• Title/Summary/Keyword: Exponential function

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An Efficient Method for Mold Thermal Cycle Analysis in Repeated Forming Process of TV Glass (TV 유리의 반복 성형공정에서 금형 열사이클 해석을 위한 효과적 방법)

  • Choi, Joo-Ho;Kim, Jun-Bum;Hwang, Jung-Hea;Ha, Duk-Sik
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.24 no.9
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    • pp.1219-1226
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    • 2000
  • An efficient method is developed for plunger thermal cycle analysis in repeated forming process of the TV glass. The plunger undergoes temperature fluctuation during a cycle due to the repeated contact and separation from the glass, which attains a cyclic steady state having same temperature history at every cycle. Straightforward analysis of this problem brings about more than 80 cycles to get reasonable solution, and yet hard to setup stopping criteria due to extremely slow convergence. An exponential fitting method is proposed to overcome the difficulty, which finds exponential function to best approximate temperature values of 3 consecutive cycles, and new cycle is restarted with the fitted value at infinite time. Numerical implementation shows that it reduces the number of cycles dramatically to only 6-18 cycles to reach convergence within 10 accuracy. A system for the analysis is constructed, in which the thermal analysis is performed by commercial software ANSYS, and the fitting of the result is done by IMSL library. From the parametric studies, one reveals some important facts that although the plunger cooling or the glass thickness is increased, its counter part in contact is not much affected, duo to the low thermal conductance of the glass.

Minimum Density Power Divergence Estimation for Normal-Exponential Distribution (정규-지수분포에 대한 최소밀도함수승간격 추정법)

  • Pak, Ro Jin
    • The Korean Journal of Applied Statistics
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    • v.27 no.3
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    • pp.397-406
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    • 2014
  • The minimum density power divergence estimation has been a popular topic in the field of robust estimation for since Basu et al. (1988). The minimum density power divergence estimator has strong robustness properties with the little loss in asymptotic efficiency relative to the maximum likelihood estimator under model conditions. However, a limitation in applying this estimation method is the algebraic difficulty on an integral involved in an estimation function. This paper considers a minimum density power divergence estimation method with approximated divergence avoiding such difficulty. As an example, we consider the normal-exponential convolution model introduced by Bolstad (2004). The estimated divergence in this case is too complicated; consequently, a Laplace approximation is employed to obtain a manageable form. Simulations and an empirical study show that the minimum density power divergence estimators based on an approximated estimated divergence for the normal-exponential model perform adequately in terms of bias and efficiency.

Finding Optimal Controls for Helicopter Maneuvers Using the Direct Multiple-Shooting Method

  • Kim, Min-Jae;Hong, Ji-Seung;Kim, Chang-Joo
    • International Journal of Aeronautical and Space Sciences
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    • v.11 no.1
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    • pp.10-18
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    • 2010
  • The purpose of this paper deals with direct multiple-shooting method (DMS) to resolve helicopter maneuver problems of helicopters. The maneuver problem is transformed into nonlinear problems and solved DMS technique. The DMS method is easy in handling constraints and it has large convergence radius compared to other strategies. When parameterized with piecewise constant controls, the problems become most effectively tractable because the search direction is easily estimated by solving the structured Karush-Kuhn-Tucker (KKT) system. However, generally the computation of function, gradients and Hessian matrices has considerably time-consuming for complex system such as helicopter. This study focused on the approximation of the KKT system using the matrix exponential and its integrals. The propose method is validated by solving optimal control problems for the linear system where the KKT system is exactly expressed with the matrix exponential and its integrals. The trajectory tracking problem of various maneuvers like bob up, sidestep near hovering flight speed and hurdle hop, slalom, transient turn, acceleration and deceleration are analyzed to investigate the effects of algorithmic details. The results show the matrix exponential approach to compute gradients and the Hessian matrix is most efficient among the implemented methods when combined with the mixed time integration method for the system dynamics. The analyses with the proposed method show good convergence and capability of tracking the prescribed trajectory. Therefore, it can be used to solve critical areas of helicopter flight dynamic problems.

Mechanical behaviour analysis of FGM plates on elastic foundation using a new exponential-trigonometric HSDT

  • Fatima Z. Zaoui;Djamel Ouinas;Abdelouahed Tounsi;Belkacem Achour;Jaime A. Vina Olay;Tayyab A. Butt
    • Steel and Composite Structures
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    • v.47 no.5
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    • pp.551-568
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    • 2023
  • In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

Comparison of Various Shear Deformation Functions for Laminated Composite/Sandwich Plates (복합적층 및 샌드위치판 전단변형함수에 관한 상호비교연구)

  • Park, Won-Tae;Chang, Suk-Yoon;Chun, Kyoung-Sik
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.1 no.3
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    • pp.1-9
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    • 2010
  • In this paper, we used various shear deformation functions for modelling isotropic, symmetric composite and sandwich plates discretized by a mixed finite element method based on the Lagrangian/Hermite interpolation functions. These shear deformation theories uses polynomial, trigonometric, hyperbolic and exponential functions through the thickness direction, allowing for zero transverse shear stresses at the top and bottom surfaces of the plate. All shear deformation functions are compared with other available analytical/3D elasticity solutions, are predicted the reasonable accuracy for investigated problems. Particularly, The present results show that the use of exponential shear deformation theory (Karama et al. 2003; Aydogu 2009) provides very good solutions for composite and sandwich plates.

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A study on Public Key Authentication using Polynomial Secret Sharing in WSN (무선센서네트워크에서 다항식 비밀분산을 이용한 공개키 인증방식에 관한 연구)

  • Kim, Il-Do;Kim, Dong-Cheon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.13 no.11
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    • pp.2479-2487
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    • 2009
  • Earlier researches on Sensor Networks preferred symmetric key-based authentication schemes in consideration of limitations in network resources. However, recent advancements in cryptographic algorithms and sensor-node manufacturing techniques have opened suggestion to public key-based solutions such as Merkle tree-based schemes. This paper proposes a new concept of public key-based authentication using Polynomial Secret Sharing that can be effectively applied to sensor networks and a detection of malicious node using the hash function. This scheme is based on exponential distributed data concept, a derivative from Shamir's (t,n) threshold scheme, in which the authentication of neighbouring nodes are done simultaneously while minimising resources of sensor nodes and providing network scalability.

The IEEE 802.11 MAC Protocol to solve Unfairness Problem in Multihop Wireless Ad Hoc Networks (다중 무선 에드혹 네트워크에서 불공정 문제를 해결하기 위한 802.11 MAC 프로토콜)

  • Nam, Jae-Hyun
    • Journal of the Korea Society of Computer and Information
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    • v.12 no.6
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    • pp.229-234
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    • 2007
  • In the IEEE 802.11 Wireless Local Area Networks (WLANs), network nodes experiencing collisions on the shared channel need to backoff for a random period of time. which is uniformly selected from the Contention Window (CW) This contention window is dynamically controlled by the Binary Exponential Backoff (BEB) algorithm. The BEB scheme suffers from a unfairness problem and low throughput under high traffic load. In this paper, I propose a new backoff algorithm for use with the IEEE 802.11 Distributed Coordination Function.

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Nonlinear Height-DBH Growth Models for Larix kaempferi in Gangwon and North Gyeongsang Province

  • Lee, Daesung;Choi, Jungkee;Seo, Yeongwan;Kim, Euigyeong
    • Journal of Forest and Environmental Science
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    • v.30 no.2
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    • pp.201-207
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    • 2014
  • This study was conducted to estimate the best-fit nonlinear height-DBH growth models for Larix kaempferi in Gangwon and North Gyeongsang province in South Korea. Exponential, Modified Logistic, Chapman-Richards, and Weibull function were used for estimating height-DBH models. To evaluate the selected models, $R^2$, RMSE, MD, MAD, and residual plots were performed in each model. Also, the coefficients and patterns in models of the previous studies were compared with those in this study. The result showed that Weibull equation was found to be the best-fit model with $R^2$=0.9837, RMSE=2.6133, MD=0.0089, and MAD=2.0896. All model parameters in our study had similar values to those in the previous models except for asymptotic parameter a. Our research result showed that Gangwon and North Gyeongsang province were superior to other provinces with regard to height growth for Larix kaempferi.

A Study on Long-term Maximum power Demand Forescasting Using Exponential Smoothing (지수평활에 의한 장기 최대전력 수요 예측에 관한 연구)

  • 고희석;이태기
    • The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.6 no.3
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    • pp.43-49
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    • 1992
  • Forecasting of electric power demand has been a basic element for electric power system operation and system development, and it's accuracy has very strong influence on reliability and economical efficience of power supply. So, in this paper, long―term maximum electric power demand has been forecasted by using the triple exponential smoothing method initiated R.G.Brown. It has been regarded this method as high accuracy and operational convenience. The smoothing function is a liner combination of all past observations and the weight given to previous observations decreases geometrically with age.

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The IEEE 802.11 MAC Protocol to solve Unfairness Problem in Multihop Wireless Ad Hoc Networks (다중 무선 에드혹 네트워크에서 불공정 문제를 해결하기 위한 802.11 MAC 프로토콜)

  • Nam, Jae-Hyun
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2007.10a
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    • pp.91-94
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    • 2007
  • In the IEEE 802.11 Wireless Local Area Networks (WLANs), network nodes experiencing collisions on the shared channel need to backoff for a random period of time, which is uniformly selected from the Contention Window (CW). This contention window is dynamically controlled by the Binary Exponential Backoff (BEB) algorithm. The BEB scheme suffers from a fairness problem and low throughput under high traffic load. In this paper, I propose a new backoff algorithm for use with the IEEE 802.11 Distributed Coordination Function.

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