• 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.

• 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 Biomedical Engineering Research
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• v.29 no.3
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• pp.231-238
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• 2008

Nelder-Mead downhill simplex method (DSM), a kind of deterministic optimization algorithms, has been used extensively for magnetoencephalography(MEG) dipolar source localization problems because it dose not require any functional differentiation. Like many other deterministic algorithms, however, it is very sensitive to the choice of initial positions and it can be easily trapped in local optima when being applied to complex inverse problems with multiple simultaneous sources. In this paper, some modifications have been made to make up for DSM's limitations and improve the accuracy of DSM. First of all, initial point determination method for DSM using magnetic fields on the sensor surface was proposed. Secondly, Univariant-DSM combined DSM with univariant method was proposed. To verify the performance of the proposed method, it was applied to simulated MEG data and practical MEG measurements.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.18 no.10
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• pp.1203-1210
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• 2007

The multibeam surveillance radar is a state-of-art of 3D radar technology. It applies the stacked beam-on-received realized by a digital beamformer. In this paper, a method of a low target altitude extraction for multibeam surveillance radar in multipath environmental condition is proposed and investigated. The model of multipath propagation and radar generation produced from the low altitude target in multibeam surveillance radar and the nelder-mead simplex multipath reduction(NMSMR) method which enables a reliable low altitude target extraction in specular reflection situations are described. The proposed algorithm is simulated to confirm the effectiveness of proposed algorithm in accordance with a various of target altitudes and radar frequencies.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.4
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• pp.45-52
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• 1987

In this paper, merits and demerits of Nelder and Mead Penalty Function Method(SUMTNM) and Flexible Tolerance Method(FTM) are investigated from the standpoint of generality, accuracy and efficiency. SUMTNM is combined with Nelder and Method and SUMT, but FTM improves the values of the objective function by using information provided by feasible points as well as certain nonfeasible points termed near-feasible points. Therefore, FTM uses more information than SUMTNM for minimizing object function. The structural analysis of a vertically corrugated bulkhead is performed by collapse mechanism and plate buckling analysis. Based on the results of this analysis, minimum structural weight design of a corrugated bulkhead by use of above two optimization techniques is carried out by investigating the effects of sizes of bulkhead on the structural weight.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1990.10a
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• pp.101-104
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• 1990

The program which could determine cross-sectional dimensions of the box girder bridge at tile stage of preliminary design was developed using the optimal technique in this study. It could minimize the cost and time required in the design of box girder bridges and the construction with the prestressed precast segmental method. Objective cost function consisted of four independent variables such as widths and depth of the cross-section. The Nelder-Mead method was used to solve the nonconstrained nonlinear problem like this.