• Title/Summary/Keyword: non-linear problem

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A Study on the Irregular Nesting Problem Using Genetic Algorithm and No Fit Polygon Methodology (유전 알고리즘과 No Fit Polygon법을 이용한 임의 형상 부재 최적배치 연구)

  • 유병항;김동준
    • Journal of Ocean Engineering and Technology
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    • v.18 no.2
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    • pp.77-82
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    • 2004
  • The purpose of this study is to develop a nesting algorithm, using a genetic algorithm to optimize nesting order, and modified No Fit Polygon(NFP) methodology to place parts with the order generated from the previous genetic algorithm. Various genetic algorithm techniques, which have thus far been applied to the Travelling Salesman Problem, were tested. The partially mapped crossover method, the inversion method for mutation, the elitist strategy, and the linear scaling method of fitness value were selected to optimize the nesting order. A modified NFP methodology, with improved searching capability for non-convex polygon, was applied repeatedly to the placement of parts according to the order generated from previous genetic algorithm. Modified NFP, combined with the genetic algorithms that have been proven in TSP, were applied to the nesting problem. For two example cases, the combined nesting algorithm, proposed in this study, shows better results than that from previous studies.

Optimization of Economic Load Dispatch Problem Using Linearly Approximated Smooth Fuel Cost Function (선형 근사 평활 발전 비용함수를 이용한 경제급전 문제의 최적화)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.14 no.3
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    • pp.191-198
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    • 2014
  • This paper proposes a simple linear function approximation method to solve an economic load dispatch problem with complex non-smooth generating cost function. This algorithm approximates a non-smooth power cost function to a linear approximate function and subsequently shuts down a generator with the highest operating cost and reduces the power of generator with more generating cost in order to balance the generating power and demands. When applied to the most prevalent benchmark economic load dispatch cases, the proposed algorithm is found to dramatically reduce the power cost than does heuristic algorithm. Moreover, it has successfully obtained results similar to those obtained through a quadratic approximate function method.

A Fuzzy Allocation Model and Its Application to Attacker Assignment Problem (FUZZY 할당모형 및 공격항공기의 표적 할당 문제에 대한 응용)

  • Yun Seok-Jun;Go Sun-Ju
    • Journal of the military operations research society of Korea
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    • v.18 no.1
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    • pp.47-60
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    • 1992
  • A class of allocation problems can be modeled in a linear programming formulation. But in reality, the coefficient of both the cost and constraint equations can not be generally determined by crisp numbers due to the imprecision or fuzziness in the related parameters. To account for this. a fuzzy version is considered and solved by transforming to a conventional non-linear programming model. This gives a solution as well as the degree that the solution satisfies the objective and constraints simultaneously and hence will be very useful to a decision maker. An attacker assignment problem for multiple fired targets has been modeled by a linear programming formulation by Lemus and David. in which the objective is to minimize the cost that might occur on attacker's losses during the mission. A fuzzy version of the model is formulated and solved by transforming it to a conventional nonlinear programming formulation following the Tanaka's approach. It is also expected that the fuzzy approach will have wide applicability in general allocation problems

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The Analysis of Non-linear Interaction Problem between the Consolidation ground and the Upper Structure (압밀지반과 상부구조의 비선형 상호작용의 해석)

  • 이외득;정진환
    • Computational Structural Engineering
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    • v.10 no.4
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    • pp.327-336
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    • 1997
  • When a structure is built on the consolidation ground, the instant elastic deflection occures according to the characteristics of the ground and the load on it. And the corresponding contact pressure is established. But, as time passes, the secondary consolidating deflection is added to the instant elastic deflection, the upper structure, due to its flexural rigidity, resist to the additional curvature. So the variation of the contact pressure occurs. And this new contact pressure exerts influence on the consolidation form again. The new consolidation form exerts influence on the contact pressure in return. This kind of interaction continues till all the consolidation of the ground is finished. So the consolidation problem can not be definded as the linear problem. This paper intends to scheme an approximate iteration method to analyse this non-linear interaction problem between the upper structure and the lower consolidation ground which supports the former.

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Two-Dimensional Localization Problem under non-Gaussian Noise in Underwater Acoustic Sensor Networks (비가우시안 노이즈가 존재하는 수중 환경에서 2차원 위치추정)

  • Lee, DaeHee;Yang, Yeon-Mo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.23 no.5
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    • pp.418-422
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    • 2013
  • This paper has considered the location estimation problem in two dimension space by using a non-linear filter under non-Gaussian noise in underwater acoustic sensor networks(UASNs). Recently, the extended Kalman filter (EKF) is widely used in location estimation. However, the EKF has a lot of problems in the non-linear system under the non-gaussian noise environment like underwater environment. In this paper, we propose the improved Two-Dimension Particle Filter (TDPF) using the re-interpretation distribution techniques based on the maximum likelihood (ML). Through the simulation, we compared and analyzed the proposed TDPF with the EKF under the non-Gaussian underwater sensor networks. Finally, we determined that the TDPF's result shows more accurate localization than EKF's result.

Small scale effect on the vibration of non-uniform nanoplates

  • Chakraverty, S.;Behera, Laxmi
    • Structural Engineering and Mechanics
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    • v.55 no.3
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    • pp.495-510
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    • 2015
  • Free vibration of non-uniform embedded nanoplates based on classical (Kirchhoff's) plate theory in conjunction with nonlocal elasticity theory has been studied. The nanoplate is assumed to be rested on two-parameter Winkler-Pasternak elastic foundation. Non-uniform material properties of nanoplates have been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinates. Detailed analysis has been reported for all possible casesof such variations. Trial functions denoting transverse deflection of the plate are expressed in simple algebraic polynomial forms. Application of the present method converts the problem into generalised eigen value problem. The study aims to investigate the effects of non-uniform parameter, elastic foundation, nonlocal parameter, boundary condition, aspect ratio and length of nanoplates on the frequency parameters. Three-dimensional mode shapes for some of the boundary conditions have also been illustrated. One may note that present method is easier to handle any sets of boundary conditions at the edges.

Delay-dependent Robust and Non-fragile Stabilization for Descriptor Systems with Parameter Uncertainties and Time-varying Delays (변수 불확실성과 시변 시간지연을 가지는 특이시스템의 지연 종속 강인 비약성 안정화)

  • Kim, Jong-Hae
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.57 no.10
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    • pp.1854-1860
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    • 2008
  • In this paper, we deal with the problem of delay-dependent robust and non-fragile stabilization for descriptor systems with parameter uncertainties and time-varying delays on the basis of strict LMI(linear matrix inequality) technique. Also, the considering controller is composed of multiplicative uncertainty. The delay-dependent robust and non-fragile stability criterion without semi-definite condition and decomposition of system matrices is obtained. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free and stable in spite of all admissible parameter uncertainties, time-varying delays, and controller fragility. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Reliability Analysis of the Non-normal Probability Problem for Limited Area using Convolution Technique (컨볼루션 기법을 이용한 영역이 제한된 비정규 확률문제의 신뢰성 해석)

  • Lee, Hyunman;Kim, Taegon;Choi, Won;Suh, Kyo;Lee, JeongJae
    • Journal of The Korean Society of Agricultural Engineers
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    • v.55 no.5
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    • pp.49-58
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    • 2013
  • Appropriate random variables and probability density functions based on statistical analysis should be defined to execute reliability analysis. Most studies have focused on only normal distributions or assumed that the variables showing non-normal characteristics follow the normal distributions. In this study, the reliability problem with non-normal probability distribution was dealt with using the convolution method in the case that the integration domains of variables are limited to a finite range. The results were compared with the traditional method (linear transformation of normal distribution) and Monte Carlo simulation method to verify that the application was in good agreement with the characteristics of probability density functions with peak shapes. However it was observed that the reproducibility was slightly reduced down in the tail parts of density function.

Multi-cracking modelling in concrete solved by a modified DR method

  • Yu, Rena C.;Ruiz, Gonzalo
    • Computers and Concrete
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    • v.1 no.4
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    • pp.371-388
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    • 2004
  • Our objective is to model static multi-cracking processes in concrete. The explicit dynamic relaxation (DR) method, which gives the solutions of non-linear static problems on the basis of the steady-state conditions of a critically damped explicit transient solution, is chosen to deal with the high geometric and material non-linearities stemming from such a complex fracture problem. One of the common difficulties of the DR method is its slow convergence rate when non-monotonic spectral response is involved. A modified concept that is distinct from the standard DR method is introduced to tackle this problem. The methodology is validated against the stable three point bending test on notched concrete beams of different sizes. The simulations accurately predict the experimental load-displacement curves. The size effect is caught naturally as a result of the calculation. Micro-cracking and non-uniform crack propagation across the fracture surface also come out directly from the 3D simulations.

Optimization of inlet velocity profile for uniform epitaxial growth (균일한 에피층 성장을 위한 입구 유속분포 최적화)

  • Cho W. K.;Choi D. H.;Kim M.-U.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.11a
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    • pp.121-126
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    • 1998
  • A numerical optimization procedure is developed to find the inlet velocity profile that yields the most uniform epitaxial layer in a vertical MOCVD reactor. It involves the solution of fully elliptic equations of motion, temperature, and concentration; the finite volume method based on SIMPLE algorithm has been adopted to solve the Navier-Stokes equations. The overall optimization process is highly nonlinear and has been efficiently treated by the sequential linear programming technique that breaks the non-linear problem into a series of linear ones. The optimal profile approximated by a 6th-degree Chebyshev polynomial is very successful in reducing the spatial non-uniformity of the growth rate. The optimization is particularly effective to the high Reynolds number flow. It is also found that a properly constructed inlet velocity profile can suppress the buoyancy driven secondary flow and improve the growth-rate uniformity.

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