• 제목/요약/키워드: Numerical approximation

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Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels

  • Wang, Qian;Lin, Hai;Kam, Pooi-Yuen
    • Journal of Communications and Networks
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    • 제18권2호
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    • pp.182-189
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    • 2016
  • The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

흡수,방사 및 선형비등방 산란 매질을 포함하는 밀폐공간내의 자연대류- 복사열전달에 대한 수치해석 (Numerical Analysis of Natural Convection-Radiation Heat Transfer in an Enclosure Containing Absorbing, emitting and Linear Anisotropic Scattering Medium)

  • 차상명;김종열;박희용
    • 대한기계학회논문집
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    • 제16권5호
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    • pp.952-964
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    • 1992
  • 본 연구에서는 2차원 정사각형 밀폐공간내에 열복사를 흡수, 방사 및 비등방 산란하는 매질이 존재할 때 자연대류와 복사의 상호작용을 선형 비등방 산란을 가정 하고 복사열전달의 계산시 P-N 근사법을 이용하여 해석하였다. 수치계산을 통하여 Planck 수, 산란알베도, 광학두께, 벽방사율 및 비등방 산란이 유동 및 온도 특성 그리고 열전달에 미치는 영향을 조사하였다.

Hermite함수를 이용한 지형곡면근사 (A Terrain Surface Approximation Using the Hermite Function)

  • 문두열;정범석;이용희
    • 한국측량학회지
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    • 제20권3호
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    • pp.265-272
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    • 2002
  • 지금까지 토공량계산을 위한 많은 방법들이 단순식에서부터 복잡한 방법으로 개발되어 왔다. 일찍이 토공량계산을 위한 기본적인 방법은 상부면적을 x, y방향으로 뻗은 경계선의 사각격자로 나누어 계산한다. 그러나 이들 방법은 많은 측량현장에서 요구되는 토공량견적을 정확하게 계산할 수 없다. 1998년 Easa는 x, y 각 방향으로 같은 선상을 따라 사각격자를 나누었다. 이 방법은 격자 양방향으로 3차의 Hermite 다항식을 이용하였다. 이것은 반드시 동일한 x, y방향의 경계를 따라 표고데이터가 존재해야 하므로 지형의 최대, 최소점 같은 점의 선택을 불가능하게 한다. 이 연구에서 제시된 토공량 계산법은 Easa(1998)방법의 단점을 피하고 장점을 결합시켰다. 제안된 방법은 가로x, 세로y 방향의 각 경계를 따라 3차의 Hermite 다항식을 이용하지만 각각의 부등간격의 격자는 양방향으로 일정하지 않고 부분적으로 비격자형태로 이루어져 있다. 새롭게 제시된 방법은 다른 재래식 방법보다 더 나은 정확도를 제공한다.

고속 권상운동과 흔들림억제 궤적추종을 위한 천정주행 크레인의 퍼지 비선형 적응제어 (Fuzzy Nonlinear Adaptive Control of Overhead Cranes for Anti-Sway Trajectory Tracking and High-Speed Hoisting Motion)

  • 박문수;좌동경;홍석교
    • 한국지능시스템학회논문지
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    • 제17권5호
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    • pp.582-590
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    • 2007
  • 천정주행 크레인의 고속 권상작업 및 흔들림 억제 궤적추종을 위한 비선형 적응제어 방법을 제시한다. 천정주행 크레인의 흔들림 운동은 트롤리의 가속도. 권상로프의 길이 및 권상속도와 강하게 결합되어 있다. 이는 비간섭 제어 기반의 흔들림 억제 궤적추종 제어법칙을 설계하는데 있어 장애요인으로 작용한다. 이러한 문제를 해결하기 위해, 트롤리의 가속도와 권상속도의 영향을 최소화하는 방법으로 불확실성이 존재하는 경우에도 흔들림 운동의 궁극적 균일 유계성을 보장하는 퍼지 비선형 적응형 흔들림 억제 궤적추종제어법칙을 제안한다. 특히, 제안한 방법은 파라미터 변화. 외란 등을 포함한 시스템 불확실성을 퍼지 불확실성 관측기를 이용하여 보상한다. 따라서, 퍼지관측기의 근사화 오차가 영으로 수렴할 때 추종오차 및 흔들림 각도의 궁극적 한계치는 영으로 감소한다. 끝으로 제안한 방법의 성능검증을 위한 모의실험 견과를 제시한다.

다수의 광심유와 산재한 제한 영역 파장 변환기로 구성된 파장분할다중화 광통신항의 성능 분석 모형 (Analytical Model for Multi-Fiber WDM Networks with Sparse and Limited Wavelength Conversion)

  • 정한유;서승우;최윤호
    • 한국통신학회논문지
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    • 제34권4B호
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    • pp.394-402
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    • 2009
  • 본 논문에서는 다수의 광섬유로 이루서진 광링크와 산재하여 있는 제한 영역 파장변환 능력을 가진 노드들로 구성된 광통신 망의 불통확률을 정확하게 계산할 수 있는 새로운 성능분석 모형을 제안한다. 제안하는 성능분석 모형은 다수의 광섬유로 이루어진 광링크 상에서 사용 가능한 파장들의 분포와 제한 영역 파장변환 이후의 사용 가능한 파장들의 분포, 그리고 다수의 광링크가 연결된 광경로에서의 불통 확률을 계산하기 위한 재귀적 공식을 도출함을 특징으로 한다. NSFNET 망에서 수행한 시뮬레이션 결과를 통해 제안하는 성능분석 모형이 광통신 망의 불통확률을 정확히 예측함을 보인다. 또한, 파장 연속성 제약이 없는 경우의 이상적인 블통화률에 근접하는 성능을 얻기 위해서 소수의 제한영역 파장변환 노드와 소수의 광섬유만으로 구성된 광링크를 포설하는 것으로 충분함을 보인다.

기사용(旣使用) 핵연료저장시(核燃料貯藏時) 핵임계(核臨界) 안전성(安全性) 결정(決定) (Criticality Safety Determination of Spent Fuel Storage Vault)

  • 육종철
    • Journal of Radiation Protection and Research
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    • 제4권1호
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    • pp.1-4
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    • 1979
  • 중성자(中性子) 수송이론(輸送理論)을 써서 기사용(旣使用) 핵연료(核燃料) 저장조(貯藏槽)에 있는 한 개(個)의 PWR용(用) 핵연료집합체(核燃料集合體)에 대(對)한 유효증배계수(有效增倍係數)($k_{eff}$)를 산출(算出)하였다. 이때 중성자(中性子) 수송방정식(輸送方程式)을 Sn-근이법(近以法)이라고 부르는 각분해법(角分害法)(Discrete ordinates method)으로 풀어서 유효증배계수(有效增倍係數)를 구했으며 이것이 핵임계(核臨界) 안전성(安全性) 결정(決定)이 된다. 본(本) 연구(硏究)에서는 각(角)과 에너지를 각각(各各) 4구간(區間)과 16군(郡)으로 분할(分割)하고 공간구간(空間區間)은 27구간(區間)으로 나누되 상이(相異)한 물질(物質)의 경계면근처(境界面近處)에서 세분(細分)하였다. 이와같은 방법(方法)으로 구한 유효증배계수(有效增倍係數)는 0.6145였는 데 이는 타연구자(他硏究者)가 계산(計算)한 반무한배열(半無限配列) 핵연료집합체(核燃料集合體)에 대한 유효증배계수(有效增倍係數)에 비(比)하여 상당히 낮은 값이었다.

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Analysis of Stokes flows by Carrera unified formulation

  • Varello, Alberto;Pagani, Alfonso;Guarnera, Daniele;Carrera, Erasmo
    • Advances in aircraft and spacecraft science
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    • 제5권3호
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    • pp.363-383
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    • 2018
  • One-dimensional (1D) models of incompressible flows, can be of interest for many applications in which fast resolution times are demanded, such as fluid-structure interaction of flows in compliant pipes and hemodynamics. This work proposes a higher-order 1D theory for the flow-field analysis of incompressible, laminar, and viscous fluids in rigid pipes. This methodology is developed in the domain of the Carrera Unified Formulation (CUF), which was first employed in structural mechanics. In the framework of 1D modelling, CUF allows to express the primary variables (i.e., velocity and pressure fields in the case of incompressible flows) as arbitrary expansions of the generalized unknowns, which are functions of the 1D computational domain coordinate. As a consequence, the governing equations can be expressed in terms of fundamental nuclei, which are invariant of the theory approximation order. Several numerical examples are considered for validating this novel methodology, including simple Poiseuille flows in circular pipes and more complex velocity/pressure profiles of Stokes fluids into non-conventional computational domains. The attention is mainly focused on the use of hierarchical McLaurin polynomials as well as piece-wise nonlocal Lagrange expansions of the generalized unknowns across the pipe section. The preliminary results show the great advantages in terms of computational costs of the proposed method. Furthermore, they provide enough confidence for future extensions to more complex fluid-dynamics problems and fluid-structure interaction analysis.

Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches

  • Tahouneh, Vahid;Naei, Mohammad Hasan;Mashhadi, Mahmoud Mosavi
    • Steel and Composite Structures
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    • 제34권2호
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    • pp.261-277
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    • 2020
  • The main objective of this research paper is to consider vibration analysis of vacancy defected graphene sheet as a nonisotropic structure via molecular dynamic and continuum approaches. The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defected graphene sheets. Molecular dynamic simulations have been performed to estimate the mechanical properties of graphene as a nonisotropic structure with single- and double- vacancy defects using open source well-known software i.e., large-scale atomic/molecular massively parallel simulator (LAMMPS). The interactions between the carbon atoms are modelled using Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. An isogeometric analysis (IGA) based upon non-uniform rational B-spline (NURBS) is employed for approximation of single-layered graphene sheets deflection field and the governing equations are derived using nonlocal elasticity theory. The dependence of small-scale effects, chirality and different defect types on vibrational characteristic of graphene sheets is investigated in this comprehensive research work. In addition, numerical results are validated and compared with those achieved using other analysis, where an excellent agreement is found. The interesting results indicate that increasing the number of missing atoms can lead to decrease the natural frequencies of graphene sheets. It is seen that the degree of the detrimental effects differ with defect type. The Young's and shear modulus of the graphene with SV defects are much smaller than graphene with DV defects. It is also observed that Single Vacancy (SV) clusters cause more reduction in the natural frequencies of SLGS than Double Vacancy (DV) clusters. The effectiveness and the accuracy of the present IGA approach have been demonstrated and it is shown that the IGA is efficient, robust and accurate in terms of nanoplate problems.

Global performances of a semi-submersible 5MW wind-turbine including second-order wave-diffraction effects

  • Kim, H.C.;Kim, M.H.
    • Ocean Systems Engineering
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    • 제5권3호
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    • pp.139-160
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    • 2015
  • The global performance of the 5MW OC4 semisubmersible floating wind turbine in random waves was numerically simulated by using the turbine-floater-mooring fully coupled and time-domain dynamic analysis program FAST-CHARM3D. There have been many papers regarding floating offshore wind turbines but the effects of second-order wave-body interactions on their global performance have rarely been studied. The second-order wave forces are actually small compared to the first-order wave forces, but its effect cannot be ignored when the natural frequencies of a floating system are outside the wave-frequency range. In the case of semi-submersible platform, second-order difference-frequency wave-diffraction forces and moments become important since surge/sway and pitch/roll natural frequencies are lower than those of typical incident waves. The computational effort related to the full second-order diffraction calculation is typically very heavy, so in many cases, the simplified approach called Newman's approximation or first-order-wave-force-only are used. However, it needs to be justified against more complete solutions with full QTF (quadratic transfer function), which is a main subject of the present study. The numerically simulated results for the 5MW OC4 semisubmersible floating wind turbine by FAST-CHARM3D are also extensively compared with the DeepCWind model test results by Technip/NREL/UMaine. The predicted motions and mooring tensions for two white-noise input-wave spectra agree well against the measure values. In this paper, the numerical static-offset and free-decay tests are also conducted to verify the system stiffness, damping, and natural frequencies against the experimental results. They also agree well to verify that the dynamic system modeling is correct to the details. The performance of the simplified approaches instead of using the full QTF are also tested.

Integrated fire dynamics and thermomechanical modeling framework for steel-concrete composite structures

  • Choi, Joonho;Kim, Heesun;Haj-ali, Rami
    • Steel and Composite Structures
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    • 제10권2호
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    • pp.129-149
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    • 2010
  • The objective of this study is to formulate a general 3D material-structural analysis framework for the thermomechanical behavior of steel-concrete structures in a fire environment. The proposed analysis framework consists of three sequential modeling parts: fire dynamics simulation, heat transfer analysis, and a thermomechanical stress analysis of the structure. The first modeling part consists of applying the NIST (National Institute of Standards and Technology) Fire Dynamics Simulator (FDS) where coupled CFD (Computational Fluid Dynamics) with thermodynamics are combined to realistically model the fire progression within the steel-concrete structure. The goal is to generate the spatial-temporal (ST) solution variables (temperature, heat flux) on the surfaces of the structure. The FDS-ST solutions are generated in a discrete form. Continuous FDS-ST approximations are then developed to represent the temperature or heat-flux at any given time or point within the structure. An extensive numerical study is carried out to examine the best ST approximation functions that strike a balance between accuracy and simplicity. The second modeling part consists of a finite-element (FE) transient heat analysis of the structure using the continuous FDS-ST surface variables as prescribed thermal boundary conditions. The third modeling part is a thermomechanical FE structural analysis using both nonlinear material and geometry. The temperature history from the second modeling part is used at all nodal points. The ABAQUS (2003) FE code is used with external user subroutines for the second and third simulation parts in order to describe the specific heat temperature nonlinear dependency that drastically affects the transient thermal solution especially for concrete materials. User subroutines are also developed to apply the continuous FDS-ST surface nodal boundary conditions in the transient heat FE analysis. The proposed modeling framework is applied to predict the temperature and deflection of the well-documented third Cardington fire test.