• Title/Summary/Keyword: Polynomial regression model

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Efficient Optimization of the Suspension Characteristics Using Response Surface Model for Korean High Speed Train (반응표면모델을 이용한 한국형 고속전철 현가장치의 효율적인 최적설계)

  • Park, C.K.;Kim, Y.G.;Bae, D.S.;Park, T.W.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.6
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    • pp.461-468
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    • 2002
  • Computer simulation is essential to design the suspension elements of railway vehicle. By computer simulation, engineers can assess the feasibility of the given design factors and change them to get a better design. But if one wishes to perform complex analysis on the simulation, such as railway vehicle dynamic, the computational time can become overwhelming. Therefore, many researchers have used a surrogate model that has a regression model performed on a data sampling of the simulation. In general, metamodels(surrogate model) take the form y($\chi$)=f($\chi$)+$\varepsilon$, where y($\chi$) is the true output, f($\chi$) is the metamodel output, and is the error. In this paper, a second order polynomial equation is used as the RSM(response surface model) for high speed train that have twenty-nine design variables and forty-six responses. After the RSM is constructed, multi-objective optimal solutions are achieved by using a nonlinear programming method called VMM(variable matric method) This paper shows that the RSM is a very efficient model to solve the complex optimization problem.

Modeling the growth of Listeria monocytogenes during refrigerated storage of un-packaging mixed press ham at household

  • Lee, Seong-Jun;Park, Myoung-Su;Bahk, Gyung-Jin
    • Journal of Preventive Veterinary Medicine
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    • v.42 no.4
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    • pp.143-147
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    • 2018
  • The present study aimed to develop growth prediction models of Listeria monocytogenes in processed meat products, such as mixed pressed hams, to perform accurate microbial risk assessments. Considering cold storage temperatures and the amount of time in the stages of consumption after opening, the growth of L. monocytogenes was determined as a function of temperature at 0, 5, 10, and $15^{\circ}C$, and time at 0, 1, 3, 6, 8, 10, 15, 20, 25, and 30 days. Based on the results of these measurements, a Baranyi model using the primary model was developed. The input parameters of the Baranyi equation in the variable temperature for polynomial regression as a secondary model were developed: $SGR=0.1715+0.0199T+0.0012T^2$, $LT=5.5730-0.3215T+0.0051T^2$ with $R^2$ values 0.9972 and 0.9772, respectively. The RMSE (Root mean squared error), $B_f$ (bias factor), and $A_f$ (accuracy factor) on the growth prediction model were determined to be 0.30, 0.72, and 1.50 in SGR (specific growth rate), and 0.10, 0.84, and 1.35 in LT (lag time), respectively. Therefore, the model developed in this study can be used to determine microorganism growth in the stages of consumption of mixed pressed hams and has potential in microbial risk assessments (MRAs).

Software Cost Estimation Model Based on Use Case Points by using Regression Model (회귀분석을 이용한 UCP 기반 소프트웨어 개발 노력 추정 모델)

  • Park, Ju-Seok;Yang, Hea-Sool
    • The Journal of the Korea Contents Association
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    • v.9 no.8
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    • pp.147-157
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    • 2009
  • Recently, there has been continued research on UCP from the development effort estimation method to a software development project applying object oriented development methodology. Current research proposes a linear model estimating the developmenteffort by multiplying a constant to AUCP which applies technical and environmental factors. However, the fact that a non-linear regression model is more appropriate as the software size increases, the development period increases exponentially. In addition, in the UCP calculation process the occurrence of FP errors due to the application of TCF and EF, it is unrealistic to estimate the size with AUCP. This paper presents the issue of current research based on UCP without considering problems of the research, for example, TCF and EF and expresses the models (linear, logarithmic, polynomial, power and exponential type) estimating the development effort directly from UUCP. Consequently, the exponential model within non-linear models exhibit more accurate results than the current linear model. Therefore, after calculating the UUCP of the developing software system, using the proposed model to estimate the development effort, it is possible to estimate the direct cost required in development.

Analytical and experimental exploration of sobol sequence based DoE for response estimation through hybrid simulation and polynomial chaos expansion

  • Rui Zhang;Chengyu Yang;Hetao Hou;Karlel Cornejo;Cheng Chen
    • Smart Structures and Systems
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    • v.31 no.2
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    • pp.113-130
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    • 2023
  • Hybrid simulation (HS) has attracted community attention in recent years as an efficient and effective experimental technique for structural performance evaluation in size-limited laboratories. Traditional hybrid simulations usually take deterministic properties for their numerical substructures therefore could not account for inherent uncertainties within the engineering structures to provide probabilistic performance assessment. Reliable structural performance evaluation, therefore, calls for stochastic hybrid simulation (SHS) to explicitly account for substructure uncertainties. The experimental design of SHS is explored in this study to account for uncertainties within analytical substructures. Both computational simulation and laboratory experiments are conducted to evaluate the pseudo-random Sobol sequence for the experimental design of SHS. Meta-modeling through polynomial chaos expansion (PCE) is established from a computational simulation of a nonlinear single-degree-of-freedom (SDOF) structure to evaluate the influence of nonlinear behavior and ground motions uncertainties. A series of hybrid simulations are further conducted in the laboratory to validate the findings from computational analysis. It is shown that the Sobol sequence provides a good starting point for the experimental design of stochastic hybrid simulation. However, nonlinear structural behavior involving stiffness and strength degradation could significantly increase the number of hybrid simulations to acquire accurate statistical estimation for the structural response of interests. Compared with the statistical moments calculated directly from hybrid simulations in the laboratory, the meta-model through PCE gives more accurate estimation, therefore, providing a more effective way for uncertainty quantification.

Optimization of Chassis Frame by Using D-Optimal Response Surface Model (D-Optimal 반응표면모델에 의한 섀시 프레임 최적설치)

  • Lee, Gwang-Gi;Gu, Ja-Gyeom;Lee, Tae-Hui
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.4 s.175
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    • pp.894-900
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    • 2000
  • Optimization of chassis frame is performed according to the minimization of eleven responses representing one total frame weight, three natural frequencies and seven strength limits of chassis frame that are analyzed by using each response surface model from D-optimal design of experiments. After each response surface model is constructed form D-optimal design and random orthogonal array, the main effect and sensitivity analyses are successfully carried out by using this approximated regression model and the optimal solutions are obtained by using a nonlinear programming method. The response surface models and the optimization algorithms are used together to obtain the optimal design of chassis frame. The eleven-polynomial response surface models of the thirteen frame members (design factors) are constructed by using D-optimal Design and the multi-disciplinary design optimization is also performed by applying dual response analysis.

Optimization of the Elastic Joint of Train Bogie Using by Response Surface Model (반응표면모델에 의한 철도 차량 대차의 탄성조인트 최적설계)

  • Park, Chan-Gyeong;Lee, Gwang-Gi
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.3 s.174
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    • pp.661-666
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    • 2000
  • Optimization of the elastic joint of train is performed according to the minimization of ten responses which represent driving safety and ride comfort of train and analyzed by using the each response se surface model from stochastic design of experiments. After the each response surface model is constructed, the main effect and sensitivity analyses are successfully performed by 2nd order approximated regression model as described in this paper. We can get the optimal solutions using by nonlinear programming method such as simplex or interval optimization algorithms. The response surface models and the optimization algorithms are used together to obtain the optimal design of the elastic joint of train. the ten 2nd order polynomial response surface models of the three translational stiffness of the elastic joint (design factors) are constructed by using CCD(Central Composite Design) and the multi-objective optimization is also performed by applying min-max and distance minimization techniques of relative target deviation.

Implementing Linear Models in Genetic Programming to Utilize Accumulated Data in Shipbuilding (조선분야의 축적된 데이터 활용을 위한 유전적프로그래밍에서의 선형(Linear) 모델 개발)

  • Lee, Kyung-Ho;Yeun, Yun-Seog;Yang, Young-Soon
    • Journal of the Society of Naval Architects of Korea
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    • v.42 no.5 s.143
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    • pp.534-541
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    • 2005
  • Until now, Korean shipyards have accumulated a great amount of data. But they do not have appropriate tools to utilize the data in practical works. Engineering data contains experts' experience and know-how in its own. It is very useful to extract knowledge or information from the accumulated existing data by using data mining technique This paper treats an evolutionary computation based on genetic programming (GP), which can be one of the components to realize data mining. The paper deals with linear models of GP for the regression or approximation problem when given learning samples are not sufficient. The linear model, which is a function of unknown parameters, is built through extracting all possible base functions from the standard GP tree by utilizing the symbolic processing algorithm. In addition to a standard linear model consisting of mathematic functions, one variant form of a linear model, which can be built using low order Taylor series and can be converted into the standard form of a polynomial, is considered in this paper. The suggested model can be utilized as a designing tool to predict design parameters with small accumulated data.

Gaussian Mixture based K2 Rifle Chamber Pressure Modeling of M193 and K100 Bullets (가우시안 혼합모델 기반 탄종별 K2 소화기의 약실압력 모델링)

  • Kim, Jong-Hwan;Lee, Byounghwak;Kim, Kyoungmin;Shin, Kyuyong;Lee, Wonwoo
    • Journal of the Korea Institute of Military Science and Technology
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    • v.22 no.1
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    • pp.27-34
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    • 2019
  • This paper presents a chamber pressure model development of K2 rifle by applying Gaussian mixture model. In order to materialize a real recoil force of a virtual reality shooting rifle in military combat training, the chamber pressure which is one of major components of the recoil force needs to be investigated and modeled. Over 200,000 data of the chamber pressure were collected by implementing live fire experiments with both K100 and M193 of 5.56 mm bullets. Gaussian mixture method was also applied to create a mathematical model that satisfies nonlinear, asymmetry, and deviations of the chamber pressure which is caused by irregular characteristics of propellant combustion. In addition, Polynomial and Fourier Regression were used for comparison of results, and the sum of squared errors, the coefficient of determination and root-mean-square errors were analyzed for performance measurement.

Moisture Content Prediction Model Development for Major Domestic Wood Species Using Near Infrared Spectroscopy (근적외선 분광분석법을 이용한 국산 주요 수종의 섬유포화점 이하 함수율 예측 모델 개발)

  • Yang, Sang-Yun;Han, Yeonjung;Park, Jun-Ho;Chung, Hyunwoo;Eom, Chang-Deuk;Yeo, Hwanmyeong
    • Journal of the Korean Wood Science and Technology
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    • v.43 no.3
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    • pp.311-319
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    • 2015
  • Near infrared (NIR) reflectance spectroscopy was employed to develop moisture content prediction model of pitch pine (Pinus rigida), red pine (Pinus densiflora), Korean pine (Pinus koraiensis), yellow poplar (Liriodendron tulipifera) wood below fiber saturation point. NIR reflectance spectra of specimens ranging from 1000 nm to 2400 nm were acquired after humidifying specimens to reach several equilibrium moisture contents. To determine the optimal moisture contents prediction model, 5 mathematical preprocessing methods (moving average (smoothing point: 3), baseline, standard normal variate (SNV), mean normalization, Savitzky-Golay $2^{nd}$ derivatives (polynomial order: 3, smoothing point: 11)) were applied to reflectance spectra of each specimen as 8 combinations. After finishing mathematical preprocessings, partial least squares (PLS) regression analysis was performed to each modified spectra. Consequently, the mathematical preprocessing methods deriving optimal moisture content prediction were 1) moving average/SNV for pitch pine and red pine, 2) moving average/SNV/Savitzky-golay $2^{nd}$ derivatives for Korean pine and yellow poplar. Every model contained three principal components.

Statistical Estimate and Prediction Values with Reference to Chronological Change of Body Height and Weight in Korean Youth (한국인 청소년 신장과 체중의 시대적 변천에 따른 통계학적 추정치에 관한 연구)

  • 강동석;성웅현;윤태영;최중명;박순영
    • Korean Journal of Health Education and Promotion
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    • v.13 no.2
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    • pp.130-166
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    • 1996
  • As compared with body height and body weight by ages and sexes, by means of the data reported under other researchers from 1967 to 1994 for 33 years, this study obtained the estimate value of body height and body weight by ages and sexes for the same period, and figured out prediction value of body height and body weight in the ages of between 6 and 14 from 1995 to 2000. These surveys and measurements took for one year from October 1st 1994 to September 30th. As shown in the 〈Table 1〉, in order to calculate the establishment, estimate value and prediction value of the chronological regression model of body height and body weight, by well-grounded 17 representative research papers, this research statistically tested propriety of liner regression model by the residual analysis in advance of being reconciled to simple liner regression model by the autonomous variable-year and the subordinate variable-body weight and measured prediction value, theoretical value from 1962 to 1994 by means of 2nd or 3rd polynomial regression model, with this redult did prediction value from 1995 to 2000. 1. Chronological Change of Body Height and Body Weight The analysis result from regression model of the chronological body height and body weight for the aged 6 - 16 in both sexes ranging from 1962 to 1994, corned from the 〈Table 2-20〉. On the one hand, the measurement value of respective researchers had a bit changes by ages with age growing, but the other hand, theoretical value, prediction value showed the regular increase by the stages and all values indicated a straight line on growth and development with age growing. That is, in case of the aged 6, males had 109.93cm in 1962 and females 108.93cm, but we found the increase that males had 1I8.0cm, females 1I3.9cm. In theoretical value, prediction value, males showed the increase from 109.88cm to 1I7.89cm and females from 109.27cm to 1I5.64cm respectively. There was the same inclination toward all ages. 2. Comparision to Measurement Value and Prediction Value of Body Height and Body Weight in 1994 As shown in the 〈Table 21〉, in case of body height, measurement value and prediction value of body height and body weight by ages and sexes almost showed the similiar inclination and poor grade, in case of body weight, prediction value in males had a bit low value by all ages, and prediction value in females had a high value in adolescence, to the contrary, a low value in adult. 3. Prediction Value of Body Height and Body Weight from 1995 to 2000 This research showed that body height and body weight remarkably increased in adolescence but slowly in adult. This study represented that Korean physique was on the increase and must be measured continually hereafter.

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