• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.677-691
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• 2018

Reliability assessment of complex structures using simulation methods is time-consuming. Thus, surrogate models are usually employed to reduce computational cost. AK-MCS is a surrogate-based Active learning method combining Kriging and Monte-Carlo Simulation for structural reliability analysis. This paper proposes three modifications of the AK-MCS method to reduce the number of calls to the performance function. The first modification is related to the definition of an initial Design of Experiments (DoE). In the original AK-MCS method, an initial DoE is created by a random selection of samples among the Monte Carlo population. Therefore, samples in the failure region have fewer chances to be selected, because a small number of samples are usually located in the failure region compared to the safe region. The proposed method in this paper is based on a uniform selection of samples in the predefined domain, so more samples may be selected from the failure region. Another important parameter in the AK-MCS method is the size of the initial DoE. The algorithm may not predict the exact limit state surface with an insufficient number of initial samples. Thus, the second modification of the AK-MCS method is proposed to overcome this problem. The third modification is relevant to the type of regression trend in the AK-MCS method. The original AK-MCS method uses an ordinary Kriging model, so the regression part of Kriging model is an unknown constant value. In this paper, the effect of regression trend in the AK-MCS method is investigated for a benchmark problem, and it is shown that the appropriate choice of regression type could reduce the number of calls to the performance function. A stepwise approach is also presented to select a suitable trend of the Kriging model. The numerical results show the effectiveness of the proposed modifications.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.2
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• pp.28-36
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• 2007

A multi-objective design exploration for a three-element airfoil consisted of a slat, a main wing, and a flap was carried out. The lift curve improvement is important to design high-lift system, thus design has to be performed with considered multi-angle. The objective functions considered here are to maximize the lift coefficient at landing and near stall conditions simultaneously. Kriging surrogate model which was constructed based on several sample designs is introduced. The solution space was explored based on the maximization of Expected Improvement (EI) value corresponding to objective functions on the Krigingmodels. The improvement of the model and the exploration of the optimum can be advanced at the same time by maximizing EI value. In this study, a total of 90 sample points are evaluated using the Reynolds averaged Navier-Stokes simulation(RANS) for the construction of the Kriging model. In order to obtain the information of the design space, two data mining techniques are applied to design result. One is functional Analysis of Variance(ANOVA) which can show quantitative information and the other is Self-Organizing Map(SOM) which can show qualitative information.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1199-1208
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• 2005

Nowadays, it is performed actively to optimize by using an approximate model. This is called the approximate optimization. In addition, the sequential approximate optimization (SAO) is the repetitive method to find an optimum by considering the convergence of an approximate optimum. In some recent studies, it is proposed to increase the fidelity of approximate models by applying the sequential sampling. However, because the accuracy and efficiency of an approximate model is directly connected with the design area and the termination criteria are not clear, sequential sampling method has the disadvantages that could support an unreasonable approximate optimum. In this study, the SAO is executed by using trust region, Kriging model and Optimal Latin Hypercube design (OLHD). Trust region is used to guarantee the convergence and Kriging model and OLHD are suitable for computer experiment. finally, this SAO method is applied to various optimization problems of highly nonlinear mathematical functions. As a result, each approximate optimum is acquired and the accuracy and efficiency of this method is verified by comparing with the result by established method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.37 no.2
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• pp.95-101
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• 2024

This paper introduces an optimized design for a sensor bracket used to measure the wear amount of an automobile brake pad, based on a dynamic kriging surrogate model. During testing, the temperature of the brake pad can increase beyond 600℃, which often causes sensor malfunction. Therefore, it is essential to optimize the shape of the sensor bracket to minimize heat transfer. To reduce the computational cost of the optimization, the heat-transfer simulation is replaced by a dynamic kriging surrogate model. Dynamic kriging utilizes the best combination of correlation and basis functions and constructs an accurate surrogate model. Following optimization, the temperature of the sensor position decreases by 7.57%. The results from the surrogate model under optimum conditions are verified by a heat-transfer simulation, and the design optimization using a surrogate model is found to be effective.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.3
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• pp.1630-1638
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• 2015

The finite element analysis has become an essential process to investigate the structural performance in many industry fields. In addition, the computer's performance is improving rapidly, but in large design problems, there is a limit to apply the optimal design techniques. For this, it is general to introduce a metamodel based optimization technique. The method to generate an approximate model can be classified into curve fitting and interpolation, and each representative one is response surface model and kriging interpolation method. This study proposes an ensemble model made of RSM and kriging to solve a structural design problem. The suggested method is applied to the designs of two bar and automobile outer tie rod.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.537-542
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• 2001

In recent engineering, the designer has become more and more dependent on computer simulation. But defining exact model using computer simulation is too expensive and time consuming in the complicate systems. Thus, designers often use approximation models, which express the relation between design variables and response variables. These models are called metamodel. In this paper, we introduce one of the metamodel, named Kriging. This model employs an interpolation scheme and is developed in the fields of spatial statistics and geostatistics. This class of interpolating model has flexibility to model response data with multiple local extreme. By reason of this multi modality, we can't use any gradient-based optimization algorithm to find global extreme value of this model. Thus we have to introduce global optimization algorithm. To do this, we introduce DE(Differential Evolution). DE algorithm is developed by Ken Price and Rainer Storn, and it has recently proven to be an efficient method for optimizing real-valued multi-modal objective functions. This algorithm is similar to GA(Genetic Algorithm) in populating points, crossing over, and mutating. But it introduces vector concept in populating process. So it is very simple and easy to use. Finally, we show how we determine Kriging metamodel and find global extreme value through two mathematical examples.

• Journal of Mechanical Science and Technology
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• v.20 no.8
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• pp.1169-1182
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• 2006

Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.6 no.1
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• pp.71-77
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• 2007

In case of the welding process, a conventional production method of gate valve, it has a merit of light weight, but also a demerit of high production cost and an impossibility in mass production due to work by hand. However, in case of the forging process, it has economic merits and can take a mass production process, too. The main focus of this paper is the optimization of preform in the forging process. This paper proposed an optimal design to improve the mechanical efficiency of gate valve made by forging method instead of welding. the optional design is conducted as application of real response model to Kriging model using computer simulation. Also, from verification of the response model with optimized results we were confirmed that the applications of Kriging method to structural optimum design using finite element analysis and equation are useful and reliable.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.10
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• pp.1042-1048
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• 2008

Disc brake noise is an important customer satisfaction and warranty issue for many manufacturers as indicated by technical literature regarding the subject coming from Motor Company. This research describes results of a study to assess disk brake squeal propensity using finite element methods and optimal technique (Kriging). In this study, finite element analysis has been performed to determine likely modes of brake squeal. This paper deals with friction-induced vibration of disc brake system under contact friction coefficient. A linear, finite element model to represent the floating caliper disc brake system is proposed. The complex eigen-values are used to investigate the dynamic stability and in order to verify simulations which are based on the FEM model. In this paper, Kriging from among the meta-modeling techniques is proposed for an optimal design scheme to reduce the brake squeal noise.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1243-1252
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• 2005

A current trend of design methodologies is to make engineers objectify or automate the decision-making process. Numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, the Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, a design procedure for global robust optimization is developed based on the kriging and global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. Robustness is determined by the DACE model to reduce real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. As the postprocess, the first order second-moment approximation method is applied to refine the robust optimum. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.