• Title, Summary, Keyword: direct integral

### Numerical Evaluation of The Rayleigh Integral Using the FFT Method for Transient Sound Radiation (FFT 방법을 이용한 음압복사에 대한 Rayleigh Integral 의 수치해석적 연구)

• Jeon, Jae-Jin
• The Journal of the Acoustical Society of Korea
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• v.7 no.4
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• pp.22-30
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• 1988
• In this paper, the sound radiation from a clamped circular plate in an infinite baffle is calculated by using the FFT technique. The radiated sound fields are obtained by two-dimensional fast Fourier transform method is the spatial domain instead of a direct numerical evaluation of Rayleigh integral for economy of the computation time. The computation time is consumed at least by 1/200 times of the direct numerical evaluation on the Rayleigh integral in acoustic fields. The FFT method can be applicable to any shaped geometry as well as circular plate. The FFT solution could be very powerful in predicting the near and far fields of complex structures.

### An EMM Approach to Derive an Energy Integral for the Direct Method of Stability Analysis in Power Systems

• Moon, Young-Hyun
• Journal of Electrical Engineering and information Science
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• v.1 no.1
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• pp.58-69
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• 1996
• This paper presents a new approach to derive an energy integral based on an Equivalent Mechanical Model(EMM), which is developed by introducing imaginary springs for line resistances. The proposed EMM shows that phasor currents and voltages are directly analogous to the two-dimensional force and displacement vectors, respectively. Through rigorous energy analysis of the proposed EMM, an exact energy integral expression is derived for multimachine systems, and several useful theorems are developed to derive an energy integral for power systems with detailed generator models the energy integral exactly reflects the internal resistance, saliency and flux-decaying effects of the generator. Finally, an illustrative example is given for a multimachine system adopting the Eq'-model for generators, which shows that the consideration of a detailed generator model does not aggravate the complicacy of the direct method of stability analysis in multimachine systems.

### Development of the Direct Boundary Element Method for Thin Bodies with General bBundary Conditions (일반 경계 조건을 가진 얇은 물체에 대한 직접 경계 요소법의 개발)

• 이강덕;이덕주
• Journal of KSNVE
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• v.7 no.6
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• pp.975-984
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• 1997
• A direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. The Helmholtz integral equation and its normal derivative integral equation are adoped simultaneously to calculate the pressure on both sides of the thin body, instead of the jump values across it, to account for the different surface conditions of each side. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. In this approach, only the neutral surface of the thin body has to be discretized. The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absoring material.

### Comparison of Experimental Data on the Fluctuation Integral Gij with the Calculated Results Based on the Activity Coefficient Model in Binary Mixtures Containing c-Hexane (c-hexane을 포함하는 이성분계 혼합물에서 활동도계수 모델을 이용한 변동적분 Gij의 계산 수치와 실험 수치의 비교)

• Hur, Kwang-II;Kwon, Yong-Jung
• Journal of Industrial Technology
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• v.20 no.A
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• pp.203-209
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• 2000
• The fluctuation integrals which give useful information in the structure of solution are associated with the mixed direct correlation integral ($C_{12}$) known. Using its weighted arithmetic mean of $C_{11}$ and $C_{22}$ and the activity coefficient model, the fluctuation integrals on solute-solute, solvent-solute, and solvent-solvent can be calculated in the function of mole fraction. In this work, several binary mixtures containing c-hexane were tested and the results on the fluctuation integrals were rather good.

### Direct Energy Method of Power System Stability Analysis and its Application by using Energy Conservation Law (에너지보존법칙을 이용한 전력계통 안정도 직접 해석법에서의 응용)

• Lee, Yong-Hoon;Cho, Byoung-Hoon;Ryu, Heon-Su;Moon, Young-Hyun
• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.10
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• pp.1207-1214
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• 1999
• Many papers have recently been presented to develop energy functions for power systems. However, earlier studies adopted case-by-case approaches, which failed to give a general approach to deal with various kinds of generator models. In this paper, two useful theorems are developed regarding the integral relationships of the generator power versus its phasor current and voltage. By using the proposed theorems, an exact energy conservation law can be derived from the complex integral. The proposed energy conservation law, which is free of the generator model, can be utilized to develop energy functions for various kinds of generator models including the speed governors and exciters. An illustrative example is given for a multimachine system with the Eq' model of generator. This thesis also shows a possibility of more accurate and fast stability analysis by using the proposed Energy Conservation Law.

### THE PERRON AND VARIATIONAL INTEGRALS

• Park, Jae Myung;Lee, Deok Ho
• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.37-41
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• 1997
• In this paper, we give a direct proof that the Perron and variational integrals are equivalent.

### REMOVAL OF HYPERSINGULARITY IN A DIRECT BEM FORMULATION

• Lee, BongJu
• Korean Journal of Mathematics
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• v.18 no.4
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• pp.425-440
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• 2010
• Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.

### A Link Between Integrals and Higher-Order Integrals of SPN Ciphers

• Li, Ruilin;Sun, Bing;Li, Chao
• ETRI Journal
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• v.35 no.1
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• pp.131-141
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• 2013
• Integral cryptanalysis, which is based on the existence of (higher-order) integral distinguishers, is a powerful cryptographic method that can be used to evaluate the security of modern block ciphers. In this paper, we focus on substitution-permutation network (SPN) ciphers and propose a criterion to characterize how an r-round integral distinguisher can be extended to an (r+1)-round higher-order integral distinguisher. This criterion, which builds a link between integrals and higher-order integrals of SPN ciphers, is in fact based on the theory of direct decomposition of a linear space defined by the linear mapping of the cipher. It can be directly utilized to unify the procedure for finding 4-round higher-order integral distinguishers of AES and ARIA and can be further extended to analyze higher-order integral distinguishers of various block cipher structures. We hope that the criterion presented in this paper will benefit the cryptanalysts and may thus lead to better cryptanalytic results.

### A Study on Robustness of a Servosystem with Nonlinear Type Uncertainty (I) - A Synthesis of 2DOF Servosystem (비선형 불확실성에 대한 서보계의 강인성에 관한 고찰(I) - 직달항을 고려한 2자유도 서보계의 구성)

• Kim, Young-Bok
• Journal of Ocean Engineering and Technology
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• v.13 no.3B
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• pp.91-98
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• 1999
• In order to reject the steady-state tracking error, it is common to introduce integral compensators in servosystems for constant reference signals. However, if the mathematical model of the plant is exact and no disturbance input exists, the integral compensation is not necessary. From this point of view, a two-degree-of-freedom(2DOF) servosystem has been proposed, in which the integral compensation is effective only when there is a modeling error or a disturbance input. The present paper considers a synthesis problems of this 32DOF servosystem with direct transfer term in the system representation. And, a method how we may obtain a gain such that desirable transient response is achieved, is proposed in the presence of the modelling error and disturbance input.

### Steady-State Integral Proportional Integral Controller for PI Motor Speed Controllers

• Hoo, Choon Lih;Haris, Sallehuddin Mohamed;Chung, Edwin Chin Yau;Mohamed, Nik Abdullah Nik
• Journal of Power Electronics
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• v.15 no.1
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• pp.177-189
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• 2015
• The output of the controller is said to exceed the input limits of the plant being controlled when a control system operates in a non-linear region. This process is called the windup phenomenon. The windup phenomenon is not preferable in the control system because it leads to performance degradation, such as overshoot and system instability. Many anti-windup strategies involve switching, where the integral component differently operates between the linear and the non-linear states. The range of state for the non-overshoot performance is better illustrated by the boundary integral error plane than the proportional-integral (PI) plane in windup inspection. This study proposes a PI controller with a separate closed-loop integral controller and reference value set with respect to the input command and external torque. The PI controller is compared with existing conventional proportional integral, conditional integration, tracking back calculation, and integral state prediction schemes by using ScicosLab simulations. The controller is also experimentally verified on a direct current motor under no-load and loading conditions. The proposed controller shows a promising potential with its ability to eliminate overshoot with short settling time using the decoupling mode in both conditions.