• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.3
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• pp.145-156
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• 2000

In this paper, we propose a new methodology which includes the optimal design procedure of Polynomial Neural Networks(PNN) structure for model identification of complex and nonlinear system. The proposed PNN algorithm is based on GMDA(Group Method of Data handling) method and its structure is similar to Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and can be generated. The each node of PNN structure uses several types of high-order polynomial such as linear, quadratic and cubic, and is connected as various kinds of multi-variable inputs. In other words, the PNN uses high-order polynomial as extended type besides quadratic polynomial used in GMDH, and the number of input of its node in each layer depends on that of variables used in the polynomial. The design procedure to obtain an optimal model structure utilizing PNN algorithm is shown in each stage. The study is illustrated with the aid of pH neutralization process data besides representative time series data for gas furnace process used widely for performance comparison, and shows that the proposed PNN algorithm can produce the model with higher accuracy than previous other works. And performance index related to approximation and prediction capabilities of model is evaluated and also discussed.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2633-2635
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• 2003

In this study, we propose a fuzzy polynomial neural networks (FPNN) and a genetically optimized fuzzy polynomial neural networks(GoFPNN) for identification of non-linear system. GoFPNN architecture is designed by a FPNN based on fuzzy set and its structure and parameters are optimized by genetic algorithms. A fuzzy neural networks(FNN) based on fuzzy set divide into two structures that is simplified inference structure and linear inference structure. The proposed FPNN is resulted from integration and extension of simplified and linear inference structure of FNN. The consequence structure of the FPNN consist of polynomials represented by networks using connection weights for rules. The networks comprehend simplified(Type 0), linear (Type 1), and quadratic(Type 3) inferences. The proposed FPNN can select polynomial type of consequence part for each rule. Therefore, proposed scheme can offer flexible structure design capability for a system characteristics. Moreover, GAs is applied to networks structure and parameters tuning of proposed FPNN, and its efficient application method is discussed, these subjects are result in GoFPNN that is optimal FPNN. To evaluate proposed model performance, a numerical experiment is carried out.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.149-151
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• 2005

In this paper, we propose the Optimal Polynomial Neural Networks(PNN) for nonlinear process. The PNN is based on Group Method of Data Handling(GMDH) method and its structure is similar to feedforward Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and can be generated. The each node of PNN structure uses several types of high-order polynomial such as linear, quadratic and modified quadratic, and is connected as various kinds of multi-variable inputs. The conventional PNN depends on experience of a designer that select No. of input variable, input variable and polynomial type. Therefore it is very difficult a organizing of optimized network. The proposed algorithm identified and selected No. of input variable, input variable and polynomial type by using Genetic Algorithms(GAs). In the sequel the proposed model shows not only superior results to the existing models, but also pliability in organizing of optimal network. Medical Imaging System(MIS) data is simulated in order to confirm the efficiency and feasibility of the proposed approach in this paper.

• Journal of information and communication convergence engineering
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• v.8 no.3
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• pp.317-322
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• 2010

This paper presents an algorithm generating inverse element over finite fields GF($3^m$), and constructing method of inverse element generator based on inverse element generating algorithm. An inverse computing method of an element over GF($3^m$) which corresponds to a polynomial over GF($3^m$) with order less than equal to m-1. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.10a
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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.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2891-2893
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• 2005

In this paper, we introduce a new category of Self-Organizing Fuzzy Polynomial Neural Networks (SOFPNN) that is based on a genetically optimized multi-layer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization. The conventional SOFPNN algorithm leads to a tendency to produce overly complex networks as well as a repetitive computation load by the trial and error method and/or the a repetitive parameter adjustment by designer. In order to generate a structurally and parametrically optimized network, such parameters need to be optimal. In this study, in solving the problems with the conventional SOFPNN, we introduce a new design approach of evolutionary optimized SOFPNN. Optimal parameters design available within FPN (viz. the no. of input variables, the order of the polynomial, input variables, and the no. of membership function) lead to structurally and parametrically optimized network which is more flexible as well as simpler architecture than the conventional SOFPNN. In addition, we determine the initial apexes of membership functions by genetic algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.2
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• pp.126-135
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• 2002

The study is concerned with an approach to the design of new architectures of fuzzy neural networks and the discussion of comprehensive design methodology supporting their development. We propose an Adaptive Fuzzy Polynomial Neural Networks(APFNN) based on Fuzzy Neural Networks(FNN) and Self-organizing Networks(SON) for model identification of complex and nonlinear systems. The proposed AFPNN is generated from the mutually combined structure of both FNN and SON. The one and the other are considered as the premise and the consequence part of AFPNN, respectively. As the premise structure of AFPNN, FNN uses both the simplified fuzzy inference and error back-propagation teaming rule. The parameters of FNN are refined(optimized) using genetic algorithms(GAs). As the consequence structure of AFPNN, SON is realized by a polynomial type of mapping(linear, quadratic and modified quadratic) between input and output variables. In this study, we introduce two kinds of AFPNN architectures, namely the basic and the modified one. The basic and the modified architectures depend on the number of input variables and the order of polynomial in each layer of consequence structure. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability. The availability and feasibility of the AFPNN are discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed AFPNN can produce the model with higher accuracy and predictive ability than any other method presented previously.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.1
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• pp.128-135
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• 2015

In this study, we develop the very short-term precipitation forecasting model as well as classifier based on polynomial radial basis function neural networks by using AWS(Automatic Weather Station) and KLAPS(Korea Local Analysis and Prediction System) meteorological data. The polynomial-based radial basis function neural networks is designed to realize precipitation forecasting model as well as classifier. The structure of the proposed RBFNNs consists of three modules such as condition, conclusion, and inference phase. The input space of the condition phase is divided by using Fuzzy C-means(FCM) and the local area of the conclusion phase is represented as four types of polynomial functions. The coefficients of connection weights are estimated by weighted least square estimation(WLSE) for modeling as well as least square estimation(LSE) method for classifier. The final output of the inference phase is obtained through fuzzy inference method. The essential parameters of the proposed model and classifier such ad input variable, polynomial order type, the number of rules, and fuzzification coefficient are optimized by means of Particle Swarm Optimization(PSO) and Differential Evolution(DE). The performance of the proposed precipitation forecasting system is evaluated by using KLAPS meteorological data.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.287-292
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• 2005

This paper presents a rational polynomial approximation method to estimate modal parameters of wind excited structures using incomplete noisy measurements of structural responses and partial measurements of wind velocities only. A stochastic model of the excitation wind force acting on the structure is estimated from partial measurements of wind velocities. Then the transfer functions of the structure are approximated as rational polynomial functions. From the poles and zeros of the estimated rational polynomial functions, the modal parameters, such as natural frequencies, damping ratios, and mode shapes are extracted. Since the frequency characteristics of wind forces acting on structures can be assumed as a smooth Gaussian process especially around the natural frequencies of the structures according to the central limit theorem (Brillinger, 1969; Yaglom, 1987), the estimated modal parameters are robust and reliable with respect to the assumed stochastic input models. To verify the proposed method, the modal parameters of a TV transmission tower excited by gust wind are estimated. Comparison study with the results of other researchers shows the efficacy of the suggested method.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.5
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• pp.3-12
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• 2016

Recently, the study on 5G mobile communication systems using the millimeter-wave frequency band have been actively promoted and the importance of compensation of the nonlinearity of power amplifier caused by the characteristics of millimeter-wave frequency propagation attenuation is increasing. In the paper, we propose a piecewise polynomial model based on subdivision coefficient which are characteristics of power amplifier separated linear section and a non-linear section. In addition, the structure of digital predistortion based on the proposed model and direct learning method are proposed to implement a digital predistortion. To verify the proposed model, digital predistortion based on the proposed model and direct learning method for 60 GHz power amplifier using LTE signal implemented in the FPGA. And the hardware test bench measured performance and complexity. The proposed model achieves 3.3 dB gain over the single polynomial model in terms of the ACLR and reduces 7.5 percent in terms of the complexity.