• 한국통신학회논문지
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• 제21권1호
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• pp.251-268
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• 1996

In this paper, a higher-order feedforward neural network called ridge polynomial network (RPN) which shows good approximation capability for nonlnear continuous functions defined on compact subsets in multi-dimensional Euclidean spaces, is presented. This network provides more efficient and regular structure as compared to ordinary higher-order feedforward networks based on Gabor-Kolmogrov polynomial expansions, while maintating their fast learning property. the ridge polynomial network is a generalization of the pi-sigma network (PSN) and uses a specialform of ridge polynomials. It is shown that any multivariate polynomial can be exactly represented in this form, and thus realized by a RPN. The approximation capability of the RPNs for arbitrary continuous functions is shown by this representation theorem and the classical weierstrass polynomial approximation theorem. The RPN provides a natural mechanism for incremental function approximation based on learning algorithm of the PSN. Simulation results on several applications such as multivariate function approximation and pattern classification assert nonlinear approximation capability of the RPN.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 춘계학술대회 학술발표 논문집
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• pp.130-133
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• 2000

In this paper, a new design methodology named FNNN(Fuzzy Polynomial Neural Network) algorithm is proposed to identify the structure and parameters of fuzzy model using PNN(Polynomial Neural Network) structure and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and modified quadratic besides the biquadratic polynomial used in the GMDH. The premise of fuzzy inference rules defines by triangular and gaussian type membership function. The fuzzy inference method uses simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture Several numerical example are used to evaluate the performance of out proposed model. Also we used the training data and testing data set to obtain a balance between the approximation and generalization of proposed model.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 추계학술대회 학술발표 논문집 제14권 제2호
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• pp.433-436
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• 2004

In this paper, we introduce a new Fuzzy Polynomial Neural Networks (FPNNS)-like structure whose neuron is based on the Fuzzy Set-based Fuzzy Inference System (FS-FIS) and is different from that of FPNNS based on the Fuzzy relation-based Fuzzy Inference System (FR-FIS) and discuss the ability of the new FPNNS-like structure named Fuzzy Set-based Polynomial Neural Networks (FSPNN). The premise parts of their fuzzy rules are not identical, while the consequent parts of the both Networks (such as FPNN and FSPNN) are identical. This difference results from the angle of a viewpoint of partition of input space of system. In other word, from a point of view of FS-FIS, the input variables are mutually independent under input space of system, while from a viewpoint of FR-FIS they are related each other. The proposed design procedure for networks architecture involves the selection of appropriate nodes with specific local characteristics such as the number of input variables, the order of the polynomial that is constant, linear, quadratic, or modified quadratic functions being viewed as the consequent part of fuzzy rules, and a collection of the specific subset of input variables. On the parameter optimization phase, we adopt Information Granulation (IC) based on HCM clustering algorithm and a standard least square method-based learning. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. To evaluate the performance of the genetically optimized FSPNN (gFSPNN), the model is experimented with using the time series dataset of gas furnace process.

• International Journal of Control, Automation, and Systems
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• 제3권2호
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• pp.183-194
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• 2005

In this study, we introduce an advanced architecture of genetically optimized Hybrid Fuzzy Neural Networks (gHFNN) and develop a comprehensive design methodology supporting their construction. A series of numeric experiments is included to illustrate the performance of the networks. The construction of gHFNN exploits fundamental technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms (GAs). The architecture of the gHFNNs results from a synergistic usage of the genetic optimization-driven hybrid system generated by combining Fuzzy Neural Networks (FNN) with Polynomial Neural Networks (PNN). In this tandem, a FNN supports the formation of the premise part of the rule-based structure of the gHFNN. The consequence part of the gHFNN is designed using PNNs. We distinguish between two types of the linear fuzzy inference rule-based FNN structures showing how this taxonomy depends upon the type of a fuzzy partition of input variables. As to the consequence part of the gHFNN, the development of the PNN dwells on two general optimization mechanisms: the structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the gHFNN, the models are experimented with a representative numerical example. A comparative analysis demonstrates that the proposed gHFNN come with higher accuracy as well as superb predictive capabilities when comparing with other neurofuzzy models.

• 대한전기학회논문지:시스템및제어부문D
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• 제55권6호
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• pp.264-273
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• 2006

In this paper, we propose a new architecture of Self-Organizing Fuzzy Polynomial Neural Networks (SOFPNN) by means of consecutive optimization and also discuss its comprehensive design methodology involving mechanisms of genetic optimization. The network is based on a structurally as well as parametrically optimized fuzzy polynomial neurons (FPNs) conducted with the aid of information granulation and genetic algorithms. In structurally identification of FPN, the design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics and addresses specific aspects of parametric optimization. In addition, the fuzzy rules used in the networks exploit the notion of information granules defined over system's variables and formed through the process of information granulation. That is, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. This granulation is realized with the aid of the hard c-menas clustering method (HCM). For the parametric identification, we obtained the effective model that the axes of MFs are identified by GA to reflect characteristic of given data. Especially, the genetically dynamic search method is introduced in the identification of parameter. It helps lead to rapidly optimal convergence over a limited region or a boundary condition. To evaluate the performance of the proposed model, the model is experimented with using two time series data(gas furnace process, nonlinear system data, and NOx process data).

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 D
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• pp.2699-2701
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• 2001

The study is concerned with an approach to the design of a new category of fuzzy neural networks. The proposed Fuzzy Polynomial Neural Networks(FPNN) with hybrid multi-layer inference architecture is based on fuzzy neural networks(FNN) and polynomial neural networks(PNN) for model identification of complex and nonlinear systems. The one and the other are considered as premise and consequence part of FPNN respectively. We introduce two kinds of FPNN architectures, namely the generic and advanced types depending on the connection points (nodes) of the layer of FNN. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process and to get output performance with superb predictive ability. The availability and feasibility of the FPNN is discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed FPNN can produce the model with higher accuracy and predictive ability than any other method presented previously.

• 대한전기학회논문지:시스템및제어부문D
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• 제52권7호
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• pp.424-433
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• 2003

Evolutionary design related to the optimal design of Polynomial Neural Networks (PNNs) structure for model identification of complex and nonlinear system is studied in this paper. The PNN structure is consisted of layers and nodes like conventional neural networks but is not fixed and can be changable according to the system environments. three types of polynomials such as linear, quadratic, and modified quadratic is used in each node that is connected with various kinds of multi-variable inputs. Inputs and order of polynomials in each node are very important element for the performance of model. In most cases these factors are decided by the background information and trial and error of designer. For the high reliability and good performance of the PNN, the factors must be decided according to a logical and systematic way. In the paper evolutionary algorithm is applied to choose the optimal input variables and order. Evolutionary (genetic) algorithm is a random search optimization technique. The evolved PNN with optimally chosen input variables and order is not fixed in advance but becomes fully optimized automatically during the identification process. Gas furnace and pH neutralization processes are used in conventional PNN version are modeled. It shows that the designed PNN architecture with evolutionary structure optimization can produce the model with higher accuracy than previous PNN and other works.

• Transactions on Control, Automation and Systems Engineering
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• 제3권1호
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• pp.43-50
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• 2001

In this paper, we propose the design procedure of advance Polynomial Neural Networks(PNN) architecture for optimal model identification of complex and nonlinear system. The proposed PNN architecture is presented as the generic and advanced type. The essence of the design procedure dwells on the Group Method of Data Handling(GMDH). PNN is a flexible neural architecture whose structure is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. In this sense, PNN is a self-organizing network. With the aid of three representative numerical examples, compari-sons show that the proposed advanced PNN algorithm can produce the model with higher accuracy than previous other works. And performance index related to approximation and generalization capabilities of model is evaluated and also discussed.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제52권7호
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• pp.424-424
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• 2003

Evolutionary design related to the optimal design of Polynomial Neural Networks (PNNs) structure for model identification of complex and nonlinear system is studied in this paper. The PNN structure is consisted of layers and nodes like conventional neural networks but is not fixed and can be changable according to the system environments. three types of polynomials such as linear, quadratic, and modified quadratic is used in each node that is connected with various kinds of multi-variable inputs. Inputs and order of polynomials in each node are very important element for the performance of model. In most cases these factors are decided by the background information and trial and error of designer. For the high reliability and good performance of the PNN, the factors must be decided according to a logical and systematic way. In the paper evolutionary algorithm is applied to choose the optimal input variables and order. Evolutionary (genetic) algorithm is a random search optimization technique. The evolved PNN with optimally chosen input variables and order is not fixed in advance but becomes fully optimized automatically during the identification process. Gas furnace and pH neutralization processes are used in conventional PNN version are modeled. It shows that the designed PNN architecture with evolutionary structure optimization can produce the model with higher accuracy than previous PNN and other works.

• 전자공학회논문지CI
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• 제39권3호
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• pp.18-31
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• 2002

본 연구는 뉴로퍼지 네트워크와 다항식 뉴럴네트워크를 합성한 하이브리드 모델링 구조인 고급 뉴로퍼지 다항식 네트워크(Advanced neurofuzzy polynomial networks ; ANFPN)를 제안한다. 제안된 네트워크 구조는 높은 비선형 규칙 기반 모델로, CI(Computational Intelligence)의 기술, 즉 퍼지집합, 뉴럴네트워크, 유전자 알고리즘에 의해 설계되어진다. 뉴로퍼지 네트워크는 ANFPN 구조의 전반부를, 다항식 뉴럴네트워크는 후반부를 구성한다. ANFPN의 전반부에서, 뉴로퍼지 네트워크는 간략추론, 오류역전파 학습 규칙을 이용한다. 멤버쉽함수의 파라미터, 학습율, 모멘텀 계수는 유전자 최적화를 이용하여 조절된다. ANFPN의 후반부 구조로서 다항식 뉴럴네트워크는 학습을 통해 생성되는(전개되는) 유연한 네트워크 구조이다. 특히 다항식 뉴럴네트워크의 층과 노드 수는 고정되어 있지 않고 동적으로 생성된다. 본 연구에서는, 2가지 형태의 ANFPN 구조를 제안한다. 즉 기본 구조와 변형된 구조이다. 여기서 기본 구조와 변형된 구조는 다항식 뉴럴네트워크 구조의 각 층에서 입력변수의 수와 회귀다항식의 차수에 의존한다. 두 결합 구조의 특징 때문에 공정 시스템의 비선형적인 특성을 고려할 수 있고 보다 우수한 예측능력을 가진 좋은 출력선응을 얻을 수 있게 한다. ANFPN의 유용성과 실용성은 2개의 수치 예제를 통해 논의된다. 제안된 ANFPN은 기존의 모델보다 높은 정밀도와 예측능력을 가진 모델을 생성함을 보인다.