• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.800-802
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• 2000

In this paper, we propose the Self-Organizing Networks(SON) based on competitive Fuzzy Polynomial Neuron(FPN) for the optimal design of nonlinear process system. The SON architectures consist of layers with activation nodes based on fuzzy inference rules. Here each activation node is presented as FPN which includes either the simplified or regression Polynomial fuzzy inference rules. The proposed SON is a network resulting from the fusion of the Polynomial Neural Networks(PNN) and a fuzzy inference system. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as liner, quadratic and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. Chaotic time series data used to evaluate the performance of our proposed model.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.4
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• pp.295-303
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• 2004

Previously it has been shown that the all pole systems resulting good time responses can be characterized by so called K-polynomial. The polynomial is defined in terms of the principal characteristic ratio $\alpha_1$ and the generalized time constant $\tau$ . In this paper, Part II presents several sensitivity analyses of such systems with respect to $\alpha_1$ and $\tau$ changes. We first deal with the root sensitivity to the perturbation of $\alpha_1$ . By way of determining the unnormalized function sensitivity, both time response sensitivity and frequency response sensitivity are derived. Finally, the root sensitivity relative to $\tau$ change is also analyzed. These results provide some useful insight and background theory when we select of and l to compose a reference model of which denominator is a K-polynomial, which is illustrated by examples.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.75-81
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• 1996

Polynomial measurement error model(MEM) with one predictor is considered. It is briefly mentioned that Chan and Mak's generalized least squares estimator(GLSE) can be derived more easily if Hermite polynomial concept is applied. It is proved that GLSE derived using new procedure is equivalent to the estimator obtained from corrected score function. Finally, much simpler proof of the asymptotic behavior of GLSE than that of Chan and Mak is provided. Much simpler formula of asymptotic covariance matrix of GLSE is a part of that proof.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.38-38
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• 2000

To fulfill recent requirements for high quality products in steel rolling process, fast responding and easily tunab control system is required and ILQ(Inverse Linear Quadratic) control system may be one of such alternatives. In this paper characteristics of ILQ control and its application to BUR(Back-Up-Roll) eccentricity in strip rolling mill is discussed and compared to polynomial control approaches. Also the rolling mill model and basic principle to control thickness of srip are introduced with control effect by polynomial methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.2
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• pp.312-320
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• 2012

In this study, we introduce a new design methodology of a granular-oriented self-organizing polynomial neural networks (GoSOPNNs) that is based on multi-layer perceptron with Context-based Polynomial Neurons (CPNs) or Polynomial Neurons (PNs). In contrast to the typical architectures encountered in polynomial neural networks (PNN), our main objective is to develop a methodological design strategy of GoSOPNNs as follows : (a) The 1st layer of the proposed network consists of Context-based Polynomial Neuron (CPN). In here, CPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of Context-based Fuzzy C-Means (C-FCM) clustering method. The context-based clustering supporting the design of information granules is completed in the space of the input data while the build of the clusters is guided by a collection of some predefined fuzzy sets (so-called contexts) defined in the output space. (b) The proposed design procedure being applied at each layer of GoSOPNN leads to the selection of preferred nodes of the network (CPNs or PNs) whose local characteristics (such as the number of contexts, the number of clusters, a collection of the specific subset of input variables, and the order of the polynomial) can be easily adjusted. These options contribute to the flexibility as well as simplicity and compactness of the resulting architecture of the network. For the evaluation of performance of the proposed GoSOPNN network, we describe a detailed characteristic of the proposed model using a well-known learning machine data(Automobile Miles Per Gallon Data, Boston Housing Data, Medical Image System Data).

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.248-258
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• 2001

The main mode of heat transfer of combustion gases at high temperature is thermal radiation of the participating gases, which are mainly carbon dioxide and water vapor. Therefore, the information of the emissivities of carbon dioxide and water vapor would be very important in the thermal performance analysis of a furnace. In this study, an exponential model for the emissivities of carbon dioxide and water vapor is derived as a function of the product of the partial pressure and characteristic length and a polynomial of reciprocal of temperature. Error analysis of the calculated values from the present model is performed for the temperature ranges of 555.6∼2777.8K and the partial-pressure-length product ranges of 0.09144∼609.6 cm-atm. For carbon dioxide, the difference between the values from the present model and the Hottels chart is less than 2.5% using a polynomial in 1/T of degree of 4. For water vapor, the model can predict the emissivity within 2.5% difference using a polynomial in 1/T of degree of 3.

• ETRI Journal
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• v.27 no.6
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• pp.747-758
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• 2005

The problem of selection among competing models has been a fundamental issue in statistical data analysis. Good fits to data can be misleading since they can result from properties of the model that have nothing to do with it being a close approximation to the source distribution of interest (for example, overfitting). In this study we focus on the preference among models from a family of polynomial regressors. Three decades of research has spawned a number of plausible techniques for the selection of models, namely, Akaike's Finite Prediction Error (FPE) and Information Criterion (AIC), Schwartz's criterion (SCH), Generalized Cross Validation (GCV), Wallace's Minimum Message Length (MML), Minimum Description Length (MDL), and Vapnik's Structural Risk Minimization (SRM). The fundamental similarity between all these principles is their attempt to define an appropriate balance between the complexity of models and their ability to explain the data. This paper presents an empirical study of the above principles in the context of model selection, where the models under consideration are univariate polynomials. The paper includes a detailed empirical evaluation of the model selection methods on six target functions, with varying sample sizes and added Gaussian noise. The results from the study appear to provide strong evidence in support of the MML- and SRM- based methods over the other standard approaches (FPE, AIC, SCH and GCV).

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.7
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• pp.378-388
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• 2000

In this paper, we propose Fuzzy Polynomial Neural Networks(FPNN) based on Polynomial Neural Networks(PNN) and Fuzzy Neural Networks(FNN) for model identification of complex and nonlinear systems. The proposed FPNN is generated from the mutually combined structure of both FNN and PNN. The one and the other are considered as the premise part and consequence part of FPNN structure respectively. As the consequence part of FPNN, PNN is based on Group Method of Data Handling(GMDH) method and its structure is similar to Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and self-organizing networks that can be generated. FPNN is available effectively for multi-input variables and high-order polynomial according to the combination of FNN with PNN. Accordingly it is possible to consider the nonlinearity characteristics of process and to get better output performance with superb predictive ability. As the premise part of FPNN, FNN uses both the simplified fuzzy inference as fuzzy inference method and error back-propagation algorithm as learning rule. The parameters such as parameters of membership functions, learning rates and momentum coefficients are adjusted using genetic algorithms. And we use two kinds of FNN structure according to the division method of fuzzy space of input variables. One is basic FNN structure and uses fuzzy input space divided by each separated input variable, the other is modified FNN structure and uses fuzzy input space divided by mutually combined input variables. In order to evaluate the performance of proposed models, we use the nonlinear function and traffic route choice process. The results show that the proposed FPNN can produce the model with higher accuracy and more robustness than any other method presented previously. And also performance index related to the approximation and prediction capabilities of model is evaluated and discussed.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.423-434
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• 2004

In this paper, we introduce a new topology of Self-Organizing Polynomial Neural Networks (SOPNN) based on genetically optimized Multi-Layer Perceptron (MLP) and discuss its comprehensive design methodology involving mechanisms of genetic optimization. Let us recall that the design of the 'conventional' SOPNN uses the extended Group Method of Data Handling (GMDH) technique to exploit polynomials as well as to consider a fixed number of input nodes at polynomial neurons (or nodes) located in each layer. However, this design process does not guarantee that the conventional SOPNN generated through learning results in optimal network architecture. The design procedure applied in the construction of each layer of the SOPNN deals with its structural optimization involving the selection of preferred nodes (or PNs) with specific local characteristics (such as the number of input variables, the order of the polynomials, and input variables) and addresses specific aspects of parametric optimization. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between the approximation and generalization (predictive) abilities of the model. To evaluate the performance of the GA-based SOPNN, the model is experimented using pH neutralization process data as well as sewage treatment process data. A comparative analysis indicates that the proposed SOPNN is the model having higher accuracy as well as more superb predictive capability than other intelligent models presented previously.reviously.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.981-989
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• 2010

In this study, we introduce a new architecture of fuzzy inference system. In the fuzzy inference system, we use Fuzzy C-Means clustering algorithm to form the premise part of the rules. The membership functions standing in the premise part of fuzzy rules do not assume any explicit functional forms, but for any input the resulting activation levels of such radial basis functions directly depend upon the distance between data points by means of the Fuzzy C-Means clustering. As the consequent part of fuzzy rules of the fuzzy inference system (being the local model representing input output relation in the corresponding sub-space), four types of polynomial are considered, namely constant, linear, quadratic and modified quadratic. This offers a significant level of design flexibility as each rule could come with a different type of the local model in its consequence. Either the Least Square Estimator (LSE) or the weighted Least Square Estimator (WLSE)-based learning is exploited to estimate the coefficients of the consequent polynomial of fuzzy rules. In fuzzy modeling, complexity and interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. The performance of the fuzzy inference system is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules(clusters) and the order of polynomial in the consequent part of the rules. Accordingly we can obtain preferred model structure through an adjustment of such parameters of the fuzzy inference system. Moreover the comparative experimental study between WLSE and LSE is analyzed according to the change of the number of clusters(rules) as well as polynomial type. The superiority of the proposed model is illustrated and also demonstrated with the use of Automobile Miles per Gallon(MPG), Boston housing called Machine Learning dataset, and Mackey-glass time series dataset.