• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.6
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• pp.948-955
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• 1987

The model reduction method of the high order linear time invariant systems is proposed. The continuous fraction expansion of Auxiliary denominator polynomial is used to obtain denominator polynomial of the reduced order model, and the numerator polynomial of the reduced order model is obtained by equating the first some moments of the original and the reduced order model, using simplified moment function. This methiod does not require the calculation of the reciprocal transformation which should be calculated in Routh approximation, furthemore the stability of the reduced order model is guaranted if original system is stable. Responses of this method showed us good characteristics.

• 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.

• Steel and Composite Structures
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• v.18 no.6
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• pp.1353-1368
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• 2015

A finite element model is presented for the analysis of composite steel-concrete beams based on a refined high-order theory. The employed theory satisfies all the kinematic and stress continuity conditions at the layer interfaces and considers effects of the transverse normal stress and transverse flexibility. The global displacement components, described by polynomial or combinations of polynomial and exponential expressions, are superposed on local ones chosen based on the layerwise or discrete-layer concepts. The present finite model does not need the incorporating any shear correction factor. Moreover, in the present $C^1$-continuous finite element model, the number of unknowns is independent of the number of layers. The proposed finite element model is validated by comparing the present results with those obtained from the three-dimensional (3D) finite element analysis. In addition to correctly predicting the distribution of all stress components of the composite steel-concrete beams, the proposed finite element model is computationally economic.

• Asian-Australasian Journal of Animal Sciences
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• v.19 no.7
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• pp.915-921
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• 2006

Various random regression models with different order of Legendre polynomials for permanent environmental and genetic effects were constructed to predict future milk yield of Holstein cows in Korea. A total of 257,908 test-day (TD) milk yield records from a total of 28,135 cows belonging to 1,090 herds were considered for estimating (co)variance of the random covariate coefficients using an expectation-maximization REML algorithm in an animal mixed model. The variances did not change much between the models, having different order of Legendre polynomial, but a decreasing trend was observed with increase in the order of Legendre polynomial in the model. The R-squared value of the model increased and the residual variance reduced with the increase in order of Legendre polynomial in the model. Therefore, a model with $5^{th}$ order of Legendre polynomial was considered for predicting future milk yield. For predicting the future milk yield of cows, 132,771 TD records from 28,135 cows were randomly selected from the above data by way of preceding partial TD record, and then future milk yields were estimated using incomplete records from each cow randomly retained. Results suggested that we could predict the next four months milk yield with an error deviation of 4 kg. The correlation of more than 70% between predicted and observed values was estimated for the next four months milk yield. Even using only 3 TD records of some cows, the average milk yield of Korean Holstein cows would be predicted with high accuracy if compared with observed milk yield. Persistency of each cow was estimated which might be useful for selecting the cows with higher persistency. The results of the present study suggested the use of a $5^{th}$ order Legendre polynomial to predict the future milk yield of each cow.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.4
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• pp.534-540
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• 2014

In this paper, we propose a fuzzy combined Polynomial Neural Network(PNN) for pattern classification. The fuzzy combined PNN comes from the generic TSK fuzzy model with several linear polynomial as the consequent part and is the expanded version of the fuzzy model. The proposed pattern classifier has the polynomial neural networks as the consequent part, instead of the general linear polynomial. PNNs are implemented by stacking the simple polynomials dynamically. To implement one layer of PNNs, the various types of simple polynomials are used so that PNNs have flexibility and versatility. Although the structural complexity of the implemented PNNs is high, the PNNs become a high order-multi input polynomial finally. To estimate the coefficients of a polynomial neuron, The weighted linear discriminant analysis. The output of fuzzy rule system with PNNs as the consequent part is the linear combination of the output of several PNNs. To evaluate the classification ability of the proposed pattern classifier, we make some experiments with several machine learning data sets.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2003.04a
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• pp.229-236
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• 2003

In this study, for efficient replacemen of sensor modelling of high-resolution satellite imagery, image segmentation method is applied to the test area of the SPOT-3 satellite imagery. After that, a third-order polynomial model in the sectioned area is compared with the RFM which is to the entire in the test area. As results, plane error of the third-order polynomial model is lower(approximately 0.8m) than that of RFM. On the other hand, height error of RFM is lower(approximately 1.0m).

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.135-142
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• 2012

In this paper, we proposed a new architecture called radial basis function-based polynomial neural networks classifier that consists of heterogeneous neural networks such as radial basis function neural networks and polynomial neural networks. The underlying architecture of the proposed model equals to polynomial neural networks(PNNs) while polynomial neurons in PNNs are composed of Fuzzy-c means-based radial basis function neural networks(FCM-based RBFNNs) instead of the conventional polynomial function. We consider PNNs to find the optimal local models and use RBFNNs to cover the high dimensionality problems. Also, in the hidden layer of RBFNNs, FCM algorithm is used to produce some clusters based on the similarity of given dataset. The proposed model depends on some parameters such as the number of input variables in PNNs, the number of clusters and fuzzification coefficient in FCM and polynomial type in RBFNNs. A multiobjective particle swarm optimization using crowding distance (MoPSO-CD) is exploited in order to carry out both structural and parametric optimization of the proposed networks. MoPSO is introduced for not only the performance of model but also complexity and interpretability. The usefulness of the proposed model as a classifier is evaluated with the aid of some benchmark datasets such as iris and liver.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.2C
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• pp.191-199
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• 2006

In this paper, we propose a method to implement a predistorter of the $rho$-th order inverse filter structure to prevent signal distortion and spectral re-growth due to the high PAPR (peak-to-average ratio) of the OFDM signals and the non-linearity of high-power amplifiers. We model the memory-less non-linearity of the high-power amplifier with a polynomial model and utilize the inverse of the model, the $rho$-th order inverse filter, for the predistorter. Once the non-linearity is modeled with a polynomial, since we can determine the $rho$-th order inverse filter only with the coefficients of the polynomial, large memory is not required. To update the coefficients of the non-linear high-power amplifier model, we can use LMS or RLS algorithms. The convergence speed is high since the number of coefficients is small, and the computation is simple since manipulation of complex numbers is not necessary.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.660-669
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• 1987

Routh approximation method is the most computationally attractive. But this method may cause time-response error because this method does not match the time-response directly. In this paper a new mixed method for obtaining stable reduced-order models for high-order continuous-time systems is proposed. It makes use of the advantages of the Routh approximation method and the Minimization of Integral Squared Error(MISE) criterion approach. In this mixed method the characteristic polynomial of the reduced-order model is first obtained from that of original system by using the Auxiliary Denominator Polynomial(ADP). The numerator polynomial is then determined so as to minimize the intergral squared-error of unit step responses. The advantages of the propsed method are that the reduced models are always stable if the original system are stable and the frequency domain and time domain characteristic of the original system will be preserved in the reduced models.

• Journal of the Korean Statistical Society
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• v.9 no.1
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• pp.61-77
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• 1980

In response surface experiments, a polynomial model is often used to fit the response surface by the method of least squares. However, if the vectors of predictor variables are multicollinear, least squares estimates of the regression parameters have a high probability of being unsatisfactory. Hoerland Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using "ridge" estimates in place of the least squares estimates. Ridge regrssion theory in literature has been mainly concerned with selection of k for the first order polynomial regression model and the precision of $\hat{\beta}(k)$, the ridge estimator of regression parameters. The problem considered in this paper is that of selecting k of ridge regression for a given polynomial regression model with an arbitrary order. A criterion is proposed for selection of k in the context of integrated mean square error of fitted responses, and illustrated with an example. Also, a type of admissibility condition is established and proved for the propose criterion.criterion.