• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.199-209
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• 2003

When a sampling theorem holds in wavelet subspaces, sampling expansions can be a good approximation to projection expansions. Even when the sampling theorem does not hold, the scaling function series with the usual coefficients replaced by sampled function values may also be a good approximation to the projection. We refer to such series as hybrid sampling series. For this series, we shall investigate the local convergence and analyze Gibbs phenomenon.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2006년도 International Symposium on GPS/GNSS Vol.2
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• pp.101-106
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• 2006

The geoidal undulations are needed for determining the orthometric heights from the Global Positioning System GPS-derived ellipsoidal heights. There are several methods for geoidal undulation determination. The paper presents a method employing a simple architecture Two Layer Multiquadric-Biharmonic Artificial Neural Network (TLMB-ANN) to approximate an area of 4200 square kilometres quasigeoid surface with GPS-levelling data. Hardy’s Multiquadric-Biharmonic functions is used as the hidden layer neurons’ activation function and Levenberg-Marquardt algorithm is used to train the artificial neural network. In numerical examples five surfaces were compared: the gravimetric geometry hybrid quasigeoid, Support Vector Machine (SVM) model, Hybrid Fuzzy Neural Network (HFNN) model, Traditional Three Layer Artificial Neural Network (ANN) with tanh activation function and TLMB-ANN surface approximation. The effectiveness of TLMB-ANN surface approximation depends on the number of control points. If the number of well-distributed control points is sufficiently large, the results are similar with those obtained by gravity and geometry hybrid method. Importantly, TLMB-ANN surface approximation model possesses good extrapolation performance with high precision.

• International Journal of Control, Automation, and Systems
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• 제1권1호
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• pp.101-110
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• 2003

This paper introduces an identification method for nonlinear models in the form of rule-based Fuzzy-Neural Networks (FNN). In this study, the development of the rule-based fuzzy neural networks focuses on the technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The FNN modeling and identification environment realizes parameter identification through synergistic usage of clustering techniques, genetic optimization and a complex search method. We use a HCM (Hard C-Means) clustering algorithm to determine initial apexes of the membership functions of the information granules used in this fuzzy model. The parameters such as apexes of membership functions, learning rates, and momentum coefficients are then adjusted using the identification algorithm of a GA hybrid scheme. The proposed GA hybrid scheme effectively combines the GA with the improved com-plex method to guarantee both global optimization and local convergence. An aggregate objective function (performance index) with a weighting factor is introduced to achieve a sound balance between approximation and generalization of the model. According to the selection and adjustment of the weighting factor of this objective function, we reveal how to design a model having sound approximation and generalization abilities. The proposed model is experimented with using several time series data (gas furnace, sewage treatment process, and NOx emission process data from gas turbine power plants).

• Interaction and multiscale mechanics
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• 제3권3호
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• pp.277-298
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• 2010

The complex variable reproducing kernel particle method (CVRKPM) and the FEM are coupled in this paper to analyze the two-dimensional potential problems. The coupled method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, resulting in improved computational efficiency. A hybrid approximation function is applied to combine the CVRKPM with the FEM. Formulations of the coupled method are presented in detail. Three numerical examples of the two-dimensional potential problems are presented to demonstrate the effectiveness of the new method.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.719-736
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• 2005

An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs' phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.

• 정보처리학회논문지B
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• 제14B권5호
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• pp.377-382
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• 2007

본 논문에서는 방사 기저함수 네트워크의 파라미터를 전 영역에서 최적화하는 학습 알고리즘을 제안한다. 기존의 학습 알고리즘들은 지역 최적화만을 수행하기 때문에 성능의 한계가 있고 최종 결과가 초기 네트워크 파라미터 값에 크게 의존하는 단점이 있다. 본 논문에서 제안하는 하이브리드 모의 담금질 기법은 모의 담금질 기법의 전 영역 탐색 능력과 경사 기반 학습 알고리즘의 지역 최적화 능력을 조합하여 전 파라미터 영역에서 해를 찾을 수 있도록 한다. 제안하는 기법을 함수 근사화 문제에 적용하여 기존의 학습 알고리즘에 비해 더 좋은 학습 및 일반화 성능을 보이는 네트워크 파라미터를 찾을 수 있으며, 초기 파라미터 값의 영향을 크게 줄일 수 있음을 보인다.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권7호
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• pp.339-349
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• 2001

This paper suggests an optimal identification method for complex and nonlinear system modeling that is based on Fuzzy-Neural Networks(FNN). The proposed Hybrid Identification Algorithm is based on Yamakawa's FNN and uses the simplified inference as fuzzy inference method and Error Back Propagation Algorithm as learning rule. In this paper, the FNN modeling implements parameter identification using HCM algorithm and hybrid structure combined with two types of optimization theories for nonlinear systems. We use a HCM(Hard C-Means) clustering algorithm to find initial apexes of membership function. The parameters such as apexes of membership functions, learning rates, and momentum coefficients are adjusted using hybrid algorithm. The proposed hybrid identification algorithm is carried out using both a genetic algorithm and the improved complex method. Also, an aggregated objective function(performance index) with weighting factor is introduced to achieve a sound balance between approximation and generalization abilities of the model. According to the selection and adjustment of a weighting factor of an aggregate objective function which depends on the number of data and a certain degree of nonlinearity(distribution of I/O data), we show that it is available and effective to design an optimal FNN model structure with mutual balance and dependency between approximation and generalization abilities. To evaluate the performance of the proposed model, we use the time series data for gas furnace, the data of sewage treatment process and traffic route choice process.

• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Journal of the Korean Data and Information Science Society
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• 제28권3호
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• International Journal of Control, Automation, and Systems
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• 제1권3호
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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.