• The Journal of the Korea Contents Association
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• v.15 no.1
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• pp.475-481
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• 2015

We use polynomial regression instead of linear regression if there is a nonlinear relation between a dependent variable and independent variables in a regression analysis. The performance of polynomial regression, however, may deteriorate because of the correlation caused by the power terms of independent variables. We present a polynomial regression model for the numerical inversion of PGF and show that polynomial regression results in the deterioration of the estimation of the coefficients. We apply principal components regression to the polynomial regression model and show that principal components regression dramatically improves the performance of the parameter estimation.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• Journal of Convergence for Information Technology
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• v.9 no.6
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• pp.1-6
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• 2019

In this study, the development of a weight estimation model of electronic scale with nonlinear characteristics is presented using polynomial regression analysis. The output voltage of the load cell was measured directly using the reference mass. And a polynomial regression model was obtained using the matrix and curve fitting function of MS Office Excel. The weight was measured in 100g units using a load cell electronic scale measuring up to 5kg and the polynomial regression model was obtained. The error was calculated for simple($1^{st}$), $2^{nd}$ and $3^{rd}$ order polynomial regression. To analyze the suitability of the regression function for each model, the coefficient of determination was presented to indicate the correlation between the estimated mass and the measured data. Using the third order polynomial model proposed here, a very accurate model was obtained with a standard deviation of 10g and the determinant coefficient of 1.0. Based on the theory of multi regression model presented here, it can be used in various statistical researches such as weather forecast, new drug development and economic indicators analysis using logistic regression analysis, which has been widely used in artificial intelligence fields.

• 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.

• Journal of Ocean Engineering and Technology
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• v.26 no.2
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• pp.39-47
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• 2012

The objective of this study was to develop a strength prediction model using a polynomial regression analysis based on the experimental results obtained from ninety samples. As the results of a correlation analysis between various mixing factors and unconfined compressive strength using SPSS (statistical package for the social sciences), the governing factors in the strength of lightweight soil were found to be the crumb rubber content, bottom ash content,and water-cement ratio. After selecting the governing factors affecting the strength through the correlation analysis, a strength prediction model, which consisted of the selected governing factors, was developed using the polynomial regression analysis. The strengths calculated from the proposed model were similar to those resulting from laboratory tests (R2=87.5%). Therefore, the proposed model can be used to predict the strength of lightweight mixtures with various mixing ratios without time-consuming experimental tests.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.3
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• pp.460-466
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• 2018

For the efficient energy consumption in an urban railway station, it is necessary to know the patterns of electrical loads for each usage in detail. The electrical loads in an urban railway station have different characteristics from other normal electrical load, such as the peak load timing during a day. The lighting, HVAC, communication, and commercial loads make up large amount of electrical load for equipment in an urban railway station, and each of them has the unique specificity. These loads for each usage were estimated without measuring device by the polynomial regression method with big data such as total amount of electrical load and weather data. In the simulation with real data, the optimal polynomial regression model was third order polynomial regression model with 9 or 10 independent variables.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.5
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• pp.103-109
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• 2004

This paper presents a fairing method for reverse engineering of a free-formed surface. Utilizing measured data points, reverse engineering is a useful method to construct a CAD model from physical model. Measured data points should be faired since raw data may have outliers. A fairing algorithm of polynomial regression model generates smooth curves of approximation in this paper. The faired curves are utilized to construct a free-formed surface. For a verifying example, an impeller blade is digitized with a CMM to collect raw data on the surfacce and a CAD model is constructed. This research produces impeller blades with 5-axis machining center through the CAD model and compares them with a physical model. As a result the produced surface modeled with the fairing method gives less error than that without the fairing.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.4 s.193
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• pp.93-101
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• 2007

Aluminum alloy which is one of the light materials has been tried to apply to light weight vehicle body. In order to do that, welding technology is very important. In case of the aluminum laser welding, the strength of welded part is reduced due to porosity, underfill, and magnesium loss. To overcome these problems, laser welding of aluminum with filler wire was suggested. In this study, experiment about laser welding of AA5182 aluminum alloy with AA5356 filler wire was performed according to process parameters such as laser power, welding speed and wire feed rate. The tensile strength was measured to find the weldability of laser welding with filler wire. The models to estimate tensile strength were suggested using three regression models and one neural network model. For regression models, one was the multiple linear regression model, another was the second order polynomial regression model, and the other was the multiple nonlinear regression model. Neural network model with 2 hidden layers which had 5 and 3 nodes respectively was investigated to find the most suitable model for the system. Estimation performance was evaluated for each model using the average error rate. Among the three regression models, the second order polynomial regression model had the best estimation performance. For all models, neural network model has the best estimation performance.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.254-259
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• 1998

A new design methology is proposed to identify the structure and parameters of fuzzy model using PNN 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 cubic besides the biquadratic polynomial used in the GMDH. The FPNN(Fuzzy Polynomial Neural Networks) algorithm uses PNN(Polynomial Neural networks) structure and a fuzzy inference method. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here a regression polynomial inference is based on consequence of fuzzy rules with a polynomial equations such as linear, quadratic and cubic equation. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture. In this paper, we will consider a model that combines the advantage of both FPNN and PNN. Also we use the training and testing data set to obtain a balance between the approximation and generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.

• Proceedings of the Korea Water Resources Association Conference
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• 2019.05a
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• pp.147-147
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• 2019

The Numerical Weather Prediction (NWP) models determine the future state of the weather by forcing current weather conditions into the atmospheric models. The NWP models approximate mathematically the physical dynamics by nonlinear differential equations; however these approximations include uncertainties. The errors of the NWP estimations can be related to the initial and boundary conditions and model parameterization. Development in the meteorological forecast models did not solve the issues related to the inevitable biases. In spite of the efforts to incorporate all sources of uncertainty into the forecast, and regardless of the methodologies applied to generate the forecast ensembles, they are still subject to errors and systematic biases. The statistical post-processing increases the accuracy of the forecast data by decreasing the errors. Error prediction of the NWP models which is updating the NWP model outputs or model output statistics is one of the ways to improve the model forecast. The regression methods (including linear, polynomial and scaling regression) are applied to the present study to improve the real time forecast skill. Such post-processing consists of two main steps. Firstly, regression is built between forecast and measurement, available during a certain training period, and secondly, the regression is applied to new forecasts. In this study, the WRF real-time forecast data, in comparison with the observed data, had systematic biases; the errors related to the NWP model forecasts were reflected in the underestimation of the meteorological data forecast by the WRF model. The promising results will indicate that the post-processing techniques applied in this study improved the meteorological forecast data provided by WRF model. A comparison between various bias correction methods will show the strength and weakness of the each methods.