient of the pre-sampled points, where determination of the correct correlation coefficient has an effect on accuracy and robustness of the kriging model. Therefore, robustness of the correlation coefficient is explored with respect to degrees of the global model. Then we propose the range of correlation coefficient to make correct and robust kriging model and the influence of the correlation coefficients on the degrees of global model with respect to the nonlinearity of the pre-sampled responses.

• Structural Engineering and Mechanics
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• v.41 no.1
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• pp.25-41
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• 2012

Kriging surrogate model provides explicit functions to represent the relationships between the inputs and outputs of a linear or nonlinear system, which is a desirable advantage for response estimation and parameter identification in structural design and model updating problem. However, little research has been carried out in applying Kriging model to crack identification. In this work, a scheme for crack identification based on a Kriging surrogate model is proposed. A modified rectangular grid (MRG) is introduced to move some sample points lying on the boundary into the internal design region, which will provide more useful information for the construction of Kriging model. The initial Kriging model is then constructed by samples of varying crack parameters (locations and sizes) and their corresponding modal frequencies. For identifying crack parameters, a robust stochastic particle swarm optimization (SPSO) algorithm is used to find the global optimal solution beyond the constructed Kriging model. To improve the accuracy of surrogate model, the finite element (FE) analysis soft ANSYS is employed to deal with the re-meshing problem during surrogate model updating. Specially, a simple method for crack number identification is proposed by finding the maximum probability factor. Finally, numerical simulations and experimental research are performed to assess the effectiveness and noise immunity of this proposed scheme.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.8 s.185
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• pp.119-126
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• 2006

Kriging model is widely used as design DACE(analysis and computer experiments) model in the field of engineering design to accomplish computationally feasible design optimization. In this paper, the optimization of gate valve was performed using Kriging based approximation model. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. In addition, we describe the definition, the prediction function and the algorithm of Kriging method and examine the accuracy of Kriging by using validation method.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.513-524
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• 2019

This study proposed an improved particle swarm optimization (IPSO) method ensemble with kriging model for model updating. By introducing genetic algorithm (GA) and grouping strategy together with elite selection into standard particle optimization (PSO), the IPSO is obtained. Kriging metamodel serves for predicting the structural responses to avoid complex computation via finite element model. The combination of IPSO and kriging model shall provide more accurate searching results and obtain global optimal solution for model updating compared with the PSO, Simulate Annealing PSO (SimuAPSO), BreedPSO and PSOGA. A plane truss structure and ASCE Benchmark frame structure are adopted to verify the proposed approach. The results indicated that the hybrid of kriging model and IPSO could serve for model updating effectively and efficiently. The updating results further illustrated that IPSO can provide superior convergent solutions compared with PSO, SimuAPSO, BreedPSO and PSOGA.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.33 no.3
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• pp.145-153
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• 2015

This study aims to accurately estimate population distribution more specifically than administrative unites using a RK (Regression-Kriging) model. The RK model is the areal interpolation technique that involves linear regression and the Kriging model. In order to estimate a population’s distribution using a sample region, four different models were used, namely; a regression model, RK model, OK (Ordinary Kriging) model and CK (Co-Kriging) model. The results were then compared with each other. Evaluation of the accuracy and validity of evaluation analysis results were the basis RMSE (Root Mean Square Error), MAE (Mean Absolute Error), G statistic and correlation coefficient (ρ). In the sample regions, every statistic value of the RK model showed better results than other models. The results of this comparative study will be useful to estimate a population distribution of the metropolitan areas with high population density

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.923-930
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• 2006

A Kriging model is a sort of approximation model and used as a deterministic model of a computationally expensive analysis or simulation. Although it has various advantages, it is difficult to assess the accuracy of the approximated model. It is generally known that a mean square error (MSE) obtained from the kriging model can't calculate statistically exact error bounds contrary to a response surface method, and a cross validation is mainly used. But the cross validation also has many uncertainties. Moreover, the cross validation can't be used when a maximum error is required in the given region. For solving this problem, we first proposed a modified mean square error which can consider relative errors. Using the modified mean square error, we developed the strategy of adding a new sample to the place that the MSE has the maximum when the MSE is used for the assessment of the kriging model. Finally, we offer guidelines for the use of the MSE which is obtained from the kriging model. Four test problems show that the proposed strategy is a proper method which can assess the accuracy of the kriging model. Based on the results of four test problems, a convergence coefficient of 0.01 is recommended for an exact function approximation.

• Advances in Computational Design
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• v.1 no.3
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• pp.235-251
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• 2016

We have performed a design optimization of a stiffened panel with curvilinear stiffeners using an artificial neural network (ANN) residual kriging based surrogate modeling approach. The ANN residual kriging based surrogate modeling involves two steps. In the first step, we approximate the objective function using ANN. In the next step we use kriging to model the residue. We optimize the panel in an iterative way. Each iteration involves two steps-shape optimization and size optimization. For both shape and size optimization, we use ANN residual kriging based surrogate model. At each optimization step, we do an initial sampling and fit an ANN residual kriging model for the objective function. Then we keep updating this surrogate model using an adaptive sampling algorithm until the minimum value of the objective function converges. The comparison of the design obtained using our optimization scheme with that obtained using a traditional genetic algorithm (GA) based optimization scheme shows satisfactory agreement. However, with this surrogate model based approach we reach optimum design with less computation effort as compared to the GA based approach which does not use any surrogate model.