• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.427-440
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• 2000

The formulas for the perturbation analysis with modes of close eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a distinct eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the eigenvalues, eigenvectors, and normality.

• Publications of The Korean Astronomical Society
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• v.26 no.2
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• pp.55-70
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• 2011

Cosmological linear perturbation theory has fundamental importance in securing the current cosmological paradigm by connecting theories with observations. Here we present an explanation of the method used in relativistic cosmological perturbation theory and show the derivation of basic perturbation equations.

• East Asian mathematical journal
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• v.39 no.1
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• pp.87-92
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• 2023

In this paper, we study the nonlinear hyperbolic system with epsilon perturbation s_tt - div[c(x)∇s] + (ε - 1)s_t = |s|^γs. Under the conditions of c, γ and other assumptions, we prove the exponential behavior rates of the modified energy perturbation.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.875-881
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• 2011

This paper describes a new method of estimating the gradient of a function with perturbation and correlation. We impose a known periodic perturbation to the input variable and observe the output of the function in order to obtain much richer and more reliable information. By taking the correlation between the input perturbation and the resultant function outputs, we can determine the gradient of the function. The computation of the correlation does not require derivatives; therefore the gradient can be estimated reliably. Robust estimation of the gradient using perturbation/correlation, which is very effective when an analytical solution is not available, is described. To verify the effectiveness of perturbation/correlation based estimation, the results of gradient estimation are compared with the analytical solutions of an example function. The effects of amplitude of the perturbation and number of samplings in a period are investigated. A minimization of a function with the gradient estimation method is performed.

• Phonetics and Speech Sciences
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• v.7 no.1
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• pp.79-86
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• 2015

This study explored the vowel effect on acoustic perturbation measures in voice quality analysis. For this study, the perturbation parameters (%jitter, %shimmer) and noise parameter (SNR) were measured with 7 Korean vowels (/a/, /ɛ/, /i/, /o/, /u/, /ɯ/, /ʌ/) using CSpeech with 50 Korean normal young adults (24 males and 26 females). A significant vowel effect was found only in %shimmer and in particular, low-back /a/vowel was significantly different from other vowels in %shimmer. The least perturbation and noise were exhibited on high-back /ɯ/ and /o/ vowel, respectively. Based on tongue height, a significant higher %shimmer was demonstrated on low vowels than high vowels. In addition, back vowels in tongue advancement and rounded vowels in lip rounding showed significantly less perturbation and noise. The least variability of perturbation and noise within individuals was demonstrated on the vowel /i/ in three repeated measures. However, there was no significant difference among 3 token measures in single session among vowels tested except the vowel /o/. Consequently, the vowel /a/ commonly used in acoustic perturbation measures exhibited higher perturbation and noise whereas higher stability and less variability were demonstrated on the high-back vowel /u/. These results suggested that the Korean high-back vowel /u/ can be more appropriate and reliable for perturbation acoustic measures.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.12
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• pp.1638-1643
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• 2019

In this paper, we propose an adaptive-perturbation-aided opportunistic precoding (APOP) scheme for multiple-input multiple-output (MIMO) systems. To update a precoding matrix in MIMO systems, the proposed algorithm produces a random perturbation in each time slot. Then the additional adaptive perturbation is also applied, which depends on the reports of achievable data-rates from users. If the prior random perturbation increased the data rate, the adaptive perturbation is set to be the same as the prior random perturbation, otherwise the negative value of the prior random perturbation is applied for adaptive perturbation. Furthermore, to enhance the achievable data rates, the information on the stored precoding matrices in the memory as well as the currently generated precoding matrix is used for scheduling. Simulation results show that compared to conventional opportunistic precoding schemes, higher data rates are achieved by the proposed APOP scheme, especially when there are a relatively small number of users.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.3
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• pp.201-207
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• 2006

A robust Kalman filtering method for uncertain stochastic systems is suggested by adopting a perturbation estimation process which is to reconstruct total uncertainty with respect to the nominal state transition equation. The predictor and corrector of discrete Kalman filter are reformulated with the perturbation estimator. Successively, the state and perturbation estimation error dynamics and the corresponding error covariance propagation equations are derived as well. Finally we have the recursive algorithm of Combined Kalman Filter-Perturbation Estimator (CKF). The proposed combined Kalman filter-perturbation estimator has the property of integrating innovations and the adaptation capability to system uncertainties. A numerical example is shown to demonstrate the effectiveness of the proposed scheme.

• Computational Structural Engineering
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• v.9 no.4
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• pp.209-217
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• 1996

An Inverse modal perturbation method was applied to estimate the assessments of the damages at the large-scaled marine structure, such as pier or dolphin, from the structural dynamic natural frequencies and mode shape. Vibrations of structural stiffness, natural frequencies and mode shapes from the eigenvalue analysis lead to the modal peturbation equations, which were considered with a second order term. This paper estimates the assessments of the damages for the structure with the decreased stiffness and shows the convergence of perturbation equation.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.2
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• pp.1-6
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• 1982

This paper reviews and describes some applications of perturbation theory in the practical analysis of linear systems which involve random parameters. Statistical measures of the system outputs are derived in terms of statistical measures of the system parameters and inputs (i.e., in the way of perturbed linear operator equations). Perturbed state transition matrix is also derived. With simple first-order and second-order linear system models, we compare the accuracy of perturbation results with the exact ones. And the convergence of perturbation series is also investigated.

• Journal of the Optical Society of Korea
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• v.9 no.1
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• pp.6-12
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• 2005

The perturbation approach is applied to solve the nonlinear Schrodinger equation, and its valid range has been determined by comparing with the results of the split-step Fourier method over a wide range of parameter values. With γ= 2㎞/sup -1/mW/sup -1/, the critical distance for the first order perturbation approach is estimated to be(equation omitted). The critical distance, Z/sub c/, is defined as the distance at which the normalized square deviation compared to the split-step Fourier method reaches 10/sup -3/. Including the second order perturbation will increase Z/sub c/ more than a factor of two, but the increased computation load makes the perturbation approach less attractive. In addition, it is shown mathematically that the perturbation approach is equivalent to the Volterra series approach, which can be used to design a nonlinear equalizer (or compensator). Finally, the perturbation approach is applied to obtain the sinusoidal response of the fiber, and its range of validity has been studied.