• Steel and Composite Structures
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• v.47 no.1
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• pp.91-102
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• 2023

To study the evaluation standard and control limit of mortar filling layer void length, in this paper, the train sub-model was developed by MATLAB and the track-bridge sub-model considering the mortar filling layer void was established by ANSYS. The two sub-models were assembled into a train-track-bridge coupling dynamic model through the wheel-rail contact relationship, and the validity was corroborated by the coupling dynamic model with the literature model. Considering the randomness of fastening stiffness, mortar elastic modulus, length of mortar filling layer void, and pier settlement, the test points were designed by the Box-Behnken method based on Design-Expert software. The coupled dynamic model was calculated, and the support vector regression (SVR) nonlinear mapping model of the wheel-rail system was established. The learning, prediction, and verification were carried out. Finally, the reliable probability of the amplification coefficient distribution of the response index of the train and structure in different ranges was obtained based on the SVR nonlinear mapping model and Latin hypercube sampling method. The limit of the length of the mortar filling layer void was, thus, obtained. The results show that the SVR nonlinear mapping model developed in this paper has a high fitting accuracy of 0.993, and the computational efficiency is significantly improved by 99.86%. It can be used to calculate the dynamic response of the wheel-rail system. The length of the mortar filling layer void significantly affects the wheel-rail vertical force, wheel weight load reduction ratio, rail vertical displacement, and track plate vertical displacement. The dynamic response of the track structure has a more significant effect on the limit value of the length of the mortar filling layer void than the dynamic response of the vehicle, and the rail vertical displacement is the most obvious. At 250 km/h - 350 km/h train running speed, the limit values of grade I, II, and III of the lengths of the mortar filling layer void are 3.932 m, 4.337 m, and 4.766 m, respectively. The results can provide some reference for the long-term service performance reliability of the ballastless track-bridge system of HRS.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.11
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• pp.2702-2719
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• 2013

A new optimal scheme based on curvelet transform is proposed for retinal image enhancement (RIE) using real-coded quantum genetic algorithm. Curvelet transform has better performance in representing edges than classical wavelet transform for its anisotropy and directional decomposition capabilities. For more precise reconstruction and better visualization, curvelet coefficients in corresponding subbands are modified by using a nonlinear enhancement mapping function. An automatic method is presented for selecting optimal parameter settings of the nonlinear mapping function via quantum genetic search strategy. The performance measures used in this paper provide some quantitative comparison among different RIE methods. The proposed method is tested on the DRIVE and STARE retinal databases and compared with some popular image enhancement methods. The experimental results demonstrate that proposed method can provide superior enhanced retinal image in terms of several image quantitative evaluation indexes.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.10a
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• pp.129-132
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• 2001

Fiber waviness is one of manufacturing defects encountered frequently in thick composite structures. It affects significantly on the behavior as well as strength of thick composites. The effects of fiber waviness on tensile/compressive nonlinear elastic behavior and strength of thick composite with fiber waviness are studied theoretically and experimentally. FEA(Finite Element Analysis) models are proposed to predict tensile/compressive nonlinear behavior and strength of thick composites. In the FEA models, both material and geometric nonlinearities were incorporated into the model using energy density, iterative mapping and incremental method. Also Tsai-Wu criteria was adopted to predict the strength of thick composites with fiber waviness. Tensile and compressive tests were conducted on the specimens with uniform fiber waviness. It was observed that the degree of fiber waviness in composites significantly affected the nonlinear behavior and strength of the composites

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.255-268
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• 2005

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.173-184
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• 2004

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region in $R^2$. We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error in $L_1$ is controlled.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.289-295
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• 2002

In this paper, a linear matrix inequality(LMI)-based robust control method, which combines model predictive control(MPC) with the feedback linearization(FL), is presented for constrained nonlinear systems with parameter uncertainty. The design procedures consist of the following 3 steps: Polytopic description of nonlinear system with a parameter uncertainty via FL, Mapping of actual input constraint by FL into constraint on new input of linearized system, Optimization of the constrained MPC problem based on LMI. To verify the performance and usefulness of the control method proposed in this paper, some simulations with application to a flexible single link manipulator are performed.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.939-942
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• 1996

This paper presents a stable learning algorithm for diagonal recurrent neural network(DRNN). DRNN is applied to a problem of controlling nonlinear dynamical systems. A architecture of DRNN is a modified model of the Recurrent Neural Network(RNN) with one hidden layer, and the hidden layer is comprised of self-recurrent neurons. DRNN has considerably fewer weights than RNN. Since there is no interlinks amongs in the hidden layer. DRNN is dynamic mapping and is better suited for dynamical systems than static forward neural network. To guarantee convergence and for faster learning, an adaptive learning rate is developed by using Lyapunov function. The ability and effectiveness of identifying and controlling a nonlinear dynamic system using the proposed algorithm is demonstrated by computer simulation.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.179-182
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• 2004

This paper deals with a new mathematical formulation of nonlinear wave profile based on Banach fixed point theorem. As application of the formulation and its solution procedure, some numerical solutions was presented in this paper and nonlinear equation was derived. Also we introduce a new operator for iteration and getting solution. A numerical study was accomplished with Stokes' first-order solution and iteration scheme, and then we can know the nonlinear characteristic of Stokes' high-order solution. That is, using only Stokes' first-oder(linear) velocity potential and an initial guess of wave profile, it is possible to realize the corresponding high-oder Stokian wave profile with tile new numerical scheme which is the method of iteration. We proved the mathematical convergence of tile proposed scheme. The nonlinear strategy of iterations has very fast convergence rate, that is, only about 6-10 iterations arc required to obtain a numerically converged solution.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.799-804
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• 2001

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.