• Title/Summary/Keyword: recursive equations

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Busy Period Analysis of the Geo/Geo/1/K Queue with a Single Vacation (단일 휴가형 Geo/Geo/1/K 대기행렬의 바쁜 기간 분석)

  • Kim, Kilhwan
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.42 no.4
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    • pp.91-105
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    • 2019
  • Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1 ≤ n ≤ K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

IRK vs Structural Integrators for Real-Time Applications in MBS

  • Dopico D.;Lugris U.;Gonzalez M.;Cuadrado J.
    • Journal of Mechanical Science and Technology
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    • v.19 no.spc1
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    • pp.388-394
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    • 2005
  • Recently, the authors have developed a method for real-time dynamics of multibody systems, which combines a semi-recursive formulation to derive the equations of motion in dependent relative coordinates, along with an augmented Lagrangian technique to impose the loop closure conditions. The following numerical integration procedures, which can be grouped into the so-called structural integrators, were tested : trapezoidal rule, Newmark dissipative schemes, HHT rule, and the Generalized-${\alpha}$ family. It was shown that, for large multi body systems, Newmark dissipative was the best election since, provided that the adequate parameters were chosen, excellent behavior was achieved in terms of efficiency and robustness with acceptable levels of accuracy. In the present paper, the performance of the described method in combination with another group of integrators, the Implicit Runge-Kutta family (IRK), is analyzed. The purpose is to clarify which kind of IRK algorithms can be more suitable for real-time applications, and to see whether they can be competitive with the already tested structural family of integrators. The final objective of the work is to provide some practical criteria for those interested in achieving real-time performance for large and complex multibody systems.

New Message-Passing Decoding Algorithm of LDPC Codes by Partitioning Check Nodes (체크 노드 분할에 의한 LDPC 부호의 새로운 메시지 전달 복호 알고리즘)

  • Kim Sung-Hwan;Jang Min-Ho;No Jong-Seon;Hong Song-Nam;Shin Dong-Joon
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.31 no.4C
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    • pp.310-317
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    • 2006
  • In this paper, we propose a new sequential message-passing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This new decoding algorithm shows better bit error rate(BER) performance than that of the conventional message-passing decoding algorithm, especially for small number of iterations. Analytical results tell us that as the number of partitioned subsets of check nodes increases, the BER performance becomes better. We also derive the recursive equations for mean values of messages at variable nodes by using density evolution with Gaussian approximation. Simulation results also confirm the analytical results.

Application of Saint-Venant's Principle to Anisotropic Beams (이방성 보 구조물 응력해석에서의 생브낭 원리)

  • Kim, Jun-Sik
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.4
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    • pp.451-455
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    • 2012
  • Asymptotic analysis is a powerful tool for the mathematically rigorous design and analysis of anisotropic beam structures. However, it has a limitation in that the asymptotic approach requires asymptotically correct boundary conditions for higher-order solutions, which are often needed for beams weak in shear. A method utilizing Saint-Venant's principle was proposed in a previous work to improve the stress state of isotropic beams and plates. In this paper, such a method is generalized for anisotropic beams, so that one does not need to consider the asymptotically correct boundary conditions for higher-order solutions. Consequently, solving the recursive system equations is not necessary, which makes the method very efficient in terms of accuracy and computational effort.

A Study on an Adaptive Model Predictive Control for Nonlinear Processes using Fuzzy Model (퍼지모델을 이용한 비선형 공정의 적응 모델예측제어에 관한 연구)

  • 박종진;우광방
    • Journal of the Korean Institute of Intelligent Systems
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    • v.6 no.2
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    • pp.97-105
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    • 1996
  • In this paper, an adaptive model predictive controller for nodinear processes using fuzzy model is proposed. Adaptive structure is implemented by recursive fuzzy modeling. The model and control law can be obtained the same as GPC, because the consequent parts of the fuzzy model comprise linear equations of input and output variables. The proposed Adaptive fuzzy model predictive controller (AFMPC) controls nonlinear process well due to the intrinsic nonlinearity of the fuzzy model. When AFMPC's output is variation in the process control input, it maintains zero steady-state offset for a constant reference input and has superior performance. The properties and performance of the proposed control scheme were examined with nonlinear plant by simulation.

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Input-Output Feedback Linearization of Sensorless IM Drives with Stator and Rotor Resistances Estimation

  • Hajian, Masood;Soltani, Jafar;Markadeh, Gholamreza Arab;Hosseinnia, Saeed
    • Journal of Power Electronics
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    • v.9 no.4
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    • pp.654-666
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    • 2009
  • Direct torque control (DTC) of induction machines (IM) is a well-known strategy of these drives control which has a fast dynamic and a good tracking response. In this paper a nonlinear DTC of speed sensorless IM drives is presented which is based on input-output feedback linearization control theory. The IM model includes iron losses using a speed dependent shunt resistance which is determined through some effective experiments. A stator flux vector is estimated through a simple integrator based on stator voltage equations in the stationary frame. A novel method is introduced for DC offset compensation which is a major problem of AC machines, especially at low speeds. Rotor speed is also determined using a rotor flux sliding-mode (SM) observer which is capable of rotor flux space vector and rotor speed simultaneous estimation. In addition, stator and rotor resistances are estimated using a simple but effective recursive least squares (RLS) method combined with the so-called SM observer. The proposed control idea is experimentally implemented in real time using a FPGA board synchronized with a personal computer (PC). Simulation and experimental results are presented to show the capability and validity of the proposed control method.

A Study on the Modified RLS Algorithm Using Orthogonal Input Vectors (직교 입력 벡터를 이용하는 수정된 RLS 알고리즘에 관한 연구)

  • Ahn, Bong Man;Kim, Kwang Woong;Ahn, Hyun Gyu;Han, Byoung Sung
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.32 no.1
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    • pp.13-19
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    • 2019
  • This paper proposes an easy algorithm for finding tapped-delay-line (TDL) filter coefficients in an adaptive filter algorithm using orthogonal input signals. The proposed algorithm can be used to obtain the coefficients and errors of a TDL filter without using an inverse orthogonalization process for the orthogonal input signals. The form of the proposed algorithm in this paper has the advantages of being easy to use and similar to the familiar recursive least-squares (RLS) algorithm. In order to evaluate the proposed algorithm, system identification simulation of the $11^{th}$-order finite-impulse-response (FIR) filter was performed. It is shown that the convergence characteristics of the learning curve and the tracking ability of the coefficient vectors are similar to those of the conventional RLS analysis. Also, the derived equations and computer simulation results ensure that the proposed algorithm can be used in a similar manner to the Levinson-Durbin algorithm.

Study on the Applicability of a New Multi-body Dynamics Program Through the Application to the Heave Compensation System (상하동요 감쇠장치 적용을 통한 새로운 다물체동역학 프로그램의 적용성 검토)

  • Ku, Nam-Kug;Ha, Sol;Roh, Myung-Il
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.4
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    • pp.247-254
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    • 2013
  • In this paper, dynamic response analysis of a heave compensation system is performed for offshore drilling operations based on multibody dynamics. With this simulation, the efficiency of the heave compensation system can be virtually confirmed before it is applied to drilling operations. The heave compensation system installed on a semi-submersible platform consists of a passive and an active heave compensator. The passive and active heave compensator are composed of several bodies that are connected to each other with various types of joints. Therefore, to carry out the dynamic response analysis, the dynamics kernel was developed based on mutibody dynamics. To construct the equations of motion of the multibody system and to determine the unknown accelerations and constraint forces, the recursive Newton-Euler formulation was adapted. Functions of the developed dynamics kernel were verified by comparing them with other commercial dynamics kernels. The hydrostatic force with nonlinear effects, the linearized hydrodynamic force, and the pneumatic and hydraulic control forces were considered as the external forces that act on the platform of the semi-submersible rig and the heave compensation system. The dynamic simulation of the heave compensation system of the semi-submersible rig, which is available for drilling operations with a 3,600m water depth, was carried out. From the results of the simulation, the efficiency of the heave compensation system were evaluated before they were applied to the offshore drilling operations. Moreover, the calculated constraint forces could serve as reference data for the design of the mechanical system.

A Study of the Abalone Outlook Model Using by Partial Equilibrium Model Approach Based on DEEM System (부분균형모형을 이용한 전복 수급전망모형 구축에 관한 연구)

  • Han, Suk-Ho;Jang, Hee-Soo;Heo, Su-Jin;Lee, Nam-Su
    • The Journal of Fisheries Business Administration
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    • v.51 no.2
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    • pp.51-69
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    • 2020
  • The purpose of this study is to construct an outlook model that is consistent with the "Fisheries Outlook" monthly published by the Fisheries Outlook Center of the Korea Maritime Institute(KMI). In particular, it was designed as a partial equilibrium model limited to abalone items, but a model was constructed with a dynamic ecological equation model(DEEM) system taking into account biological breeding and shipping time. The results of this study are significant in that they can be used as basic data for model development of various items in the future. In this study, due to the limitation of monthly data, the market equilibrium price was calculated by using the recursive model construction method to be calculated directly as an inverse demand. A model was built in the form of a structural equation model that can explain economic causality rather than a conventional time series analysis model. The research results and implications are as follows. As a result of the estimation of the amount of young seashells planting, it was estimated that the coefficient of the amount of young seashells planting from the previous year was estimated to be 0.82 so that there was no significant difference in the amount of young seashells planting this year and last year. It is also meant to be nurtured for a long time after aquaculture license and limited aquaculture area(edge style) and implantation. The economic factor, the coefficient of price from last year was estimated at 0.47. In the case of breeding quantity, it was estimated that the longer the breeding period, the larger the coefficient of breeding quantity in the previous period. It was analyzed that the impact of shipments on the breeding volume increased. In the case of shipments, the coefficient of production price was estimated unelastically. As the period of rearing increased, the estimation coefficient decreased. Such result indicates that the expected price, which is an economic factor variable and that had less influence on the intention to shipments. In addition, the elasticity of the breeding quantity was estimated more unelastically as the breeding period increased. This is also correlated with the relative coefficient size of the expected price. The abalone supply and demand forecast model developed in this study is significant in that it reduces the prediction error than the existing model using the ecological equation modeling system and the economic causal model. However, there are limitations in establishing a system of simultaneous equations that can be linked to production and consumption between industries and items. This is left as a future research project.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).