• The Journal of the Korea Contents Association
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• v.11 no.3
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• pp.48-55
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• 2011

In this paper, we analyze the input-output characteristics of fuzzy inference systems according to the division of entire input spaces and the fuzzy reasoning methods to identify the fuzzy model for nonlinear process. And fuzzy model is expressed by identifying the structure and parameters of the system by means of input variables, fuzzy partition of input spaces, and consequence polynomial functions. In the premise part of the rules Min-Max method using the minimum and maximum values of input data set and C-Means clustering algorithm forming input data into the hard clusters are used for identification of fuzzy model and membership function is used as a series of triangular membership function. In the consequence part of the rules fuzzy reasoning is conducted by two types of inferences. The identification of the consequence parameters, namely polynomial coefficients, of the rules are carried out by the standard least square method. And lastly, we use gas furnace process which is widely used in nonlinear process and we evaluate the performance for this nonlinear process.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2567-2569
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• 2003

본 논문은 비선형 시스템의 퍼지모델을 위해 정보 Granules 기반 퍼지추론 시스템 모델의 최적화를 제시한다. 퍼지모델은 주로 경험적 방법에 의해 추출되기 때문에 보다 구체적이고 체계적인 방법에 의한 동정 및 최적화 될 필요성이 요구된다. 제안된 규칙베이스 퍼지모델은 HCM 클러스터링 방법, 컴플렉스 알고리즘 및 퍼지추론 방법을 이용하여 시스템 구조와 파라미터 동정을 수행한다. 두 가지 형태의 퍼지모델 추론 방법은 간략추론, 선형추론에 의해 시행된다. 본 논문에서는 퍼지모델의 입력변수와 퍼지 입력 공간 분할 및 입출력 데이타의 중심값을 구해서 후반부 다항식함수에 의한 정보 Granules 기반 구조 동정과 파라미터 동정을 통해 비선형 시스템을 표현한다. 전반부 파라미터의 동정에는 HCM 클러스터링 방법과 컴플렉스 알고리즘을 사용하고, 후반부는 표준 HCM 클러스터링과 표준 최소자승법을 사용하여 동정한다. 그리고 학습 및 테스트 데이타의 성능견과의 상호균형을 얻기 위한 하중값을 가진 성능지수를 제시함으로써 근사화와 예측성능의 향상을 꾀한다. 제안된 비선형 모델의 성능평가를 통해 그 우수성을 보인다.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.2
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• pp.20-28
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• 1998

To accurately predict the motion of a submergible, the nonlinear structure of dynamic model should be selected and corresponding parameters should be estimated using model test. Providing the model structure, only the values of parameters are unknown and the estimation can thus be formulated as a standard least square problem. Unfortunately, the nonlinear model structure of submersibles is rarely known a prior and method of model structure determination from measurement data of model test should be developed and included as a vital part of the estimation procedure. In this study, the well-known linear least square algorithm for the analysis of model tests and a way to measure the goodness are reviewed, and the identification algorithm based on an orthogonal decomposition method of Gram-Schmidt is extended to combine structure selection and maneuvering coefficients estimation in a very simple and efficient manner. Finally, the efficiency of this algorithm is verified by using simulation and applying to the analysis of model test of a submerged body. As a result, it was verified that this combined method might be very erective in selecting the structure of dynamic model estimating the maneuvering coefficients from measurement fiat of model test.

• Environmental and Resource Economics Review
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• v.24 no.4
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• pp.607-627
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• 2015

As observed and experienced in EU ETS, allowance price volatility is one of major concerns in decision making process for $CO_2$ abatement investment. The problem of linearly non-separable profits functions could emerge when one power company holds several power plants with different technology specifications. Under this circumstance, conventional analytical solution for investment option is no longer available, thereby calling for the development of numerical analysis. This paper attempts to develop a Monte-Carlo least squares model to analyze investment options for power companies under emission trading scheme regulations. Stochastic allowance price is considered, and simulation is performed to verify model performance.

• Journal of Digital Convergence
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• v.14 no.1
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• pp.203-209
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• 2016

In this paper, we introduce a fuzzy inference systems for nonlinear inference using fuzzy cluster. Typically, the generation of fuzzy rules for nonlinear inference causes the problem that the number of fuzzy rules increases exponentially if the input vectors increase. To handle this problem, the fuzzy rules of fuzzy model are designed by dividing the input vector space in the scatter form using fuzzy clustering algorithm which expresses fuzzy cluster. From this method, complex nonlinear process can be modeled. The premise part of the fuzzy rules is determined by means of FCM clustering algorithm with fuzzy clusters. The consequence part of the fuzzy rules have four kinds of polynomial functions and the coefficient parameters of each rule are estimated by using the standard least-squares method. And we use the data widely used in nonlinear process for the performance and the nonlinear characteristics of the nonlinear process. Experimental results show that the non-linear inference is possible.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.11
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• pp.5379-5388
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• 2012

In fuzzy modeling for nonlinear process, the fuzzy rules are typically formed by selection of the input variables, the number of space division and membership functions. The Generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, complex nonlinear process can be modeled by generating the fuzzy rules by means of fuzzy division of input space. Therefore, in this paper, rules of non-fuzzy inference systems are generated by partitioning the input space in the scatter form using HCM clustering algorithm. The premise parameters of the rules are determined by membership matrix by means of HCM clustering algorithm. The consequence part of the rules is represented in the form of polynomial functions and the consequence parameters of each rule are identified by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process. Through this experiment, we showed that high-dimensional nonlinear systems can be modeled by a very small number of rules.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.5 no.4
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• pp.224-231
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• 2012

In this paper, we introduce a fuzzy inference systems based on fuzzy c-means clustering algorithm for fuzzy modeling of nonlinear process. Typically, the generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, the fuzzy rules of fuzzy model are generated by partitioning the input space in the scatter form using FCM clustering algorithm. The premise parameters of the fuzzy rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the coefficient parameters of each rule are determined by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process.

• Sleep Medicine and Psychophysiology
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• v.6 no.1
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• pp.52-60
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• 1999

Objectives: With the object of finding the appropriate conditions and algorithms for dimensional analysis of human EEG, we calculated correlation dimensions in the various condition of sampling rate and data aquisition time and improved the computation algorithm by taking advantage of bit operation instead of log operation. Methods: EEG signals from 13 scalp lead of a man were digitized with A-D converter under the condition of 12 bit resolution and 1000 Hertz of sampling rate during 32 seconds. From the original data, we made 15 time series data which have different sampling rate of 62.5, 125, 250, 500, 1000 hertz and data acqusition time of 10, 20, 30 second, respectively. New algorithm to shorten the calculation time using bit operation and the Least Trimmed Squares(LTS) estimator to get the optimal slope was applied to these data. Results: The values of the correlation dimension showed the increasing pattern as the data acquisition time becomes longer. The data with sampling rate of 62.5 Hz showed the highest value of correlation dimension regardless of sampling time but the correlation dimension at other sampling rates revealed similar values. The computation with bit operation instead of log operation had a statistically significant effect of shortening of calculation time and LTS method estimated more stably the slope of correlation dimension than the Least Squares estimator. Conclusion: The bit operation and LTS methods were successfully utilized to time-saving and efficient calculation of correlation dimension. In addition, time series of 20-sec length with sampling rate of 125 Hz was adequate to estimate the dimensional complexity of human EEG.

• Journal of the Korean Institute of Intelligent Systems
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• v.9 no.5
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• pp.555-565
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• 1999

The optimal identification algorithm of fuzzy systems is presented for rule-based fuzzy modeling of nonlinear complex systems. Nonlinear systems are expressed using the identification of structure such as input variables and fuzzy input subspaces, and parameters of a fuzzy model. In this paper, the rule-based fuzzy modeling implements system structure and parameter identification using the fuzzy inference methods and hybrid structure combined with two types of optimization theories for nonlinear systems. Two types of inference methods of a fuzzy model are the simplified inference and linear inference. The proposed hybrid optimal identification algorithm is carried out using both a genetic algorithm and the improved complex method. Here, a genetic algorithm is utilized for determining initial parameters of membership function of premise fuzzy rules, and the improved complex method which is a powerful auto-tuning algorithm is carried out to obtain fine parameters of membership function. Accordingly, in order to optimize fuzzy model, we use the optimal algorithm with a hybrid type for the identification of premise parameters and standard least square method for the identification of consequence parameters of a fuzzy model. Also, an aggregate performance index with weighting factor is proposed to achieve a balance between performance results of fuzzy model produced for the training and testing data. Two numerical examples are used to evaluate the performance of the proposed model.

• Korean Journal of Optics and Photonics
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• v.4 no.4
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• pp.397-402
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• 1993

This paper presents a new computational algorithm of phase-shifting interferometry which can effectively eliminate the uncertainty errors of the reference phases encountered in obtaining multiple interferograms. The algorithm treats the reference phases as additional unknowns and determines their exact values by analyzing interferograms using numerical least square technique. A series of simulations prove that this algorithm can improve measuring accuracy being unaffected by the nonlinear and random errors of phase-shifters.