• Journal of Industrial Technology
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• v.22 no.B
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• pp.35-44
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• 2002

To find the optimal solution as rapidly and exactly as possible with Nelder-Mead simplex algorithm, the present values of the reflection, expansion, contraction and/or shrink parameters of this algorithm are needed to be changed at appropriate time during the search process. The reflection parameter is selected in this study in order to be changed because reflection, expansion and contraction process can be simultaneously effected by only this parameter. Two independent indices for determining whether the present value of the reflection parameter of this algorithm should be changed or not during the search process are suggested in this study. Those indices were made of the equations of Nelder-Mead simplex algorithm's convergence criterion and Dennis-Wood's convergence criterion, respectively. It is appeared that the optimal solution can be find with smaller numbers of objective function evaluation than the original Nelder-Mead's one with fixed parameter when the those indices are used during the search process. and the more remarkable reduction effect of the number of an objective function evaluation can be obtained when the latter index is used.

• Journal of Industrial Technology
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• v.19
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• pp.361-368
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• 1999

The Nelder-Mead simplex algorithm has become on of the most widely used methods for nonlinear unconstrained optimization, since 1965. Recently, this algorithm has been reevaluated and many papers on this algorithm are being published. The MATLAB computer software, highly renown in engineering, also provides the Nelder-Mead algorithm and the Denis-Woods modification with FMINS function. The authors made C++ code of these algorithms and compared with FMINS on the convergence behavior and the exactness of solutions. It shows that MATLAB's FMINS is inferior to author's C++ code. So, FMINS should be corrected for every user.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.710-710
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• 2012

구형펄스모형(Rectangular Pulse Model)에서 반영하지 못하는 강우의 군집특성을 잘 반영하는 NSRPM(Neyman-Scott Rectangular Pulse Model) 강우생성 모형은 수자원 분야에 널리 쓰이고 있다. 일반적으로 NSRPM의 5개의 매개변수를 추정하는 최적화기법으로 DFP(Davidon-Fletcher-Powell)과 유전자알고리즘(Genetic Algorithm)을 사용하고 있다. 그러나 DFP는 주어진 초기 값에 따라 민감하며 각 반복 단계마다 헤시안행렬(Hessian Matrix)을 계산하여야 하며 추정된 전체의 해가 국지해에 수렴 할 수 있는 단점이 있다. 유전자 알고리즘을 DFP와 다르게 헤시안 행렬을 사용하지 않고 최적화를 할 수 있다는 장점이 있으나 시간이 오래 걸리는 단점이 있다. 이에 본 연구에서는 이러한 단점을 보완, 강화 하기위해서 최적화 기법으로 반복 단계마다 미분계산이 필요하지 않고 빠른 속도로 계산이 가능한 Nelder-Mead 알고리즘 이용하여 NSRPM매개변수를 추정하고 정확도를 비교하였다. 표 1은 각 기법을 이용하여 추정된 매개변수를 이용하여 생성한 강우의 통계특성과 관측된 통계특성의 상대오차를 나타낸 것이다. 괄호 안 숫자는 중첩되지 않는 누적시간을 나타낸다. 상대오차는 다음과 같다(식 1). 분석결과 Nelder-Mead 기법이 1시간의 평균, 공분산과 6시간 분산 등 전체적으로 GA, DFP보다 높은 정확도를 보였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1105-1116
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• 2014

A stochastic rainfall model, NSRPM (Neyman-Scott Rectangular Pulse Model), is able to reflect the cluster characteristics of rainfall events which is unable in the RPM (Rectangular Pulse Model). Therefore NSRPM has advantage in the hydrological applications. The NSRPM consists of five model parameters and the parameters are estimated using optimization techniques such as DFP (Davidon-Fletcher-Powell) method and genetic algorithm. However the DFP method is very sensitive in initial values and is easily converge to local minimum. Also genetic algorithm has disadvantage of long computation time. Nelder-Mead method has several advantages of short computation time and no need of a proper initial value. In this study, the applicability of parameter estimation methods was evaluated using rainfall data of 59 national rainfall networks from 1973-2011. Overall results demonstrated that accuracy in parameter estimation is in the order of Nelder-Mead method, genetic algorithm, and DFP method.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.2
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• pp.29-37
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• 1998

Linear equations of motion for submersibles are one of the rest important design parameters, which are used as a governing equation for the shape design and the controller design. But, the estimated maneuvering coefficients in equations of motion by using empirical formulae, theoretical calculations or model tests might have some errors. Therefore the maneuvering coefficients should be verified from sea trial test. In this study, parallel extended Kalman filter method, Nelder & Mead Simplex method and genetic algorithm were applied to the parameter identification of roll maneuvering coefficients based on sea trial data. As a result, it was verified that Nelder & Mead Simplex method gave the most satisfactory results for the mathmatical models and the sea trial data used in this study.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1447-1456
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• 2017

Accurate inference of parameters of a stochastic rainfall generation model is essential to improve the applicability of the rainfall generation model which modeled the rainfall process and the structure of rainfall events. In this study, the model parameters of a stochastic rainfall generation model, NSRPM (Neyman-Scott rectangular pulse model), were estimated using DFP (Davidon-Fletcher-Powell), GA (genetic algorithm), Nelder-Mead, and DE (differential evolution) methods. Summer season hourly rainfall data of 20 rainfall observation sites within the Nakdong river basin from 1973 to 2017 were used to estimate parameters and the regional applicability of inference methods were analyzed. Overall results demonstrated that DE and Nelder-Mead methods generate better results than that of DFP and GA methods.

• Journal of Electrical Engineering and Technology
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• v.11 no.6
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• pp.1863-1871
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• 2016

This paper presents an application of fractional order controller for the control of multi input multi output twin rotor aerodynamic system. Dynamics of the considered system are highly nonlinear and there exists a significant cross-coupling between the horizontal and vertical axes (pitch & yaw). In this paper, a fractional order model of twin rotor aerodynamic system is identified using input output data from nonlinear system. Based upon identified fractional order model, a fractional order PID controller is designed to control the angular position of level bar of twin rotor aerodynamic system. The parameters of controller are tuned using Nelder-Mead optimization and compared with particle swarm optimization techniques. Simulation results on the nonlinear model show a significant improvement in the performance of fractional order PID controller as compared to a classical PID controller.

• Steel and Composite Structures
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• v.19 no.4
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• pp.995-1009
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• 2015

This study presents design optimization of spot welded structures to attain maximum strength by using the Nelder-Mead (Simplex) method. It is the main idea of the algorithm that the simulation run is executed several times to satisfy predefined convergence criteria and every run uses the starting points of the previous configurations. The material and size of the sheet plates are the pre-assigned parameters which do not change in the optimization cycle. Locations of the spot welds, on the other hand, are chosen to be design variables. In order to calculate the objective function, which is the maximum equivalent stress, ANSYS, general purpose finite element analysis software, is used. To obtain global optimum locations of spot welds a methodology is proposed by modifying the Nelder-Mead (Simplex) method. The procedure is applied to a number of representative problems to demonstrate the validity and effectiveness of the proposed method. It is shown that it is possible to obtain the global optimum values without stacking local minimum ones by using proposed methodology.

• Smart Structures and Systems
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• v.17 no.6
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• pp.957-980
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• 2016

Structural damage detection (SDD) is a challenging task in the field of structural health monitoring (SHM). As an exploring attempt to the SDD problem, a hybrid self-adaptive Firefly-Nelder-Mead (SA-FNM) algorithm is proposed for the SDD problem in this study. First of all, the basic principle of firefly algorithm (FA) is introduced. The Nelder-Mead (NM) algorithm is incorporated into FA for improving the local searching ability. A new strategy for exchanging the information in the firefly group is introduced into the SA-FNM for reducing the computation cost. A random walk strategy for the best firefly and a self-adaptive control strategy of three key parameters, such as light absorption, randomization parameter and critical distance, are proposed for preferably balancing the exploitation and exploration ability of the SA-FNM. The computing performance of the SA-FNM is evaluated and compared with the basic FA by three benchmark functions. Secondly, the SDD problem is mathematically converted into a constrained optimization problem, which is then hopefully solved by the SA-FNM algorithm. A multi-step method is proposed for finding the minimum fitness with a big probability. In order to assess the accuracy and the feasibility of the proposed method, a two-storey rigid frame structure without considering the finite element model (FEM) error and a steel beam with considering the model error are taken examples for numerical simulations. Finally, a series of experimental studies on damage detection of a steel beam with four damage patterns are performed in laboratory. The illustrated results show that the proposed method can accurately identify the structural damage. Some valuable conclusions are made and related issues are discussed as well.

• Journal of Microbiology and Biotechnology
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• v.22 no.7
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• pp.939-946
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• 2012

Antibiotic production with Streptomyces sindenensis MTCC 8122 was optimized under submerged fermentation conditions by artificial neural network (ANN) coupled with genetic algorithm (GA) and Nelder-Mead downhill simplex (NMDS). Feed forward back-propagation ANN was trained to establish the mathematical relationship among the medium components and length of incubation period for achieving maximum antibiotic yield. The optimization strategy involved growing the culture with varying concentrations of various medium components for different incubation periods. Under non-optimized condition, antibiotic production was found to be $95{\mu}g/ml$, which nearly doubled ($176{\mu}g/ml$) with the ANN-GA optimization. ANN-NMDS optimization was found to be more efficacious, and maximum antibiotic production ($197{\mu}g/ml$) was obtained by cultivating the cells with (g/l) fructose 2.7602, $MgSO_4$ 1.2369, $(NH_4)_2PO_4$ 0.2742, DL-threonine 3.069%, and soyabean meal 1.952%, for 9.8531 days of incubation, which was roughly 12% higher than the yield obtained by ANN coupled with GA under the same conditions.