• Advances in environmental research
• /
• v.7 no.1
• /
• pp.29-37
• /
• 2018

A simple mathematical model for predicting fixed bed adsorption dynamics is described. The model is characterized by a linear adsorption isotherm and a linear driving force expression for mass transfer. Its analytic solution can be approximated with an algebraic equation in closed form which is easily evaluated by spreadsheet computation. To demonstrate one application of the fixed bed model, a previously published adsorption system is used as a case study in this work. The adsorption system examined here describes chromium breakthrough in a fixed bed adsorber packed with imidazole functionalized adsorbent particles and is characterized by a nonlinear adsorption isotherm. However, the equilibrium behavior of the fixed bed adsorber is in essence governed by a linear adsorption isotherm due to the use of a low influent chromium concentration. It is shown that chromium breakthrough is predicted reasonably well by the fixed bed model. The model's parameters can be easily extracted from independent batch experiments. The proposed modeling approach is very simple and rapid, and only Excel is used for computation.

• Proceedings of the KSME Conference
• /
• 2001.06b
• /
• pp.410-415
• /
• 2001

Hydraulic mounts have been used as an alternative to the conventional rubber mounts for they can provide more desirable stiffness and damping properties which may vary with frequency and excitation amplitude. Although a lumped-parameter non-linear model of the hydraulic mount developed by a simple fluid dynamic analysis can be successfully used for representing the inertia track dynamics, a linear model is still preferred. In this paper, an analytic technique for making a linear model of the hydraulic mount is proposed.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.29 no.12
• /
• pp.638-644
• /
• 2017

Optimal cooling operation algorithm was developed based on a simulation case of a single family house model equipped with renewable energy facility. EnergyPlus simulation results were used as virtual test data. The model contained three energy storage elements: thermal heat capacity of the living room, chilled water storage tank, and battery. Their charging and discharging schedules were optimized so that daily electricity bill became minimal. As an optimization tool, linear programming was considered because it was possible to obtain results in real time. For its adoption, EnergyPlus-based house model had to be linearly approximated. Results of this study revealed that dynamic cooling load of the living room could be approximated by a linear RC model. Scheduling based on the linear programming was then compared to that by a nonlinear optimization algorithm which was made using GenOpt developed by a national lab in USA. They showed quite similar performances. Therefore, linear programming can be a practical solution to optimal operation scheduling if linear dynamic models are tuned to simulate their real equivalents with reasonable accuracy.

• Journal of the Society of Naval Architects of Korea
• /
• v.42 no.5 s.143
• /
• pp.534-541
• /
• 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.

• Korean Journal of Soil Science and Fertilizer
• /
• v.43 no.2
• /
• pp.174-179
• /
• 2010

In order to interpret yield response of sugar beet to nitrogen fertilizer, and pig manure compost in saline-sodic soil of reclaimed tidal land, 4 kinds of response model, i.e., quadratic, exponential, square root, and linear response, and plateau model, are applied. The root fresh yield of sugar beet decreased exponentially with the increase of soil EC. The root fresh yield of sugar beet to nitrogen fertilizer was fitted best to the linear response, and plateau model among 4 yield response models with highly significant determination coefficient ($R^2=0.92^{**}$). The optimum N rate determined on the model was 138 kg N $ha^{-1}$. The root fresh yield of sugar beet to pig manure compost was fitted best to the quadratic model among 4 yield response models with highly significant determination coefficient ($R^2=0.99^{**}$). The maximum N rate determined on the model was 9.17 ton $ha^{-1}$. In conclusion, the proper model to interpret the yield of sugar beet in saline-sodic soil differs with the kinds of nutrient, linear response, and plateau model for fertilizer nitrogen, and quadratic model to pig manure compost.

• The Korean Journal of Applied Statistics
• /
• v.36 no.6
• /
• pp.573-589
• /
• 2023

In a piecewise linear trend model, the change points coincide with the mean change points of the first differenced time series. Therefore, by detecting the mean change points of the first differenced time series, one can estimate the change points of the piecewise linear trend model. In this paper, based on this fact, a method is proposed for detecting change points of the piecewise linear trend model using the simple moving average of the first differenced time series rather than estimates of the slope or residuals. Our Monte Carlo simulation experiments show that the proposed method performs well in estimating the number of change points not only when the error terms in the piecewise linear trend model are independent but also when they are serially correlated.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2002.04a
• /
• pp.122-126
• /
• 2002

Contaminant transport in porous media is characterized by solving an advection-dispersion equation(ADE). The ADE can cover equilibrium phenomena of interest, which include sorption, decay, and chemical reactions. Among these phenomena, sorption mechanism is described by several types of sorption isotherm. If we assume the sorption isotherm as linear, the solution of ADE can be easily procured. However, if we consider the sorption isotherm as non-linear isotherm like a Dual Reactive Domain Model (DRDM), the resulting differential equation becomes non-linear. In this case, the solution of ADE cannot be easily acquired by an analytic method. In this paper, we present the numerical analysis of ADE using a DRDM. The results reveal that even if sorption data may be fitted well using linear or non-linear isotherm, the characteristics of contaminant transport of the two cases are different from each other. To be concrete, the retardation of linear isotherm has stronger effect than that of the DRDM. As the non-linearity of sorption isotherm increases, the difference of retardation effects of the two cases becomes larger. For a pulse source, the maximum concentration of the linear model is higher than that of the DRDM, but the plume of the DRDM moves faster than that of the linear model. Behaviors of contaminant transport using the DRDM are consistent with common features of a linear model. For instance, biodegradation effect becomes larger as time goes by The faster the seepage velocity is, the faster the plume of contaminant moves. The plume of the contaminant is distributed evenly over overall domain in the event of high dispersion coefficient.

• Asian-Australasian Journal of Animal Sciences
• /
• v.11 no.6
• /
• pp.642-647
• /
• 1998

A Poisson error model as a generalized linear mixed model (GLMM) has been suggested for genetic analysis of counted observations. One of the assumptions in this model is the normality for random effects. Since this assumption is not always appropriate, a more flexible model is needed. For count traits, a Poisson hierarchical generalized linear model (HGLM) that does not require the normality for random effects was proposed. In this paper, a Poisson-Gamma HGLM was examined along with corresponding analytical methods. While a difficulty arises with Poisson GLMM in making inferences to the expected values of observations, it can be avoided with the Poisson-Gamma HGLM. A numerical example with simulated embryo yield data is presented.

• Journal of the Korean Society for Precision Engineering
• /
• v.16 no.7
• /
• pp.178-187
• /
• 1999

In order to identify a transfer function model with noise, penalty function method has been widely used. In this method, estimation process for possible model parameters from low to higher order proceeds the model identification process. In this study, based on linear estimation method, a new approach unifying the estimation and the identification of ARMAX model is proposed. For the parameter estimation of a transfer function model with noise, linear estimation method by noise separation is suggested instead of nonlinear estimation method. The feasibility of the proposed model identification and estimation method is verified through simulations, namely by applying the method to time series model. In the case of time series model with noise, the proposed method successfully identifies the transfer function model with noise without going through model parameter identification process in advance. A new algorithm effectively achieving model identification and parameter estimation in unified frame has been proposed. This approach is different from the conventional method used for identification of ARMAX model which needs separate parameter estimation and model identification processes. The consistency and the accuracy of the proposed method has been verified through simulations.

• Communications for Statistical Applications and Methods
• /
• v.15 no.6
• /
• pp.837-842
• /
• 2008

Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.