• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.10-13
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• 1995

This paper considers the linear-quadratic optimal regulator problem for nonstandard singularly perturbed systems making use of the recursive technique. We first derive a generalized Riccati differential equation by the Hamilton-Jacobi equation. In order to obtain the feedback gain, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(.epsilon.). The existence of a bounded solution of error term can be proved by the implicit function theorem. It is enough to show that the corresponding Jacobian matrix is nonsingular at .epsilon. = 0. As a result, the solution of optimal regulator problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(.epsilon.$^{k}$ ). The proposed technique represents a significant improvement since the existing method for the standard singularly perturbed systems can not be applied to the nonstandard singularly perturbed systems.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.10
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• pp.2819-2830
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• 2009

Load bearing structural members in a wide variety of applications accumulate damage over their service life. During experiment much effort and cost is needed for measuring structural safety assessment. The sparseness and errors of measured data have to be considered during the safety estimation of structures. This paper introduces parameter estimation and damage identification algorithm by a system identification using static and dynamic response. The equation error estimator and response error widely used in system identification are based on the minimization of least squared error between measured and calculated responses by a mathematical model of a structure. Since each estimator has a specific form of application in noisy environment and proposes different definitions for these forms. To study the behaviour of the estimators in noisy environment Using Monte Carlo simulation, and a data measured pertubation scheme is adopted to investigate the influence of measurement errors on identification results. The assessment result by static and dynamic response were compared, and the efficiency and applicabilities of the proposed algorithm are demonstrated through simulated static and dynamic responses of a dimensional truss type structures.

• Proceedings of the Optical Society of Korea Conference
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• 1990.02a
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• pp.237-241
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• 1990

A detailed theoretical and experimental study of k-na exchange in soda lime silicate glasses by RTP is presented. Concentration profiles i.e. index profiles are given by complementary error function added Gaussian function. The estimated diffusion coefficient is 1.54${\mu}{\textrm}{m}$2/min.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.5
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• pp.1-9
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• 1995

The purpose of this study is to develop a computer simulation program for analyzing load transmission characteristics of a helical gear system in design stage. In this analysis, the rotational delay, load distribution, root stress, and contact area are investigated. That is, the influence function of deflection is obtained by finite element analysis and the influence function of approach and gear tooth error are considered. Load distribution, rotational delay, and contact area are calculated by solving load-deflection equation which includes these influence functions and tooth error, and the influence function of the bending moment is obtained by finite element analysis. The root stress is calculated by the load distribution and the influence function of the bending moment. The results of the simulation are cross-checked through a specially designed experimental set-up.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.2
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• pp.38-50
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• 1982

A new type of digital phase-locked loop (DPLL) called the modified digital Costas loop is proposed and analyzed. The main feature of the proposed loop is that the phase error detector of the loop has linear characteristic. This results from the use of the tan-1 (.) function in the loop. Accordingly, the DPLL can be characterized by a modulo-2$\pi$ linear difference equation. This paper is diveide into two parts. In Part I we describe the proposed system, and analyze the performance of the first-and second-order loops in the absence of noise by the Phase Plane technique. The locking ranges for the DPLL's to achieve exact locking independently of initial conditions have been obtained in closed forms. Also, the false lock and oscillation phenomena occurring under some initial conditions have been considered. These results have been verified by computer simulation. In Part ll we analyze the proposed system in the presence of noise. The steady state probability density function, mean and variance of the phase error have been obtained by solving the Chapman-Kolmogorov equation. These results will be presented in Part ll.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.4
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• pp.245-249
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• 2011

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.809-827
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• 2015

In this paper, seismic energy response of inelastic steel structures under earthquake excitations is investigated. For this purpose, a numerical procedure based on nonlinear dynamic analysis is developed by considering material, geometric and connection nonlinearities. Material nonlinearity is modeled by the inversion of Ramberg-Osgood equation. Nonlinearity caused by the interaction between the axial force and bending moment is also defined considering stability functions, while the geometric nonlinearity caused by axial forces is described using geometric stiffness matrix. Cyclic behaviour of steel connections is taken into account by employing independent hardening model. Dynamic equation of motion is solved by Newmark's constant acceleration method in the time history domain. Energy response analysis of space frames is performed by using this proposed numerical method. Finally, for the first time, the distribution of the different energy types versus time at the duration of the earthquake ground motion is obtained where in addition error analysis for the numerical solutions is carried out and plotted depending on the relative error calculated as a function of energy balance versus time.

• ETRI Journal
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• v.45 no.1
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.4
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• pp.158-164
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• 1994

A volumetric error compensation method was stueide with measuring systematic error of a Coordinate Measuring Machine(CMM). The volumetric error equations were proposed for a Moving Bridge type CMM. Using the error equations, error vectors in the measuring volume were corrected by a software method. The CMM was controlled by the compensation program separately in the measuring and moving function of the CMM proving. The linear accuracy of the CMM was measured by the Laser Interferometer and compared with the data before the volumetric error compensation. This method was proved as low cost and effective to reduce the systematic error of the CMM, as no hardware modification is required.