• Title/Summary/Keyword: recursive equation

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Solution Methods for OD Trip Estimation in Stochastic Assignment (확률적 통행배정하에서 기종점 통행량추정 모형의 개발)

  • Im, Yong-Taek
    • Journal of Korean Society of Transportation
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    • v.24 no.4 s.90
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    • pp.149-159
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    • 2006
  • Traditional trip tables are estimated through large-scale surveys such as household survey, roadside interviews, and license Plate matching. These methods are, however, expensive and time consuming. This paper presents two origin-destination (OD) trip matrix estimation methods from link traffic counts in stochastic assignment, which contains perceived errors of drivers for alternatives. The methods are formulated based on the relation between link flows and OD demands in logit formula. The first method can be expressed to minimize the difference between observed link flows and estimated flows, derived from traffic assignment and be solved by gradient method. The second method can be formulated based on dynamic process, which nay describe the daily movement patterns of drivers and be solved by a recursive equation. A numerical example is used for assessing the methods, and shows the performances and properties of the models.

Non-recursive Path Model Analysis on the Relationship between Perceived Safety Management Activities and Safety of Construction Sites (건설현장의 지각된 안전관리 활동과 안전성과의 관계에 대한 비재귀 경로모형분석)

  • Yong Hoon Kim
    • Journal of the Society of Disaster Information
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    • v.18 no.4
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    • pp.786-794
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    • 2022
  • In construction sites, effective preventive safety management is required beyond post-processing safety management. Purpose: The purpose of this study is to present a model and analyze the relationship between safety management activities, safety culture key elements, safety, unsafe behavior management, and safety for autonomous and preventive safety management. Method: The relationship was analyzed by applying the survey data to the structural equation, and the path to safety outcomes from exogenous variables was explored and major issues were presented by interpreting the part suggested by the hypothesis verified by the analysis results. Result: As a result of analyzing the preliminary model and the path model, the appropriate model fit was confirmed, and the significant effect of exogenous variables on endogenous variables was confirmed. Conclusion: It is judged that it can contribute to continuously improving safety performance before safety accidents occur through safety management activities, safety and unsafe behavior management, and management of key elements of safety culture.

A Study on the Recursive Identification of Modal Parameters (회귀적 방법에 의한 모우드 변수 규명에 관한 연구)

  • 고장욱;이재응
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1995.04a
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    • pp.147-152
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    • 1995
  • 실험에 의한 모우드 해석 방법들은 1980년대부터 활발히 연구되어 많은 새로운 방법들이 개발되어 발표되었다. 그러나 개발된 대부분의 방법들은 측정된 데이타를 일괄처리하는 밸치(또는 off-line) 방법들이다. 최근에는 시간에 따라서 변하는 구조물의 동특성을 규명하는 분야에 모우드 해석 방법이 응용되어 사용되고 있다. 이러한 응용분야에서는 모우드 변수들의 변화되는 값을 새로운 데이타가 샘플링 될 때마다 그 값들을 수정하면서 추정할 수 있는 회귀적인(recursive 또는 on-line) 방법을 사용하여야 한다. Davies와 Hammond[1]는 회귀적 선형 자승법(Recursive Least Squares : RLS)을 이용하여 모우드 변수를 구하고 이를 벧치방법인 Instrumental Variable 방법과 Fourier 방법의 결과와 비교하였다. 그러나, 그 결과에서 보여준것처럼 RLS 방법은 잡음 대 시호비가 낮을 때에만 모우드 변수 값들을 정확하게 추정할 수 있었다. Sundararajan과 Montgomrey[2]는 회귀적 선형 최소자승 격자필터(lattice filter)를 이용하여 구조물의 차수(order)와 고유진동형, 그리고 진폭을 결정한 후 이를 토대로 회귀적 gradient형태의 방정식 오차 규명 방법(equation-error identification algorithm)에 의하여 모우드 변수들을 추정하였다. 이 방법은 2차원 격자구조물의 모우드 변수 추정에 사용되었으며, 또한 적응모우드제어에도 성공적으로 이용되었다. 그러나, 이 방법도 잡음 대 신호비가 낮은 환경에서만 사용할 수 있다는 단점이 있다. 위에서 언급한 방법들은 모두 RLS 방법을 기초로 하여 개발되었으나, RLS 방법은 전형적인 결정적(deterministic)방법으로서 잡음이 섞인 데이타를 처리하기에는 부적절한 방법임이 널리 알려진 사실이다[3]. 최근에 Ben Mrad와 Fassois[4]는 신호에 잡음이 존재하여도 이를 잘 처리할 수 있는 확률적(stochastic) 방법을 개발하여 기존의 결정적 방법들과 그 결과를 비교하였다. 그러나, 개발된 방법은 응답 신호에 백색잡음(white noise)이 섞이는 특수한 경우에만 사용할 수 있게 만들어져서 이 방법의 실질적인 적용에는 어려움이 있다. 본 연구에서는 기존의 방법들의 단점을 극복할 수 있는 새로운 회귀적 모우드 변수 규명 방법을 개발하였다. 이는 Fassois와 Lee가 ARMAX모델의 계수를 효율적으로 추정하기 위하여 개발한 뱉치방법인 Suboptimum Maximum Likelihood 방법[5]를 기초로 하여 개발하였다. 개발된 방법의 장점은 응답 신호에 유색잡음이 존재하여도 모우드 변수들을 항상 정확하게 구할 수 있으며, 또한 알고리즘의 안정성이 보장된 것이다.

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Curvature Radius of Equivalent Lens Obtained by Recursive Numerical Solving of Gaussian Equations (재귀적 수치 계산법을 이용한 등가 렌즈의 곡률 계산)

  • Lee, Kyu Haeng
    • Korean Journal of Optics and Photonics
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    • v.33 no.6
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    • pp.275-286
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    • 2022
  • As a first step in the optical design process, we derive a recursive numerical calculation method that can give a solution to the Gaussian equation that the paraxial rays satisfy. Given the refractive power, the angle of incidence to the first principal plane of the lens, the angle of exit to the second principal plane of the lens, and the distance between the principal planes, the radii of curvature of the front and back surfaces of a lens can be obtained by applying the recursive numerical calculation method proposed in this paper according to the thickness of the lens. If a module consists of two or more lenses, the thickness and radius of curvature of each lens can be similarly determined after selecting the distance between the principal planes of the lens under the condition of the design specification while increasing the number of lenses one by one.

Seismic response of a highway bridge in case of vehicle-bridge dynamic interaction

  • Erdogan, Yildirim S.;Catbas, Necati F.
    • Earthquakes and Structures
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    • v.18 no.1
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    • pp.1-14
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    • 2020
  • The vehicle-bridge interaction (VBI) analysis might be cumbersome and computationally expensive in bridge engineering due to the necessity of solving large number of coupled system of equations. However, VBI analysis can provide valuable insights into the dynamic behavior of highway bridges under specific loading conditions. Hence, this paper presents a numerical study on the dynamic behavior of a conventional highway bridge under strong near-field and far-field earthquake motions considering the VBI effects. A recursive substructuring method, which enables solving bridge and vehicle equations of motion separately and suitable to be adapted to general purpose finite element softwares, was used. A thorough analysis that provides valuable information about the effect of various traffic conditions, vehicle velocity, road roughness and effect of soil conditions under far-field and near-field strong earthquake motions has been presented. A real-life concrete highway bridge was chosen for numerical demonstrations. In addition, sprung mass models of vehicles consist of conventional truck and car models were created using physical and dynamic properties adopted from literature. Various scenarios, of which the results may help to highlight the different aspects of the dynamic response of concrete highway bridges under strong earthquakes, have been considered.

Adaptive Control of End Milling Machine to Improve Machining Straightness (직선도 개선을 위한 엔드밀링머시인 의 적응제어)

  • 김종선;정성종;이종원
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.9 no.5
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    • pp.590-597
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    • 1985
  • A recursive geometric adaptive control method to compensate for machining straightness error in the finished surface due to tool deflection and guideway error generated by end milling process is developed. The relationship between the tool deflection and the feedrate is modeled by a modified Taylor's tool life equation. Without a priori knowledge on the variations off cutting parameters, time varying parameters are then estimated by an exponentially windowed recursive least squares method with only post-process measurements of the straightness error. The location error is controlled by shifting the milling bed in the direction perpendicular to the finished surface and adding a certain amount of feedrate with respect to the tool deflection model before cutting. The waviness error is compensated by adjusting the feedrate during machining. Experimental results show that location error is controlled within a range of fixturing error of the bed on the guideway and that about 60% reduction in the waviness error can be achieved within a few steps of parameter adaption under wide operating ranges of cutting conditions even if the parameters do not converge to fixed values.

Multi-modal Vibration Control of Intelligent Laminated Composite Plates Using System Identification and Optimal Control (시스템식별과 최적제어를 이용한 지능형 복합적층판의 다중보드 진동제어)

  • 김정수;강영규;박현철
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.1
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    • pp.5-11
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    • 2002
  • Active vibration control of intelligent laminated composite plates is performed experimental1y Laminated composite place is modeled by the system identification method. For the system identification process, the laminated composite place is excited by two piezoelectric actuators with PRBS signals. At the same time, the displacement of the laminated composite plate is measured by a gap sensor. From these excited PRBS signals and the measured displacement sequence, system parameters of the laminated composite plate are estimated using a recursive prediction error method. Model of the laminated composite plate with two piezoeletric actuators is assumed to be the form of ARMAX. From the estimated ARHMAX model, a state space equation of the observable canonical form is obtained. With this state space equation, a controller and an observer for active vibration control is designed using the optimal control method. Controller and observer are implemented on a digital system. Experiments on the vibration control are Performed with changing the outer layer fiber orientation of intelligent composite plates.

Identification of Closed Loop System by Subspace Method (부분공간법에 의한 페루프 시스템의 동정)

  • Lee, Dong-Cheol;Bae, Jong-Il;Hong, Soon-Il;Kim, Jong-Kyung;Jo, Bong-Kwan
    • Proceedings of the KIEE Conference
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    • 2003.07d
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    • pp.2143-2145
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    • 2003
  • In the linear system identification using the discrete time constant coefficients, there is a subspace method based on 4SID recently much suggested instead of the parametric method like as the maximum likelihood method. The subspace method is not related with the impulse response and difference equation in its input-output equation, but with the system matrix of the direct state space model from the input-output data. The subspace method is a very useful tool to adopt in the multivariable system identification, but it has a shortage unable to adopt in the closed-loop system identification. In this paper, we are suggested the methods to get rid of the shortage of the subspace method in the closed-loop system identification. The subspace method is used in the estimate of the output prediction values from the estimating of the state space vector. And we have compared the results with the outputs of the recursive least square method in the numerical simulation.

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A novel method for solving structural problems: Elastoplastic analysis of a pressurized thick heterogeneous sphere

  • Abbas Heydari
    • Advances in Computational Design
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    • v.9 no.1
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    • pp.39-52
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    • 2024
  • If the governing differential equation arising from engineering problems is treated as an analytic, continuous and derivable function, it can be expanded by one point as a series of finite numbers. For the function to be zero for each value of its domain, the coefficients of each term of the same power must be zero. This results in a recursive relationship which, after applying the natural conditions or the boundary conditions, makes it possible to obtain the values of the derivatives of the function with acceptable accuracy. The elastoplastic analysis of an inhomogeneous thick sphere of metallic materials with linear variation of the modulus of elasticity, yield stress and Poisson's ratio as a function of radius subjected to internal pressure is presented. The Beltrami-Michell equation is established by combining equilibrium, compatibility and constitutive equations. Assuming axisymmetric conditions, the spherical coordinate parameters can be used as principal stress axes. Since there is no analytical solution, the natural boundary conditions are applied and the governing equations are solved using a proposed new method. The maximum effective stress of the von Mises yield criterion occurs at the inner surface; therefore, the negative sign of the linear yield stress gradation parameter should be considered to calculate the optimal yield pressure. The numerical examples are performed and the plots of the numerical results are presented. The validation of the numerical results is observed by modeling the elastoplastic heterogeneous thick sphere as a pressurized multilayer composite reservoir in Abaqus software. The subroutine USDFLD was additionally written to model the continuous gradation of the material.

Curing Induced Residual Stresses in Laminated Cylindrical Shells

  • Lee, Soo-Yong
    • Journal of Mechanical Science and Technology
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    • v.14 no.1
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    • pp.19-29
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    • 2000
  • A viscoelastic finite element analysis is presented to investigate residual stresses occurred in a laminated cylindrical shell during cure. An incremental viscoelastic constitutive equation that can describe stress relaxation during the cure is derived as a recursive formula which can be used conveniently for a numerical analysis. The finite element analysis program is developed on the basis of a 3-D degenerated shell element and the first order shear deformation theory, and is verified by comparing with an one dimensional exact solution. Viscoelastic effect on the residual stresses in the laminated shell during the cure is investigated by performing both the viscoelastic and linear elastic analyses considering thermal deformation and chemical shrinkage simultaneously. The results show that there is big difference between viscoelastic stresses and linear elastic stresses. The effect of cooling rates and cooling paths on the residual stresses is also examined.

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