• Title/Summary/Keyword: Polynomial regression model

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An Alternative Model for Determining the Optimal Fertilizer Level (수도(水稻) 적정시비량(適正施肥量) 결정(決定)에 대한 대체모형(代替模型))

  • Chang, Suk-Hwan
    • Korean Journal of Soil Science and Fertilizer
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    • v.13 no.1
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    • pp.21-32
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    • 1980
  • Linear models, with and without site variables, have been investigated in order to develop an alternative methodology for determining optimal fertilizer levels. The resultant models are : (1) Model I is an ordinary quadratic response function formed by combining the simple response function estimated at each site in block diagonal form, and has parameters [${\gamma}^{(1)}_{m{\ell}}$], for m=1, 2, ${\cdots}$, n sites and degrees of polynomial, ${\ell}$=0, 1, 2. (2) Mode II is a multiple regression model with a set of site variables (including an intercept) repeated for each fertilizer level and the linear and quadratic terms of the fertilizer variables arranged in block diagonal form as in Model I. The parameters are equal to [${\beta}_h\;{\gamma}^{(2)}_{m{\ell}}$] for h=0, 1, 2, ${\cdots}$, k site variable, m=1, 2, ${\cdots}$ and ${\ell}$=1, 2. (3) Model III is a classical response surface model, I. e., a common quadratic polynomial model for the fertilizer variables augmented with site variables and interactions between site variables and the linear fertilizer terms. The parameters are equal to [${\beta}_h\;{\gamma}_{\ell}\;{\theta}_h$], for h=0, 1, ${\cdots}$, k, ${\ell}$=1, 2, and h'=1, 2, ${\cdots}$, k. (4) Model IV has the same basic structure as Mode I, but estimation procedure involves two stages. In stage 1, yields for each fertilizer level are regressed on the site variables and the resulting predicted yields for each site are then regressed on the fertilizer variables in stage 2. Each model has been evaluated under the assumption that Model III is the postulated true response function. Under this assumption, Models I, II and IV give biased estimators of the linear fertilizer response parameter which depend on the interaction between site variables and applied fertilizer variables. When the interaction is significant, Model III is the most efficient for calculation of optimal fertilizer level. It has been found that Model IV is always more efficient than Models I and II, with efficiency depending on the magnitude of ${\lambda}m$, the mth diagonal element of X (X' X)' X' where X is the site variable matrix. When the site variable by linear fertilizer interaction parameters are zero or when the estimated interactions are not important, it is demonstrated that Model IV can be a reasonable alternative model for calculation of optimal fertilizer level. The efficiencies of the models are compared us ing data from 256 fertilizer trials on rice conducted in Korea. Although Model III is usually preferred, the empirical results from the data analysis support the feasibility of using Model IV in practice when the estimated interaction term between measured soil organic matter and applied nitrogen is not important.

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Corrosion Inhibition of Copper-nickel Alloy: Experimental and Theoretical Studies

  • Khadom, Anees A.;Yaro, Aprael S.;Musa, Ahmed Y.;Mohamad, Abu Bakar;Kadhum, Abdul Amir H.
    • Journal of the Korean Chemical Society
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    • v.56 no.4
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    • pp.406-415
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    • 2012
  • The corrosion inhibition of copper-nickel alloy by Ethylenediamine (EDA) and Diethylenetriamine (DETA) in 1.5M HCl has been investigated by weight loss technique at different temperatures. Maximum value of inhibitor efficiency was 75% at $35^{\circ}C$ and 0.2 M inhibitor concentration EDA, while the lower value was 4% at $35^{\circ}C$ and 0.01 M inhibitor concentration DETA. Two mathematical models were used to represent the corrosion rate data, second order polynomial model and exponential model respectively. Nonlinear regression analysis showed that the first model was better than the second model with high correlation coefficient. The reactivity of studied inhibitors was analyzed through theoretical calculations based on density functional theory (DFT). The results showed that the reactive sites were located on the nitrogen (N1, N2 and N4) atoms.

Structural design of Optimized Interval Type-2 FCM Based RBFNN : Focused on Modeling and Pattern Classifier (최적화된 Interval Type-2 FCM based RBFNN 구조 설계 : 모델링과 패턴분류기를 중심으로)

  • Kim, Eun-Hu;Song, Chan-Seok;Oh, Sung-Kwun;Kim, Hyun-Ki
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.66 no.4
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    • pp.692-700
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    • 2017
  • In this paper, we propose the structural design of Interval Type-2 FCM based RBFNN. Proposed model consists of three modules such as condition, conclusion and inference parts. In the condition part, Interval Type-2 FCM clustering which is extended from FCM clustering is used. In the conclusion part, the parameter coefficients of the consequence part are estimated through LSE(Least Square Estimation) and WLSE(Weighted Least Square Estimation). In the inference part, final model outputs are acquired by fuzzy inference method from linear combination of both polynomial and activation level obtained through Interval Type-2 FCM and acquired activation level through Interval Type-2 FCM. Additionally, The several parameters for the proposed model are identified by using differential evolution. Final model outputs obtained through benchmark data are shown and also compared with other already studied models' performance. The proposed algorithm is performed by using Iris and Vehicle data for pattern classification. For the validation of regression problem modeling performance, modeling experiments are carried out by using MPG and Boston Housing data.

Optimizing the composition of the medium for the viable cells of Bifidobacterium animalis subsp. lactis JNU306 using response surface methodology

  • Dang, Thi Duyen;Yong, Cheng Chung;Rheem, Sungsue;Oh, Sejong
    • Journal of Animal Science and Technology
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    • v.63 no.3
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    • pp.603-613
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    • 2021
  • This research improved the growth potential of Bifidobacterium animalis subsp lactis strain JNU306, a commercial medium that is appropriate for large-scale production, in yeast extract, soy peptone, glucose, L-cysteine, and ferrous sulfate. Response surface methodology (RSM) was used to optimize the components of this medium, using a central composite design and subsequent analyses. A second-order polynomial regression model, which was fitted to the data at first, significantly lacked fitness. Thus, through further analyses, the model with linear and quadratic terms plus two-way, three-way, and four-way interactions was selected as the final model. Through this model, the optimized medium composition was found as 2.8791% yeast extract, 2.8030% peptone soy, 0.6196% glucose, 0.2823% L-cysteine, and 0.0055% ferrous sulfate, w/v. This optimized medium ensured that the maximum biomass was no lower than the biomass from the commonly used blood-liver (BL) medium. The application of RSM improved the biomass production of this strain in a more cost-effective way by creating an optimum medium. This result shows that B. animalis subsp lactis JNU306 may be used as a commercial starter culture in manufacturing probiotics, including dairy products.

Effect of Various Regression Functions on Structural Optimizations Using the Central Composite Method (중심합성법에 의한 구조최적화에서 회귀함수변화의 영향)

  • Park, Jung-Sun;Jeon, Yong-Sung;Im, Jong-Bin
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.1
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    • pp.26-32
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    • 2005
  • In this paper, the effect of various regression models is investigated on structural optimization using the central composite method. Three bar truss and the upper platform of a satellite are optimized using various regression models that are polynomial, exponential and log functions. Response surface method is non-gradient, semi-global, discrete and fast converging in optimization problem. Sampling points are extracted by the design of experiments using the central composite method. Response surface is generated using the various regression functions. Structural analysis for calculating constraints is executed to find static and dynamic responses. From this study, it is verified that the response surface method has advantage in optimum value and computation time in comparison to other optimization methods.

Design Optimization for 3D Woven Materials Based on Regression Analysis (회귀 분석에 기반한 3차원 엮임 재료의 최적설계)

  • Byungmo, Kim;Kichan, Sim;Seung-Hyun, Ha
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.35 no.6
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    • pp.351-356
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    • 2022
  • In this paper, we present the regression analysis and design optimization for improving the permeability of 3D woven materials based on numerical analysis data. First, the parametric analysis model is generated with variables that define the gap sizes between each directional wire of the woven material. Then, material properties such as bulk modulus, thermal conductivity coefficient, and permeability are calculated using numerical analysis, and these material data are used in the polynomial-based regression analysis. The Pareto optimal solution is obtained between bulk modulus and permeability by using multi-objective optimization and shows their trade-off relation. In addition, gradient-based design optimization is applied to maximize the fluid permeability for 3D woven materials, and the optimal designs are obtained according to the various minimum bulk modulus constraints. Finally, the optimal solutions from regression equations are verified to demonstrate the accuracy of the proposed method.

A Study on the Estimation Model of Liquid Evaporation Rate for Classification of Flammable Liquid Explosion Hazardous Area (인화성액체의 폭발위험장소 설정을 위한 증발율 추정 모델 연구)

  • Jung, Yong Jae;Lee, Chang Jun
    • Journal of the Korean Society of Safety
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    • v.33 no.4
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    • pp.21-29
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    • 2018
  • In many companies handling flammable liquids, explosion-proof electrical equipment have been installed according to the Korean Industrial Standards (KS C IEC 60079-10-1). In these standards, hazardous area for explosive gas atmospheres has to be classified by the evaluation of the evaporation rate of flammable liquid leakage. The evaporation rate is an important factor to determine the zones classification and hazardous area distance. However, there is no systematic method or rule for the estimation of evaporation rate in these standards and the first principle equations of a evaporation rate are very difficult. Thus, it is really hard for industrial workplaces to employ these equations. Thus, this problem can trigger inaccurate results for evaluating evaporation range. In this study, empirical models for estimating an evaporation rate of flammable liquid have been developed to tackle this problem. Throughout the sensitivity analysis of the first principle equations, it can be found that main factors for the evaporation rate are wind speed and temperature and empirical models have to be nonlinear. Polynomial regression is employed to build empirical models. Methanol, benzene, para-xylene and toluene are selected as case studies to verify the accuracy of empirical models.

Optimizing Medium Components for the Maximum Growth of Lactobacillus plantarum JNU 2116 Using Response Surface Methodology

  • Yoo, Heeseop;Rheem, Insoo;Rheem, Sungsue;Oh, Sejong
    • Food Science of Animal Resources
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    • v.38 no.2
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    • pp.240-250
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    • 2018
  • This study was undertaken to find the optimum soy-peptone, glucose, yeast extract, and magnesium sulfate amounts for the maximum growth of Lactobacillus plantarum JNU 2116 and to assess the effects of these medium factors through the use of response surface methodology. A central composite design was used as the experimental design for the allocation of treatment combinations. In the analysis of the experiment, due to a significant lack of fit of the second-order polynomial regression model that was used at first, cubic terms were added to the model, and then two-way interaction terms were deleted from the model since they were found to be all statistically insignificant. A relative comparison among the four factors showed that the growth of L. plantarum JNU 2116 was affected strongly by yeast extract, moderately by glucose and peptone, and slightly by magnesium sulfate. The estimated optimum amounts of the medium factors for the growth of L. plantarum JNU 2116 are as follows: soy-peptone 0.213%, glucose 1.232%, yeast extract 1.97%, and magnesium sulfate 0.08%. These results may contribute to the production of L. plantarum L67 as a starter culture that may have potential application in yogurt and fermented meat products.

반응표면분석(反應表面分析)과 그의 전산화(電算化)

  • Park, Seong-Hyeon
    • Journal of Korean Society for Quality Management
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    • v.7 no.1
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    • pp.3-14
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    • 1979
  • The primary objective of this paper is to aid the scientists and engineers in applying response surface procedures to obtain optimum operating conditions for many technical fields, particularly, for industrial manufacturing process. When a set of data is available from an experimental design, it is often of interest to fit a second order polynomial regression model in k independent variables, and find the condition of the independent variables (e. g., temperature, pressure, etc.) that optimize the response variable (e. g., yield, strength, etc.). This paper proposes a method how to obtain the optimum operating condition, and how 10 find the condition by using the computer. A computer program written in FORTRAN language is attached for the readers who may want to use the computer program.

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Developement of Soil Moisture Meter using Capacitance Probe (정전용량 탐침을 이용한 토양수분 측정장치 개발)

  • Kim, Ki-Bok;Lee, Nam-Ho;Lee, Jong-Whan;Lee, Seung-Seok
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • 2001.10a
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    • pp.65-68
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    • 2001
  • This study was conducted to develop a soil moisture meter using capacitance probe. A parallel cylinder type capacitance probe (C-probe) was fabricated The 5 MHz of crystal oscillator was constructed to detect the capacitance change of the C-probe with moist soil. A third order polynomial regression model for volumetric water content having oscillation frequency changes at 5 MHz as independent variables presented the determination coefficient of 0.979 and root mean square error of $0.031\;cm^{3}cm^{3}$ for all soil samples. A prototype soil moisture meter consisting of the sample container, C-probe, oscillator, frequency counter and related signal procession units presented the correlation coefficient of 0.987 and the root mean square error of $0.032\;cm^{3}cm^{3}$ as compared with the oven drying method for unknown soil samples.

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