• Title/Summary/Keyword: Solution parameter

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Image Reconstruction Using Iterative Regularization Scheme Based on Residual Error in Electrical Impedance Tomography (전기 임피던스 단층촬영법에서 잔류오차 기반의 반복적 조정기법을 이용한 영상 복원)

  • Kang, Suk-In;Kim, Kyung-Youn
    • Journal of IKEEE
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    • v.18 no.2
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    • pp.272-281
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    • 2014
  • In electrical impedance tomography (EIT), modified Newton Raphson (mNR) method is widely used inverse algorithm for static image reconstruction due to its convergence speed and estimation accuracy. The unknown conductivity distribution is estimated iteratively by minimizing a cost functional such that the residual error namely the difference in measured and calculated voltages is reduced. Although, mNR method has good estimation performance, EIT inverse problem still suffers from ill-conditioned and ill-posedness nature. To mitigate the ill-posedness, generally, regularization methods are adopted. The inverse solution is highly dependent on the choice of regularization parameter. In most cases, the regularization parameter has a constant value and is chosen based on experience or trail and error approach. In situations, when the internal distribution changes or with high measurement noise, the solution does not get converged with the use of constant regularization parameter. Therefore, in this paper, in order to improve the image reconstruction performance, we propose a new scheme to determine the regularization parameter. The regularization parameter is computed based on residual error and updated every iteration. The proposed scheme is tested with numerical simulations and laboratory phantom experiments. The results show an improved reconstruction performance when using the proposed regularization scheme as compared to constant regularization scheme.

Forced vibrations of an elastic rectangular plate supported by a unilateral two-parameter foundation via the Chebyshev polynomials expansion

  • Zekai Celep;Zeki Ozcan
    • Structural Engineering and Mechanics
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    • v.90 no.6
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    • pp.551-568
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    • 2024
  • The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

Magneto-thermo-elastic response of a rotating functionally graded cylinder

  • Hosseini, Mohammad;Dini, Ali
    • Structural Engineering and Mechanics
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    • v.56 no.1
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    • pp.137-156
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    • 2015
  • In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.

Nonlinear in-plane free oscillations of suspended cable investigated by homotopy analysis method

  • Zhao, Yaobing;Sun, Ceshi;Wang, Zhiqian;Peng, Jian
    • Structural Engineering and Mechanics
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    • v.50 no.4
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    • pp.487-500
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    • 2014
  • An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton's principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated.

Dynamic response of a Timoshenko beam on a tensionless Pasternak foundation

  • Coskun, Irfan;Engin, Hasan;Tekin, Ayfer
    • Structural Engineering and Mechanics
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    • v.37 no.5
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    • pp.489-507
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    • 2011
  • The dynamic response of a Timoshenko beam on a tensionless Pasternak foundation is investigated by assuming that the beam is subjected to a concentrated harmonic load at its middle. This action results in the creation of lift-off regions between the beam and the foundation that effect the character of the response. Although small displacements for the beam and the foundation are assumed, the problem becomes nonlinear since the contact/lift-off regions are not known at the outset. The governing equations of the beam, which are coupled in deflection and rotation, are obtained in both the contact and lift-off regions. After removing the coupling, the essentials of the problem (the contact regions) are determined by using an analytical-numerical method. The results are presented in figures to demonstrate the effects of some parameters on the extent of the contact lengths and displacements. The results are also compared with those of Bernoulli-Euler, shear, and Rayleigh beams. It is observed that the solution is not unique; for a fixed value of the frequency parameter, more than one solution (contact length) exists. The contact length of the beam increases with the increase of the frequency and rotary-inertia parameters, whereas it decreases with increasing shear foundation parameter.

Osmotic Concentration of Apples and Its Effect on Browning Reaction during Air Dehydration (사과의 삼투압농축과 열품건조시 갈색화 반응에 미치는 효과)

  • 김명환
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.19 no.2
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    • pp.121-126
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    • 1990
  • Internal mass transfer during osmotic concentration of apples in sugar solutions was exami-ned as a function of concentration temperature and immersion time of those solutions using moisture loss sugar gain molality and rate parameter. Influence of osmotic concentration processes on browning reaction was also evaluated compared to control In creasin the concen-tration and temperature of sugar solutions increased moistrue loss sugar gain molality and rate parameter. Water loss was rapid early in the process and then levelled off, The same phenomena were occurred on sugar gain only in higher concentration(60$^{\circ}$ brix). IN lower concentration (30$^{\circ}$brix) sugar gain was gradually increased during whole process. Moisture loss during osmotic concentration using a sugar solution(60$^{\circ}$ brix 6$0^{\circ}C$) with 180min immer-sion time was 45.79% Effect of osmotic concentration befor air dried to 4% M.C(wet basis) on browning reaction was significant. Minimum browning reaction during air drying was carried out using a pretreatment such as osmotic concentration in sugar solution(60$^{\circ}$brix 45$^{\circ}C$) with 150min immersion time(O.D=0.01) compared to control(O.D=0.17)

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AN ASYMPTOTIC FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS OF CONVECTION-DIFFUSION TYPE WITH DISCONTINUOUS SOURCE TERM

  • Babu, A. Ramesh;Ramanujam, N.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1057-1069
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    • 2008
  • We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

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Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory

  • Rahmani, Omid;Deyhim, Soroush;Hosseini, S. Amir Hossein
    • Steel and Composite Structures
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    • v.27 no.3
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    • pp.371-388
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    • 2018
  • In this paper, a new model based on nonlocal high order theory is proposed to study the size effect on the bending of nano-sandwich beams with a compliance core. In this model, in contrast to most of the available sandwich theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core are obtained through an elasticity solution. Equations of motion and boundary conditions for nano-sandwich beam are derived by using Hamilton's principle and an analytical solution is presented for simply supported nano-sandwich beam. The results are validated with previous studies in the literature. These results can be utilized in the study of nano-sensors and nano-actuators. The effect of nonlocal parameter, Young's modulus of the core and aspect ratio on the deflection of the nano-sandwich beam is investigated. It is concluded that by including the small-scale effects, the deflection of the skins is increased and by increasing the nonlocal parameter, the influence of small-scale effects on the deflections is increased.

Application of multi-objective genetic algorithm for waste load allocation in a river basin (오염부하량 할당에 있어서 다목적 유전알고리즘의 적용 방법에 관한 연구)

  • Cho, Jae-Heon
    • Journal of Environmental Impact Assessment
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    • v.22 no.6
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    • pp.713-724
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    • 2013
  • In terms of waste load allocation, inequality of waste load discharge must be considered as well as economic aspects such as minimization of waste load abatement. The inequality of waste load discharge between areas was calculated with Gini coefficient and was included as one of the objective functions of the multi-objective waste load allocation. In the past, multi-objective functions were usually weighted and then transformed into a single objective optimization problem. Recently, however, due to the difficulties of applying weighting factors, multi-objective genetic algorithms (GA) that require only one execution for optimization is being developed. This study analyzes multi-objective waste load allocation using NSGA-II-aJG that applies Pareto-dominance theory and it's adaptation of jumping gene. A sensitivity analysis was conducted for the parameters that have significant influence on the solution of multi-objective GA such as population size, crossover probability, mutation probability, length of chromosome, jumping gene probability. Among the five aforementioned parameters, mutation probability turned out to be the most sensitive parameter towards the objective function of minimization of waste load abatement. Spacing and maximum spread are indexes that show the distribution and range of optimum solution, and these two values were the optimum or near optimal values for the selected parameter values to minimize waste load abatement.

DETERMINATION OF GPS HEIGHT WITH INCORPORATION OF USING SURFACE METEOROLOGICAL MEASUREMENTS

  • Wang, Chuan-Sheng;Liou, Yuei-An;Yeh, Ta-Kang
    • Proceedings of the KSRS Conference
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    • 2008.10a
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    • pp.313-316
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    • 2008
  • Although the positioning accuracy of the Global Positioning System (GPS) has been studied extensively and used widely, it is still limited due to errors from sources such as the ionospheric effect, orbital uncertainty, antenna phase center variation, signal multipath and tropospheric influence. This investigation addresses the tropospheric effect on GPS height determination. Data obtained from GPS receivers and co-located surface meteorological instruments in 2003 are adopted in this study. The Ministry of the Interior (MOl), Taiwan, established these GPS receivers as continuous operating reference stations. Two different approaches, parameter estimation and external correction, are utilized to correct the zenith tropospheric delay (ZTD) by applying the surface meteorological measurements (SMM) data. Yet, incorrect pressure measurement leads to very poor accuracy. The GPS height can be affected by a few meters, and the root-mean-square (rms) of the daily solution ranges from a few millimeters to centimeters, no matter what the approach adopted. The effect is least obvious when using SMM data for the parameter estimation approach, but the constant corrections of the GPS height occur more often at higher altitudes. As for the external correction approach, the Saastamoinen model with SMM data makes the repeatability of the GPS height maintained at few centimeters, while the rms of the daily solution displays an improvement of about 2-3 mm.

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