• Title/Summary/Keyword: Domain Discretization

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Linear decentralized learning control for the robot moving on the horizontal plane

  • Lee, Soo-Cheol
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1995.04a
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    • pp.869-879
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    • 1995
  • The new field of learning control develops controllers that learn to improve their performance at executing a given task, based on experience performing this task. The simplest forms of learning control are based on the same concept as integral control, but operating in the domain of the repetitions of the task. In the previous paper, I had studied the use of such controllers in a decentralized system, such as a robot with the controller for each link acting independently. The basic result of the paper is to show that stability of the learning controllers for all subsystems when the coupling between subsystems is turned off, assures stability of the decentralized learning in the coupled system, provided that the sample time in the digital learning controller is sufficiently short. In this paper, we present two examples. The first illustrates the effect of coupling between subsystems in the system dynamics, and the second studies the application of decentralized learning control to robot problems. The latter example illustrates the application of decentralized learning control to nonlinear systems, and also studies the effect of the coupling between subsystems introduced in the input matrix by the discretization of the system equations. The conclusion is that for sufficiently small learning gain, and sufficiently small sample time, the simple learning control law based on integral control applied to each robot axis will produce zero tracking error in spite o the dynamic coupling in the robot equations. Of course, the results of this paper have much more general application than just to the robotics tracking problem. Convergence in decentralized systems is seen to depend only on the input and output matrices, provided the sample time is suffiently small.

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Geometrically nonlinear dynamic analysis of FG graphene platelets-reinforced nanocomposite cylinder: MLPG method based on a modified nonlinear micromechanical model

  • Rad, Mohammad Hossein Ghadiri;Shahabian, Farzad;Hosseini, Seyed Mahmoud
    • Steel and Composite Structures
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    • v.35 no.1
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    • pp.77-92
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    • 2020
  • The present paper outlined a procedure for geometrically nonlinear dynamic analysis of functionally graded graphene platelets-reinforced (GPLR-FG) nanocomposite cylinder subjected to mechanical shock loading. The governing equation of motion for large deformation problems is derived using meshless local Petrov-Galerkin (MLPG) method based on total lagrangian approach. In the MLPG method, the radial point interpolation technique is employed to construct the shape functions. A micromechanical model based on the Halpin-Tsai model and rule of mixture is used for formulation the nonlinear functionally graded distribution of GPLs in polymer matrix of composites. Energy dissipation in analyses of the structure responding to dynamic loads is considered using the Rayleigh damping. The Newmark-Newton/Raphson method which is an incremental-iterative approach is implemented to solve the nonlinear dynamic equations. The results of the proposed method for homogenous material are compared with the finite element ones. A very good agreement is achieved between the MLPG and FEM with very fine meshing. In addition, the results have demonstrated that the MLPG method is more effective method compared with the FEM for very large deformation problems due to avoiding mesh distortion issues. Finally, the effect of GPLs distribution on strength, stiffness and dynamic characteristics of the cylinder are discussed in details. The obtained results show that the distribution of GPLs changed the mechanical properties, so a classification of different types and volume fraction exponent is established. Indeed by comparing the obtained results, the best compromise of nanocomposite cylinder is determined in terms of mechanical and dynamic properties for different load patterns. All these applications have shown that the present MLPG method is very effective for geometrically nonlinear analyses of GPLR-FG nanocomposite cylinder because of vanishing mesh distortion issue in large deformation problems. In addition, since in proposed method the distributed nodes are used for discretization the problem domain (rather than the meshing), modeling the functionally graded media yields to more accurate results.

Nonlinear Control by Feedback Linearization for Panel Flutter at Elevated Temperature (열하중을 받는 패널플러터의 궤환 선형화에 의한 비선형제어)

  • 문성환;이광주
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.34 no.9
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    • pp.45-52
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    • 2006
  • In this study, a nonlinear control by feedback linearization method, one of nonlinear control schemes based on the nonlinear model, is proposed to suppress the flutter of a supersonic composite panel using piezoelectric materials. Most of the previous panel flutter controllers are the LQR(Linear Quadratic Regulator) which is based on the linear model. A nonlinear feedback linearizing controller proposed in this study considers the nonlinear characteristics of the system model. We use the actuator implemented by piezoceramic PZT. Using the principle of virtual displacements and a finite element discretization with the conforming four-node rectangular element, we first derive the discretized dynamic equations of motion, which are transformed into a nonlinear coupled-modal equations of motion of state space form. The effectiveness of the proposed method is also compared with the LQR based on the linear model through numerical simulations in the time domain using the Newmark method.

Development of an Elastic Analysis Technique Using the Mixed Volume and Boundary Integral Equation Method (혼합 체적-경계 적분방정식법을 이용한 탄성해석 방법 개발)

  • Lee, Jeong-Gi;Heo, Gang-Il;Jin, Won-Jae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.4
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    • pp.775-786
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    • 2002
  • A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of elastic wave scattering problems and plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. In the formulation of this method, the continuity condition at each interface is automatically satisfied, and in contrast to finite element methods, where the full domain needs to be discretized, this method requires discretization of the inclusions only. Finally, this method takes full advantage of the pre- and post-processing capabilities developed in FEM and BIEM. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, and the analysis of plane wave scattering problems in unbounded isotropic matrix with isotropic inclusions and voids, it will be established that this new method is very accurate and effective for solving plane wave scattering problems and plane elastic problems in unbounded solids containing general anisotropic inclusions and voids/cracks or isotropic inclusions.

Structural modal identification and MCMC-based model updating by a Bayesian approach

  • Zhang, F.L.;Yang, Y.P.;Ye, X.W.;Yang, J.H.;Han, B.K.
    • Smart Structures and Systems
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    • v.24 no.5
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    • pp.631-639
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    • 2019
  • Finite element analysis is one of the important methods to study the structural performance. Due to the simplification, discretization and error of structural parameters, numerical model errors always exist. Besides, structural characteristics may also change because of material aging, structural damage, etc., making the initial finite element model cannot simulate the operational response of the structure accurately. Based on Bayesian methods, the initial model can be updated to obtain a more accurate numerical model. This paper presents the work on the field test, modal identification and model updating of a Chinese reinforced concrete pagoda. Based on the ambient vibration test, the acceleration response of the structure under operational environment was collected. The first six translational modes of the structure were identified by the enhanced frequency domain decomposition method. The initial finite element model of the pagoda was established, and the elastic modulus of columns, beams and slabs were selected as model parameters to be updated. Assuming the error between the measured mode and the calculated one follows a Gaussian distribution, the posterior probability density function (PDF) of the parameter to be updated is obtained and the uncertainty is quantitatively evaluated based on the Bayesian statistical theory and the Metropolis-Hastings algorithm, and then the optimal values of model parameters can be obtained. The results show that the difference between the calculated frequency of the finite element model and the measured one is reduced, and the modal correlation of the mode shape is improved. The updated numerical model can be used to evaluate the safety of the structure as a benchmark model for structural health monitoring (SHM).

Development of a Numerical Model of Shallow-Water Flow using Cut-cell System (분할격자체계를 이용한 천수흐름 수치모형의 개발)

  • Kim, Hyung-Jun;Lee, Seung-Oh;Cho, Yong-Sik
    • Journal of the Korean Society of Hazard Mitigation
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    • v.8 no.4
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    • pp.91-100
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    • 2008
  • Numerical implementation with a Cartesian cut-cell method is conducted in this study. A Cartesian cut-cell method is an easy and efficient mesh generation methodology for complex geometries. In this method, a background Cartesian grid is employed for most of computational domain and a cut-cell grid is applied for the peculiar grids where the flow characteristics are changed such as solid boundary to enhance the accuracy, applicability and efficiency. Accurate representation of complex geometries can be obtained by using the cut-cell method. The cut-cell grids are constructed with irregular meshes which have various shape and size. Therefore, the finite volume method is applied to numerical discretization on a irregular domain. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. The weighted average flux method applied on the Cartesian cut cell grid for stabilization of the numerical results. To validate the numerical model using the Cartesian cut-cell grids, the model is applied to the rectangular tank problem of which the exact solutions exist. As a comparison of numerical results with the analytical solutions, the numerical scheme well represents flow characteristics such as free surface elevation and velocities in x-and y-directions in a rectangular tank with the Cartesian and cut-cell grids.

Development and evaluation of a 2-dimensional land surface flood analysis model using uniform square grid (정형 사각 격자 기반의 2차원 지표면 침수해석 모형 개발 및 평가)

  • Choi, Yun-Seok;Kim, Joo-Hun;Choi, Cheon-Kyu;Kim, Kyung-Tak
    • Journal of Korea Water Resources Association
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    • v.52 no.5
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    • pp.361-372
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    • 2019
  • The purpose of this study is to develop a two-dimensional land surface flood analysis model based on uniform square grid using the governing equations except for the convective acceleration term in the momentum equation. Finite volume method and implicit method were applied to spatial and temporal discretization. In order to reduce the execution time of the model, parallel computation techniques using CPU were applied. To verify the developed model, the model was compared with the analytical solution and the behavior of the model was evaluated through numerical experiments in the virtual domain. In addition, inundation analyzes were performed at different spatial resolutions for the domestic Janghowon area and the Sebou river area in Morocco, and the results were compared with the analysis results using the CAESER-LISFLOOD (CLF) model. In model verification, simulation results were well matched with the analytical solution, and the flow analyses in the virtual domain were also evaluated to be reasonable. The results of inundation simulations in the Janghowon and the Sebou river area by this study and CLF model were similar with each other and for Janghowon area, the simulation result was also similar to the flooding area of flood hazard map. The different parts in the simulation results of this study and the CLF model were compared and evaluated for each case. The results of this study suggest that the model proposed in this study can simulate the flooding well in the floodplain. However, in case of flood analysis using the model presented in this study, the characteristics and limitations of the model by domain composition method, governing equation and numerical method should be fully considered.

Performance Comparison of Clustering using Discritization Algorithm (이산화 알고리즘을 이용한 계층적 클러스터링의 실험적 성능 평가)

  • Won, Jae Kang;Lee, Jeong Chan;Jung, Yong Gyu;Lee, Young Ho
    • Journal of Service Research and Studies
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    • v.3 no.2
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    • pp.53-60
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    • 2013
  • Datamining from the large data in the form of various techniques for obtaining information have been developed. In recent years one of the most sought areas of pattern recognition and machine learning method is created with most of existing learning algorithms based on categorical attributes to a rule or decision model. However, the real-world data, it may consist of numeric attributes in many cases. In addition it contains attributes with numerical values to the normal categorical attribute. In this case, therefore, it is required processes in order to use the data to learn an appropriate value for the type attribute. In this paper, the domain of the numeric attributes are divided into several segments using learning algorithm techniques of discritization. It is described Clustering with other data mining techniques. Large amount of first cluster with characteristics is similar records from the database into smaller groups that split multiple given finite patterns in the pattern space. It is close to each other of a set of patterns that together make up a bunch. Among the set without specifying a particular category in a given data by extracting a pattern. It will be described similar grouping of data clustering technique to classify the data.

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