• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.7
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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.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.7
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.2
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• pp.398-406
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• 2011

In this paper, we introduce a new architecture of PSO-based Polynomial Neural Networks (PNN) and discuss its comprehensive design methodology. The conventional PNN is based on a extended Group Method of Data Handling (GMDH) method, and utilized the polynomial order (viz. linear, quadratic, and modified quadratic) as well as the number of node inputs fixed (selected in advance by designer) at Polynomial Neurons located in each layer through a growth process of the network. Moreover it does not guarantee that the conventional PNN generated through learning results in the optimal network architecture. The PSO-based PNN results in a structurally optimized structure and comes with a higher level of flexibility that the one encountered in the conventional PNN. The PSO-based design procedure being applied at each layer of PNN leads to the selection of preferred PNs with specific local characteristics (such as the number of input variables, input variables, and the order of the polynomial) available within the PNN. In the sequel, two general optimization mechanisms of the PSO-based PNN are explored: the structural optimization is realized via PSO whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the PSO-based PNN, the model is experimented with using Gas furnace process data, and pH neutralization process data. For the characteristic analysis of the given entire data with non-linearity and the construction of efficient model, the given entire system data is partitioned into two type such as Division I(Training dataset and Testing dataset) and Division II(Training dataset, Validation dataset, and Testing dataset). A comparative analysis shows that the proposed PSO-based PNN is model with higher accuracy as well as more superb predictive capability than other intelligent models presented previously.

• 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.