• Structural Engineering and Mechanics
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• 제10권5호
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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.

• 천문학논총
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• 제26권2호
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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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• 제39권1호
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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.

• 제어로봇시스템학회논문지
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• 제17권9호
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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.

• 말소리와 음성과학
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• 제7권1호
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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.

• 한국정보통신학회논문지
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• 제23권12호
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• pp.1638-1643
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• 2019

본 논문에서는 MIMO (Multiple-Input Multiple Output, 다중입출력) 시스템을 위한 적응형 섭동을 이용한 기회적 프리코딩(Adaptive Perturbation-aided Opportunistic Precoding) 방식을 제안한다. 제안 프리코딩 방식에서는 MIMO 시스템을 위한 프리코딩 행렬을 생성할 때 랜덤한 섭동 뿐 아니라 사용자로부터 받은 전송률 정보에 의해 결정되는 적응적 변화값을 함께 이용한다. 이전 시간의 랜덤 섭동이 전송속도를 상승시켰을 경우 적응형 섭동을 이전 랜덤 섭동과 동일하게 하고, 그렇지 않을 경우 이전 랜덤한 섭동 값의 음의 값에 해당하는 값을 적용시킨다. 또한 전송 속도 최적화를 위해 스케줄링에서 현재 생성된 프리코딩 행렬 뿐 아니라 메모리에 저장된 최근 프리코딩 행렬 정보도 함께 이용한다. 모의실험 결과에서 기존 프리코딩 방식에 비해 제안한 섭동 기반 기회적 프리코딩 방식이 높은 전송속도를 얻으며, 특히 사용자의 수가 적은 환경에서 전송 속도 이득이 큰 것을 확인할 수 있다.

• 제어로봇시스템학회논문지
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• 제12권3호
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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.

• 전산구조공학
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• 제9권4호
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• pp.209-217
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• 1996

구조물의 손상전후에 나타나는 고유진동수와 모드 형상으로 부터 Inverse Modal Perturbation기법을 이용하여 잔교식 부두나 돌핀과 같은 대규모 항만구조물의 손상도 추정을 위한 모드 기여도 계수를 근사적으로 직접 구하는 방법을 제시하였다. 잔교식 항만구조물의 고유치 해석을 통해 구조물의 강성 변화량과 구조물의 고유진동수와 모드 형상의 변화량과 요소 손상도 계수를 도입하여 Inverse Modal Perturbation의 2차항을 고려한 관계식을 유도하고 손상전후에 구조물의 강성 감소로 나타나는 구조물의 손상도를 추정하여 수렴정도를 고찰하였다.

• 대한전자공학회논문지
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• 제19권2호
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• pp.1-6
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• 1982

본 논문에서는 런덤파라미터를 포함하는 선형 시스템의 실제 해석에 perturbation 이론의 응용을 보이고 있다. 시스템의 출력의 통계치가 시스템의 파라미터와 입력의 통계치들에 의해 (perturb된 선형 연산자 방정식에 의해) 구해졌고, perturb된 state 변환 매트릭스도 유도되었다. 간단한 일차, 이차 선형 시스템 모델을 가지고, 정확한 해와 perturbation 결과사이의 정확도가 비교되어 졌고 perturbation series의 수렴도도 조사되어 졌다.

• Journal of the Optical Society of Korea
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• 제9권1호
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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.