• Title/Summary/Keyword: third-order polynomial model

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Development of a Real-Time Soil Moisture Meter using Oscillation Frequency Shift Method

  • Kim, Ki-Bok;Lee, Nam-Ho;Lee, Jong-Whan;Lee, Seoung-Seok;Noh, Sang-Ha
    • Agricultural and Biosystems Engineering
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    • v.2 no.2
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    • pp.63-68
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    • 2001
  • The objective of this study was to develop a real-time soil moisture meter using RF impedance. The impedance suchas capacitance and resistance (or conductance) was analyzed using parallel cylinder type capacitance probe(C-probe) and Q-meter (HP4342). The capacitance and conductance of soil increased as volumetric water content increased. The 5 MHz of modified Colpitts type crystal oscillator was designed to detect the capacitance change of the C-probe with moist soil. A third order polynomial regression model was proposed to describe the relationship between RF impedance and volumetric water content. The prototype real time moisture meter consisted of the C-probe, sample container, oscillator, frequency counter and related signal processing units. The calibration equation for measurement of volumetric moisture content of soil was developed and validated. The correlation coefficient and root mean square error between measured volumetric water content by oven method and predicted values by prototype moisture meter for unknown soil samples were 0.984 and 0.032$cm^3$$cm\^3$, respectively.

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Isogeometric Collocation Method to solve the strong form equation of UI-RM Plate Theory

  • Katili, Irwan;Aristio, Ricky;Setyanto, Samuel Budhi
    • Structural Engineering and Mechanics
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    • v.76 no.4
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    • pp.435-449
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    • 2020
  • This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.

Models for Estimating Genetic Parameters of Milk Production Traits Using Random Regression Models in Korean Holstein Cattle

  • Cho, C.I.;Alam, M.;Choi, T.J.;Choy, Y.H.;Choi, J.G.;Lee, S.S.;Cho, K.H.
    • Asian-Australasian Journal of Animal Sciences
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    • v.29 no.5
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    • pp.607-614
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    • 2016
  • The objectives of the study were to estimate genetic parameters for milk production traits of Holstein cattle using random regression models (RRMs), and to compare the goodness of fit of various RRMs with homogeneous and heterogeneous residual variances. A total of 126,980 test-day milk production records of the first parity Holstein cows between 2007 and 2014 from the Dairy Cattle Improvement Center of National Agricultural Cooperative Federation in South Korea were used. These records included milk yield (MILK), fat yield (FAT), protein yield (PROT), and solids-not-fat yield (SNF). The statistical models included random effects of genetic and permanent environments using Legendre polynomials (LP) of the third to fifth order (L3-L5), fixed effects of herd-test day, year-season at calving, and a fixed regression for the test-day record (third to fifth order). The residual variances in the models were either homogeneous (HOM) or heterogeneous (15 classes, HET15; 60 classes, HET60). A total of nine models (3 orders of $polynomials{\times}3$ types of residual variance) including L3-HOM, L3-HET15, L3-HET60, L4-HOM, L4-HET15, L4-HET60, L5-HOM, L5-HET15, and L5-HET60 were compared using Akaike information criteria (AIC) and/or Schwarz Bayesian information criteria (BIC) statistics to identify the model(s) of best fit for their respective traits. The lowest BIC value was observed for the models L5-HET15 (MILK; PROT; SNF) and L4-HET15 (FAT), which fit the best. In general, the BIC values of HET15 models for a particular polynomial order was lower than that of the HET60 model in most cases. This implies that the orders of LP and types of residual variances affect the goodness of models. Also, the heterogeneity of residual variances should be considered for the test-day analysis. The heritability estimates of from the best fitted models ranged from 0.08 to 0.15 for MILK, 0.06 to 0.14 for FAT, 0.08 to 0.12 for PROT, and 0.07 to 0.13 for SNF according to days in milk of first lactation. Genetic variances for studied traits tended to decrease during the earlier stages of lactation, which were followed by increases in the middle and decreases further at the end of lactation. With regards to the fitness of the models and the differential genetic parameters across the lactation stages, we could estimate genetic parameters more accurately from RRMs than from lactation models. Therefore, we suggest using RRMs in place of lactation models to make national dairy cattle genetic evaluations for milk production traits in Korea.

A Robust Design of Response Surface Methods (반응표면방법론에서의 강건한 실험계획)

  • 임용빈;오만숙
    • The Korean Journal of Applied Statistics
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    • v.15 no.2
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    • pp.395-403
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    • 2002
  • In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.

Models Describing Growth Characteristics of Holstein Dairy Cows Raised in Korea

  • Vijayakumar, Mayakrishnan;Choy, Yun-Ho;Kim, Tae-Il;Lim, Dong-Hyun;Park, Seong-Min;Alam, Mahboob;Choi, Hee-Chul;Ki, Kwang-Seok;Lee, Hyun-Jeong
    • Journal of The Korean Society of Grassland and Forage Science
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    • v.40 no.3
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    • pp.167-176
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    • 2020
  • The objective of the present study was to determine the best model to describe and quantify the changes in live body weight, height at withers, height at rump, body length and chest girth of Holstein cows raised under Korean feeding conditions for 50 months. The five standard growth models namely polynomial linear regression models, regression of growth variables on the first and second-order of ages in days (model 1) and regression of growth variables on age covariates from first to the third-order (model 2) as well as non-linear models were fitted and evaluated for representing growth pattern of Holstein cows raised in Korean feeding circumstances. Nonlinear models fitted were three exponential growth curve models; Brody, Gompertz, and von Bertalanffy functional models. For this purpose, a total of 22 Holstein cows raised in Korea used in the period from April 2016 to May 2020. Each model fitted to monthly growth curve records of dairy cows by using PROC NLIN procedure in SAS program. On the basis of the results, nonlinear models showed the lower root mean square of error (RMSE) for live body weight, height at withers, height at rump, body length and chest girth (12.22, 1.95, 1.55, 4.04, 2.06) with higher correlation coefficiency (R2) values for live body weight, height at withers, height at rump, body length and chest girth (0.99, 0.99, 0.99, 1.00, 1.00). Overall, the evaluation of the different growth models indicated that the Gompertz model used in the study seemed to be the most appropriate one for standard growth of Holstein cows raised under Korean feeding system.

Evaluation of Dynamic p-y Curve Based on the Numerical Analysis (수치해석기반의 동적 p-y 곡선 산정)

  • Park, Jeong-Sik;Jeong, Sang-Seom
    • Journal of the Korean Geotechnical Society
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    • v.33 no.12
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    • pp.59-73
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    • 2017
  • Numerical analysis using 3D finite element program (PLAXIS 3D) evaluated the interaction of soil - pile structure under dynamic surface loading. The dynamic p-y curve of the 1-g shaking table experiment by numerical analysis was calculated, and the parametric studies were presented by considering the pile-soil condition, the pile tip condition, and the loading condition. The frequency of 1.4 Hz is almost equal to the natural frequency of the pile - soil system. The p and y values of resonance phenomenon are significantly different from the results of other frequencies. The results can be summarized by a third order polynomial function representing the trend line in the p-y curve. In the case of a single pile, the shape of the dominant curve was found to be an ellipse by mathematical proof. The elliptic equation can be used for the dynamic design or analysis of soil-pile system.

Numerical Analysis for Dynamic Characteristics of Next-Generation High-Speed Railway Bridge (차세대 고속철 통과 교량의 동적특성에 대한 수치해석)

  • Oh, Soon-Taek;Lee, Dong-Jun;Yi, Seong-Tae;Jeong, Byeong-Jun
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.26 no.2
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    • pp.9-17
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    • 2022
  • To take into account of the increasing speed of next generation high-speed trains, a new design code for the traffic safety of railway bridges is required. To solve dynamic responses of the bridge, this research offers a numerical analyses of PSC (Pre-stressed Concrete) box girder bridge, which is most representative of all the bridges on Gyungbu high-speed train line. This model takes into account of the inertial mass forces by the 38-degree-of-freedom and interaction forces as well as track irregularities. Our numerical analyses analyze the maximum vertical deflection and DAF (Dynamic Amplification Factor) between simple span and two-span continuous bridges to show the dynamic stability of the bridge. The third-order polynomial regression equations we use predict the maximum vertical deflections depending on varying running speeds of the train. We also compare the vertical deflections at several cross-sectional positions to check the influence of running speeds and the maximum irregularity at a longitudinal level. Moreover, our model analyzes the influence lines of vertical deflection accelerations of the bridge to evaluate traffic safety.

Studies on the Time Distribution of Heavy Storms (暴雨의 時間的 分布에 關한 硏究)

  • Lee, Keun-Hoo
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.26 no.2
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    • pp.69-84
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    • 1984
  • This study was carried out to investigate the time distribution of single storms and to establish the model of storm patterns in korea. Rainfall recording charts collected from 42 metheorological stations covering the Korean peninsula were analyzed. A single storm was defined as a rain period seperated from preceding and succeeding rainfall by 6 hours and more. Among the defined single storms, 1199 storms exceeding total rainfall of 80 mm were qualified for the study. Storm patterns were cklassified by quartile classification method and the relationship between cummulative percent of rainfalls and cummulative storm time was established for each quartile storm group. Time distribution models for each stations were prepared through the various analytical and inferential procedures. Obtained results are summarized as follows: 1. The percentile frequency of quartile storms for the first to the fourth quartile were 22.0%, 26.5%, 28.9% and 22.6%, respectively. The large variation of percentile frequency was show between the same quartile storms. The advanced type storm pattern was predominant in the west coastal type storm patterns predominantly when compared to the single storms with small total rainfalls. 3. The single storms with long storm durations tended to show delayed type storm patterns predominantly when compared to the single storms with short storm durations. 4. The percentile time distribution of quartile storms for 42 rin gaging stations was estimated. Large variations were observed between the percentiles of time distributions of different stations. 5. No significant differences were generally found between the time distribution of rainfalls with greater total rainfall and with less total rainfall. This fact suggests that the size of the total rainfall of single storms was not the main factor affecting the time distribution of heavy storms. 6. Also, no significant difference were found between the time distribution of rainfalls with long duration and with short duration. The fact indicates that the storm duration was no the main factor affecting the time distribution of heavy storms. 7. In Korea, among all single storms, 39.0% show 80 to 100mm of total rainfall which stands for the mode of the frequency distribution of total rainfalls. The median value of rainfalls for all single storms from the 42 stations was 108mm. The shape of the frequency distribution of total rainfalls showed right skewed features. No significant differences were shown in the shape of distribution histograms for total rainfall of quartile storms. The mode of rainfalls for the advanced type quartile storms was 80~100mm and their frequencies were 39~43% for respective quartiles. For the delayed type quartile storms, the mode was 80~100mm and their frequencies were 36!38%. 8. In Korea, 29% of all single storms show 720 to 1080 minutes of storm durations which was the highest frequency in the frequency distribution of storm durations. The median of the storm duration for all single storms form 42 stations was 1026 minutes. The shape of the frequency distribution was right skewed feature. For the advanced type storms, the higher frequency of occurrence was shown by the single storms with short durations, whereas for the delayed type quartile storms, the higher frequency was shown gy the long duration single storms. 9. The total rainfall of single storms was positively correlated to storm durations in all the stations throughout the nation. This fact was also true for most of the quartile storms. 10. The third order polynomial regression models were established for estimating the time distribution of quartile storms at different stations. The model test by relative error method resulted good agreements between estimated and observed values with the relative error of less than 0.10 in average.

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