• Title/Summary/Keyword: Polynomial fitting model

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Minimization of Surface Roughness for High Speed Machining by Surface Fitting (곡면 Fitting을 이용한 고속가공 표면거칠기의 최소화)

  • Jung Jong-Yun;Cho Hea-Young;Lee Choon-Man;Moon Dug-Hee
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.27 no.2
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    • pp.37-43
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    • 2004
  • High speed machining is a machining process which cuts materials with the fast movement and rotation of a spindle in a machine tool. It reduces machining time because of the high feed and the high speed of a spindle. In addition it gets rid of post processes for high precision machining. When the high speed machining is applied to especially hardened steel, operators should select the proper parameters of machining. This can produce machining surfaces which is qualified with good surface roughness. This paper presents a method for selecting machining parameters to minimize surface roughness with high speed machining in cutting the hardened steels. Experimental data for surface roughness are collected in a machining shop based on the cutting feed and the spindle rotation. The data fits in hi-cubic polynomial surface of mathematical form. From the model this research minimize the surface roughness to find the optimal values of the feed and the spindle speed. This paper presents a program which automatically generates optimal solutions from the raw data of experiments.

Estimation of Covariance Functions for Growth of Angora Goats

  • Liu, Wenzhong;Zhang, Yuan;Zhou, Zhongxiao
    • Asian-Australasian Journal of Animal Sciences
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    • v.22 no.7
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    • pp.931-936
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    • 2009
  • Body weights of 862 Angora goats between birth and 36 months of age, recorded on a semiyearly basis from 1988 to 2000, were used to estimate genetic, permanent environmental and phenotypic covariance functions. These functions were estimated by fitting a random regression model with 6th order polynomial for direct additive genetic and animal permanent environmental effects and 4th and 5th order polynomial for maternal genetic and permanent environmental effects, respectively. A phenotypic covariance function was estimated by modelling overall animal and maternal effects. The results showed that the most variable coefficient was the intercept for both direct and maternal additive genetic effects. The direct additive genetic (co)variances increased with age and reached a maximum at about 30 months, whereas the maternal additive genetic (co)variances increased rapidly from birth and reached a maximum at weaning, and then decreased with age. Animal permanent environmental (co)variances increased with age from birth to 30 months with lower rate before 12 months and higher rate between 12 and 30 months. Maternal permanent environmental (co)variances changed little before 6 months but then increased slowly and reached a maximum at about 30 months. These results suggested that the contribution of maternal additive genetic and permanent environmental effects to growth variation differed from those of direct additive genetic and animal permanent environmental effects not only in expression time, but also in action magnitude. The phenotypic (co)variance estimates increased with age from birth to 36 months of age.

Dynamic increase factor for progressive collapse analysis of semi-rigid steel frames

  • Zhu, Yan Fei;Chen, Chang Hong;Yao, Yao;Keer, Leon M.;Huang, Ying
    • Steel and Composite Structures
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    • v.28 no.2
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    • pp.209-221
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    • 2018
  • An empirical and efficient method is presented for calculating the dynamic increase factor to amplify the applied loads on the affected bays of a steel frame structure with semi-rigid connections. The nonlinear static alternate path analysis is used to evaluate the dynamic responses. First, the polynomial models of the extended end plate and the top and seat connection are modified, and the proposed polynomial model of the flush end plate connection shows good agreement as compared with experimental results. Next, a beam model with nonlinear spring elements and plastic hinges is utilized to incorporate the combined effect of connection flexibility and material nonlinearity. A new step-by-step analysis procedure is established to obtain quickly the dynamic increase factor based on a combination of the pushdown analysis and nonlinear dynamic analysis. Finally, the modified dynamic increase factor equation, defined as a function of the maximum ratio value of energy demand to energy capacity of an affected beam, is derived by curve fitting data points generated by the different analysis cases with different column removal scenarios and five types of semi-rigid connections.

Thermal Behavior of Critical Micelle Concentration from the Standpoint of Flory-Huggins Model

  • Lim, Kyung-Hee
    • Bulletin of the Korean Chemical Society
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    • v.30 no.9
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    • pp.2001-2006
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    • 2009
  • Temperature dependence of the critical micelle concentration (CMC), $x_{CMC}$, in micellization can be described by ln $x_{CMC}$ = A + BT + C lnT + D/T, which has been derived statistical-mechanically. Here A, B, C, and D are fitting parameters. The equation fits the CMC data better than conventionally used polynomial equations of temperature. Moreover, it yields the unique(exponent) value of 2 when the CMC is expressed in a power-law form. This finding is quite significant, because it may point to the universality of the thermal behavior of CMC. Hence, in this article, the nature of the equation ln $x_{CMC}$ = A + BT + C lnT + D/T is examined from a lattice-theory point of view through the Flory-Huggins model. It is found that a linear behavior of heat capacity change of micellization is responsible for the CMC equation of temperature.

A Study on the Modal Parameters of the scaled building structure (축소 건물모델의 모달 파라미터 추정에 관한 연구)

  • Park, Hae-Dong;Park, Jin-Il;Choi, Hyun;Kim, Doo-Hoon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.06a
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    • pp.571-575
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    • 2000
  • The physical properties of the spatial model, mass, stiffness and damping matrix, can be defined by a specific natural frequency, damping ratio and mode shape. These modal parameters can be determined from a set of frequency response function(FRF) measured by exciting the structure and measuring the responses at various points around the structure. In this paper, The Transfer Matrix is obtained by experimental modal analysis for the 3-story scaled building model which TMD is installed on top and the physical properties of the spatial model is determined using the residue matrix and the location of poles from FRF measurement using polynomial curve fitting methods.

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A Study On the Simulation Model of the Transformation of Random Variables Using FBI (Fortran Based Interpreter) (FBI(Fortran Based Interpreter)를 이용한 확률변수 변환의 시뮬레이션 모델에 관한 연구)

  • Kim, Won-Gyeong
    • Journal of Korean Institute of Industrial Engineers
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    • v.13 no.2
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    • pp.105-115
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    • 1987
  • Although there are many theoretical methods for the transformation of random variables. it is difficult to find probability density functions for the new random variables because of the complexity in mathematics. The author developed a simulation model solving the above difficulties using FBI (Fortran Based Interpreter) routines. The FBI is a kind of language Interpreter analyzing the arithmetic statement in character data forms. In this paper. the FBI routines will be explained and the structure and applications of simulation model will be also demonstrated. Polynomial curve fitting method is applied to define the probability density function which can not be defined by well-known pdf. This program can also be used for instructing mathematical statistics and identifying distribution of the simulated data.

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The Choice of an Optimal Growth Function Considering Environmental Factors and Production Style (생산방식과 환경요인들을 고려한 최적성장함수의 선택에 관한 연구)

  • Choi, Jong Du
    • Environmental and Resource Economics Review
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    • v.13 no.4
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    • pp.717-734
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    • 2004
  • This paper examined the statistical goodness-of-fit tests for biological growth model in bioeconomic analysis. Some authors estimated usually growth function for fish in the world. However, few studies have estimated growth equations for the bivalve species. Thus, this paper studied the common functional forms of fitting growth equations for cham scallops considering environmental factors and production styles. The following functional forms are considered: linear, log-reciprocal, double log, polynomial and linear with interactions. Results of fitting these various functional forms with real data are compared and evaluated using standard statistical goodness-of-fit tests. Results also indicate that log-reciprocal function is statistically the best fit to the real data. Therefore, the log-reciprocal function is decided the best function describing cham scallop biological growth and hence might be useful for economic evaluation(i.e., optimal harvesting time).

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Assay Error for Improved Pharmacokinetic Modeling and Simulation of Vancomycin (반코마이신의 약물동태학적 모델링과 시뮬레이션의 향상을 위한 분석오차)

  • Burm, Jin Pil
    • YAKHAK HOEJI
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    • v.57 no.1
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    • pp.32-36
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    • 2013
  • The purpose of this study was to determine the influence of assay error for improved pharmacokinetic modeling and simulation of vancomycin on the Bayesian and nonlinear least squares regression analysis in 24 Korean gastric cancer patients. Vancomycin 1.0 g was administered intravenously over 1 hr every 12 hr. Three specimens were collected at 72 hr after the first dose from all patients at the following times, at 0.5 hr before regularly scheduled infusion, at 0.5 hr and 2 hr after the end of 1 hr infusion. Serum vancomycin levels were analyzed by fluorescence polarization immunoassay technique with TDX-FLX. The standard deviation (SD) of the assay over its working range had been determined at the serum vancomycin concentrations of 0, 20, 40, 60, 80 and $120{\mu}g/ml$ in quadruplicate. The polynomial equation of vancomycin assay error was found to be SD $({\mu}g/ml)=0.0224+0.0540C+0.00173C^2$ ($R^2=0.935$). There were differences in the influence of weight with vancomycin assay error on pharmacokinetic parameters of vancomycin using the nonlinear least squares regression analysis but there were no differences on the Bayesian analysis. This polynomial equation can be used to improve the precision of fitting of pharmacokinetic models to optimize the process of model simulation both for population and for individualized pharmacokinetic models. The result suggests the improvement of dosage regimens for the better and safer care of patients receiving vancomycin.

Parametric model for the dielectric function of InGaAs alloy films (Parametric model을 이용한 InGaAs 박막의 유전함수 연구)

  • 인용섭;김태중;최재규;김영동
    • Journal of the Korean Vacuum Society
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    • v.12 no.1
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    • pp.20-24
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    • 2003
  • We Performed the modeling of the dielectric functions of InGaAs by using the parametric semiconductor model. Parametric model describes the analytic dielectric function as the summation of several energy-bounded Gaussian-broadened polynomials and provides a reasonably well parameterized function which can accurately reproduce the optical constants of InGaAs materials. We obtained the values of fitting parameters of an arbitrary composition $\chi$ through the parametric model. And then, from these parameters we could obtain the unknown dielectric functions of InGaAs alloy films ($0\leq\chi\leq1$).

A developed design optimization model for semi-rigid steel frames using teaching-learning-based optimization and genetic algorithms

  • Shallan, Osman;Maaly, Hassan M.;Hamdy, Osman
    • Structural Engineering and Mechanics
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    • v.66 no.2
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    • pp.173-183
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    • 2018
  • This paper proposes a developed optimization model for steel frames with semi-rigid beam-to-column connections and fixed bases using teaching-learning-based optimization (TLBO) and genetic algorithm (GA) techniques. This method uses rotational deformations of frame members ends as an optimization variable to simultaneously obtain the optimum cross-sections and the most suitable beam-to-column connection type. The total cost of members plus connections cost of the frame are minimized. Frye and Morris (1975) polynomial model is used for modeling nonlinearity of semi-rigid connections, and the $P-{\Delta}$ effect and geometric nonlinearity are considered through a stepped analysis process. The stress and displacement constraints of AISC-LRFD (2016) specifications, along with size fitting constraints, are considered in the design procedure. The developed model is applied to three benchmark steel frames, and the results are compared with previous literature results. The comparisons show that developed model using both LTBO and GA achieves better results than previous approaches in the literature.