• Title/Summary/Keyword: Bilinearity

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Minimization of Trim Loss Problem in Paper Mill Scheduling Using MINLP (MINLP를 이용한 제지 공정의 파지 손실 최소화)

  • Na, Sung-hoon;Ko, Dae-Ho;Moon, Il
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.392-392
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    • 2000
  • This study performs optimization of paper mill scheduling using MINLP(Mixed-Integer Non-Linear Programming) method and 2-step decomposing strategy. Paper mill process is normally composed of five units: paper machine, coater, rewinder, sheet cutter and roll wrapper/ream wrapper. Various kinds of papers are produced through these units. The bottleneck of this process is how to cut product papers efficiently from raw paper reel and this is called trim loss problem or cutting stock problem. As the trim must be burned or recycled through energy consumption, minimizing quantity of the trim is important. To minimize it, the trim loss problem is mathematically formulated in MINLP form of minimizing cutting patterns and trim as well as satisfying customer's elder. The MINLP form of the problem includes bilinearity causing non-linearity and non-convexity. Bilinearity is eliminated by parameterization of one variable and the MINLP form is decomposed to MILP(Mixed-Integer Linear programming) form. And the MILP problem is optimized by means of the optimization package. Thus trim loss problem is efficiently minimized by this 2-step optimization method.

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Efficient and Secure Pairing Algorithm over Binary Fields (안전하고 효율적인 이진 필드상의 페어링 알고리즘)

  • Choi, Doo-Ho;Han, Dong-Guk;Kim, Ho-Won
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • 2008.02a
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    • pp.69-72
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    • 2008
  • 최근 PKI-less 공개키 암호 시스템에 대한 연구가 진척되면서, 페어링(Pairing) 기반의 암호 시스템이 주목을 받고 있다. 페어링 기반의 암호 시스템은 두 개의 타원 곡선 상의 점을 유한체의 값으로 보내는 양방향 선형성(Bilinearity)을 가지는 페어링 함수를 기반으로 구성되는 암호 시스템이다. 페어링 기반의 암호 시스템 구현을 위해서는 페어링 연산 알고리즘이 필수적이며, 효율적인 페어링 연산을 위한 많은 연구가 진행되고 있다. 이러한 페어링 알고리즘에도 기존의 타원곡선 스칼라곱 알고리즘에서 야기되었던 부채널 공격이 동일하게 적용되기 때문에, 안전한 페어링 알고리즘을 위해서는 부채널 공격에 대한 저항성을 갖는 알고리즘이 필요하다. 이에 본 논문에서는 부채널 공격에도 안전하면서 비교적 효율적인 이진 필드 상의 페어링 알고리즘을 제시한다. 본 페어링 알고리즘은 기존의 부체널 공격 저항성을 갖는 페어링 알고리즘 중 가장 효율적인 알고리즘에 비해 효율성이 17% 정도 향상되었다.

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Static and dynamic analysis of cable-suspended concrete beams

  • Kumar, Pankaj;Ganguli, Abhijit;Benipal, Gurmail
    • Structural Engineering and Mechanics
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    • v.64 no.5
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    • pp.611-620
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    • 2017
  • A new theory of weightless sagging planer elasto-flexible cables under point loads is developed earlier by the authors and used for predicting the nonlinear dynamic response of cable-suspended linear elastic beams. However, this theory is not valid for nonlinear elastic cracked concrete beams possessing different positive and negative flexural rigidity. In the present paper, the flexural response of simply supported cracked concrete beams suspended from cables by two hangers is presented. Following a procedure established earlier, rate-type constitutive equations and third order nonlinear differential equations of motion for the structures undergoing small elastic displacements are derived. Upon general quasi-static loading, negative nodal forces, moments and support reactions may be introduced in the cable-suspended concrete beams and linear modal frequencies may abruptly change. Subharmonic resonances are predicted under harmonic loading. Uncoupling of the nodal response is proposed as a more general criterion of crossover phenomenon. Significance of the bilinearity ratio of the concrete beam and elasto-configurational displacements of the cable for the structural response is brought out. The relevance of the proposed theory for the analysis and the design of the cable-suspended bridges is critically evaluated.

Bilinear elastodynamical models of cracked concrete beams

  • Pandey, Umesh Kumar;Benipal, Gurmail S.
    • Structural Engineering and Mechanics
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    • v.39 no.4
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    • pp.465-498
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    • 2011
  • Concrete structures are generally cracked in flexural tension at working loads. Concrete beams with asymmetric section details and crack patterns exhibit different flexural rigidity depending upon the sense of the applied flexural moment. In this paper, three different models, having the same natural period, of such SDOF bilinear dynamical systems have been proposed. The Model-I and Model-II have constant damping coefficient, but the latter is characterized by two stiffness coefficients depending upon the sense of vibration amplitude. The Model-III, additionally, has two damping coefficients as well. In this paper, the dynamical response of Model-III to sinusoidal loading has been investigated and compared with that of Model-II studied earlier. It has been found that Model-III exhibits regular and irregular sub-harmonics, jump phenomena and strong sensitivity to initial conditions, forcing frequency, system period as well as the sense of peak sinusoidal force. The constant sustained load has been found to affect the natural period of the dynamical system. The predictions of Model-I have been compared with those of the approximate linear model adopted in present practice. The behaviour exhibited by different models of the SDOF cracked elastic concrete structures under working loads and the theoretical and practical implications of the approach followed have been critically evaluated.

Low Cycle Fatigue Characteristics of A356 Cast Aluminum Alloy and Fatigue Life Models (주조 알루미늄합금 A356의 저주기 피로특성 및 피로수명 모델)

  • 고승기
    • Transactions of the Korean Society of Automotive Engineers
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    • v.1 no.1
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    • pp.131-139
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    • 1993
  • Low cycle fatigue characteristics of cast aluminum alloy A356 with a yield strength and ultimate strength of 229 and 283 MPa respectively was evaluated using smooth axial specimen under strain controlled condition. Reversals to failure ranged from 16 to 107. The cast aluminum alloy exhibited cyclically strain-gardening behavior. The results of low cycle fatigue tests indicated that the conventional low cycle fatigue tests indicated that the conventional low cycle fatigue life model was not a satisfactory representation of the data. This occurred because the elastic strain-life curve was not-log-log linear and this phenomena caused a nonconservative and unsafe fatigue life prediction at both extremes of long and short lives. A linear log-log total strain-life model and a bilinear log-log elastic strain-life model were proposed in order to improve the representation of data compared to the conventional low cycle fatigue life model. Both proposed fatigue life models were statistically analyzed using F tests and successfully satisfied. However, the low cycle fatigue life model generated by the bilinear log-log elastic strain-life equation yielded a discontinuous curve with nonconservatism in the region of discontinuity. Among the models examined, the linear log-log total strain-life model provided the best representation of the low cycle fatigue data. Low cycle fatigue life prediction method based on the local strain approach could conveniently incorporated both proposed fatigue life models.

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