• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1195-1219
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• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.

• Journal of Computational Design and Engineering
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• v.1 no.3
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• pp.187-193
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• 2014

One of the hottest challenges in automotive industry is related to weight reduction in sheet metal forming processes, in order to produce a high quality metal part with minimal material cost. Stamping is the most widely used sheet metal forming process; but its implementation comes with several fabrication flaws such as springback and failure. A global and simple approach to circumvent these unwanted process drawbacks consists in optimizing the initial blank shape with innovative methods. The aim of this paper is to introduce an efficient methodology to deal with complex, computationally expensive multicriteria optimization problems. Our approach is based on the combination of methods to capture the Pareto Front, approximate criteria (to save computational costs) and global optimizers. To illustrate the efficiency, we consider the stamping of an industrial workpiece as test-case. Our approach is applied to the springback and failure criteria. To optimize these two criteria, a global optimization algorithm was chosen. It is the Simulated Annealing algorithm hybridized with the Simultaneous Perturbation Stochastic Approximation in order to gain in time and in precision. The multicriteria problems amounts to the capture of the Pareto Front associated to the two criteria. Normal Boundary Intersection and Normalized Normal Constraint Method are considered for generating a set of Pareto-optimal solutions with the characteristic of uniform distribution of front points. The computational results are compared to those obtained with the well-known Non-dominated Sorting Genetic Algorithm II. The results show that our proposed approach is efficient to deal with the multicriteria shape optimization of highly non-linear mechanical systems.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.231-238
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• 2002

As a modeling method where the merits of fuzzy inference system and evolutionary computation are put together, evolutionary fuzzy modeling performs global approximate optimization. The paper proposes fuzzy clustering as fuzzy rule generation process which is one of the most important steps in evolutionary fuzzy modeling. With application of fuzzy clustering into the experiment or simulation results, fuzzy rules which properly describe non-linear and complex design problem can be obtained. The efficiency of evolutionary fuzzy modeling can be improved utilizing the membership degrees of data to clusters from the results of fuzzy clustering. To ensure the validity of the proposed method, the real design problem of an automotive inner trim is applied and the global approximation is achieved. Evolutionary fuzzy modeling is performed for several cases which differ in the number of clusters and the criterion of rule selection and their results are compared to prove that the proposed method can provide proper fuzzy rules for a given system and reduce computation time while maintaining the errors of modeling as a satisfactory level.

• Ocean Systems Engineering
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• v.5 no.3
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• pp.139-160
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• 2015

The global performance of the 5MW OC4 semisubmersible floating wind turbine in random waves was numerically simulated by using the turbine-floater-mooring fully coupled and time-domain dynamic analysis program FAST-CHARM3D. There have been many papers regarding floating offshore wind turbines but the effects of second-order wave-body interactions on their global performance have rarely been studied. The second-order wave forces are actually small compared to the first-order wave forces, but its effect cannot be ignored when the natural frequencies of a floating system are outside the wave-frequency range. In the case of semi-submersible platform, second-order difference-frequency wave-diffraction forces and moments become important since surge/sway and pitch/roll natural frequencies are lower than those of typical incident waves. The computational effort related to the full second-order diffraction calculation is typically very heavy, so in many cases, the simplified approach called Newman's approximation or first-order-wave-force-only are used. However, it needs to be justified against more complete solutions with full QTF (quadratic transfer function), which is a main subject of the present study. The numerically simulated results for the 5MW OC4 semisubmersible floating wind turbine by FAST-CHARM3D are also extensively compared with the DeepCWind model test results by Technip/NREL/UMaine. The predicted motions and mooring tensions for two white-noise input-wave spectra agree well against the measure values. In this paper, the numerical static-offset and free-decay tests are also conducted to verify the system stiffness, damping, and natural frequencies against the experimental results. They also agree well to verify that the dynamic system modeling is correct to the details. The performance of the simplified approaches instead of using the full QTF are also tested.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.315-328
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• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

• International Journal of Control, Automation, and Systems
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• v.1 no.3
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• pp.289-300
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• 2003

In this paper, we introduce an identification method in Fuzzy Relation-based Fuzzy Neural Networks (FRFNN) through a hybrid identification algorithm. The proposed FRFNN modeling implement system structure and parameter identification in the efficient form of "If...., then... " statements, and exploit the theory of system optimization and fuzzy rules. The FRFNN modeling and identification environment realizes parameter identification through a synergistic usage of genetic optimization and complex search method. The hybrid identification algorithm is carried out by combining both genetic optimization and the improved complex method in order to guarantee both global optimization and local convergence. An aggregate objective function with a weighting factor is introduced to achieve a sound balance between approximation and generalization of the model. The proposed model is experimented with using two nonlinear data. The obtained experimental results reveal that the proposed networks exhibit high accuracy and generalization capabilities in comparison to other models.er models.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.303-310
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• 2005

The systems with probe and SIL(Solid Immersion Lens) mechanisms have been researched as the technology to perform NFR(Near Field Recording). Most of them use the flying head mechanism to accomplish high recording density and fast data transfer rate. In this paper, ABS shape of flying head was optimized with the object of securing the maximum compliance ability of OFH. We suggest low different optimization processes to predict the static flying characteristics for the OFH. Two different approximation methods, regression analysis and back propagation neural network were used. And we compared the result of directly connected(between CAE and optimizer) method and two approximated optimization results. Design Optimization Tool(DOT) and ${\mu}GA$ were used as the optimizers.

• 전기의세계
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• v.21 no.3
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• pp.48-52
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• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.7
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• pp.1315-1320
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• 2007

In this paper, we introduce a new fuzzy model called fuzzy combined polynomial neural networks, which are based on the representative fuzzy model named polynomial fuzzy model. In the design procedure of the proposed fuzzy model, the coefficients on consequent parts are estimated by using not general least square estimation algorithm that is a sort of global learning algorithm but weighted least square estimation algorithm, a sort of local learning algorithm. We are able to adopt various type of structures as the consequent part of fuzzy model when using a local learning algorithm. Among various structures, we select Polynomial Neural Networks which have nonlinear characteristic and the final result of which is a complex mathematical polynomial. The approximation ability of the proposed model can be improved using Polynomial Neural Networks as the consequent part.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.09a
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• pp.211-219
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• 1995

블록-삼각(Block-angular)구조를 갖는 선형 제약식과 분리되지 않는 콘벡스 목적함수의 대규모 비분리 콘벡스 최적화 문제의 해법으로 번들-분해법 (Bundle Based Decomposition)을 이용한 알고리즘 SQA(Separable Quadratic Approximation)은 비분리 콘벡스 프로그램을 분리가능한 2차계획 법(Separable Quadratic Programming) 문제로 근사화시켜 번들-분해법을 축 차적으로 적용한다. 본 연구는 수렴성(local convergence & global convergence) 및 알고리즘 구현 [1]에 이어 이에 대한 수치적용 결과를 중심 으로 소개한다. 수치 적용은 ANSI C로 작성된 SQA 프로그램을 SUN SPARC II에서 실행하였으며 이때 대규모 비분리 최적화 문제의 비분리 목 적함수와 블록-삼각 구조의 선형 제약식들이 계수들은 ANSI C의 랜덤함수 로부터 임의의 값들을 이용하였다. 이와같은 다양한 비분리 콘벡스 최적화 문제에 대한 수렴성, 반복회수 및 처리시간등의 결과와 함께 GAMS/MINOS 의 최적해를 소개한다.