• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.139-149
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• 2018

Many practical engineering problems are associated with nonlinear systems subjected to nonstationary random excitations. Equivalent linearization methods are commonly used to seek for approximate solutions to this kind of problems. Compared to various approaches developed in the frequency and mixed time-frequency domains, though directly solving the system equation of motion in the time domain would improve computation efficiency, only limited studies are available. Considering the fact that the orthogonal functions have been widely used to effectively improve the accuracy of the approximated responses and reduce the computational cost in various engineering applications, an orthogonal-function-based equivalent linearization method in the time domain has been proposed in the current paper for nonlinear systems subjected to nonstationary random excitations. In the numerical examples, the proposed approach is applied to a SDOF system with a set-up spring and a SDOF Duffing oscillator subjected to stationary and nonstationary excitations. In addition, its applicability to nonlinear MDOF systems is examined by a 3DOF Duffing system subjected to nonstationary excitation. Results show that the proposed method can accurately predict the nonlinear system response and the formulation of the proposed approach allows it to be capable of handling any general type of nonstationary random excitations, such as the seismic load.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.2
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• pp.79-93
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• 1997

This paper presents a linear shift-invariant system euqivalent to morphological dilation for a memoryless uniform source in the sense of the power spectral density function, and comares it with dialtion. This equivalent LSI system is found through spectral decomposition and, for dilation and with windwo size L, it is shown to be a finite impulse response filter composed of L-1 delays, L multipliers and three adders. Th ecoefficients of the equivalent systems are tabulated. The comparisons of dilation and its equivalent LSI system show that probability density functions of the output sequences of the two systems are quite different. In particular, the probability density functon from dilation of an independent and identically distributed uniform source over the unit interval (0, 1) shows heavy probability in around 1, while that from the equivalent LSI system shows probability concentration around themean vlaue and symmetricity about it. This difference is due to the fact that dilation is a non-linear process while the equivalent system is linear and shift-ivariant. In the case that dikation is fabored over LSI filters in subjective perforance tests, one of the factors can be traced to this difference in the probability distribution.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.5B no.1
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• pp.34-38
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• 2005

The finite element method is very flexible for new shapes and provides flux distribution, magnetomotive force, eddy currents, and torques. However, it requires lengthy computational time in order to achieve desired accuracy. The magnetic equivalent circuit method takes less computation time than the finite element method. Therefore, the finite element method is mainly used to confirm the completed design. The magnetic equivalent circuit method is convenient for complicated analysis of the transient state of the induction motor. The magnetic equivalent circuit method is restricted to only one direction of magnetic flux. In this paper, the construction elements (that is, stator iron, rotor iron, yoke, air gap, etc.) of the squirrel cage induction motor were represented by a flux tube and the air gap magnetomotive force was calculated by the magnetic equivalent circuit method. Starting transient torque and phase current of the squirrel cage induction motor were verified by the theoretical calculation and the experiment.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.175-178
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• 2005

In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.

• International Journal of Control, Automation, and Systems
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• v.1 no.4
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• pp.401-411
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• 2003

Important results about two-degree-of-freedom PID controllers are surveyed for the tutorial purpose, including equivalent transformations, various explanations about the effect of the two-degree-of-freedom structure, relation to the preceded-derivative PID and the I-PD controllers, and an optimal tuning method.

• ETRI Journal
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• v.25 no.1
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• pp.9-18
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• 2003

We mathematically analyze the passband vestigial sideband (VSB) system for the Advanced Television Systems Committee (ATSC) digital television standard and present a baseband-equivalent VSB model. The obtained baseband VSB model is represented by convolution of the transmission signal (before modulation) and the baseband equivalent of the complex VSB channel. Due to the operation of the physical channel as an RF passband and the asymmetrical property of VSB modulation, it is necessary to use a complex model. However, the passband channel may be reduced to an equivalent baseband. We show how to apply standard channel model information such as delay, gain, and phase for multiple signal paths to compute both the channel frequency response with a given carrier frequency and the resulting demodulated impulse response. Simulation results illustrate that the baseband VSB model is equivalent to the passband VSB model.

• Journal of Applied Reliability
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• v.15 no.4
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• pp.256-261
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• 2015

The aim of this paper is to present some issues to be discussed in relation to failure rate of a system that has identical parallel units. It is assumed that Time-to-Failure of each unit has the same exponential distribution and all units are repairable with a periodic maintenance of time interval T. Effective failure rate is widely recommended for nonrepairable systems as the reciprocal of MTTF but it should not be applied for repairable systems if delayed maintenance is used. And equivalent failure rate of an imaginary system is taken into consideration, the reliability value of which is the same as that of the redundant system when time interval T is given. With a numerical example, failure rate, effective failure rate, and equivalent failure rate of the redundant system are analyzed comparatively.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.227-230
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• 2000

Chuas circuit is a simple electronic network which exhibits a variety of bifurcation and attractors. The circuit consists of two capacitors, an inductor, a linear resistor, and a nonlinear resistor. In this paper, a transmitter and a receiver using two identical Chuas circuits are proposed and synchronizations of a equivalent wire and wireless power line are investigated. Since the synchronization of the equivalent wire and wireless system is impossible by coupled synchronization, theory having both the drive-response and the coupled synchronization is proposed. As a result, the chaos synchronization has delay characteristics in the equivalent wire and wireless transmission system caused by the line parameters L and C.

• Proceedings of the KIEE Conference
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• 1988.11a
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• pp.388-393
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• 1988

New circuit D-Q transformation concept is introduced to analyze AC converters such as inverters, rectifiers and cyclo-converters with ease. The equivalent linear time invariant circuit is obtained by substituting switches with equivalent turn-ratio variable transformers and changing balanced AC reactors into equivalent DC reactors combined by gyrators. This circuit enables us to utilize the powerful linear system analysis techniques such as Laplace transform otherwise which could not be applied to the time varying switching systems. Direct substitution of switches of DC converters with transformers is shown as a preliminary. Then the modeling procedure is shown for a controlled rectifier-inverter circuit. Finally an analysis example is proposed for a buck-boost inverter and the result is compared with the conventional approach. This approach is applicable to all AC converter families to determine the AC transfer functions and the DC operating points. It is identified that the switching systems are equivalent to the RLC filter circuits with transformers and gyrators.

• Wind and Structures
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• v.6 no.4
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• pp.249-262
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• 2003

The purpose of this study is to propose a procedure for evaluating quantitatively the increase of the equivalent damping ratio of a structure with passive/active vibration control systems subjected to a stationary wind load. A Lyapunov function governing the response of a structure and its differential equation are formulated first. Then the state-space equation of the structure coupled with the secondary damping system is solved. The results are substituted into the differential equation of the Lyapunov function and its derivative. The equivalent damping ratios are obtained from the Lyapunov function of the combined system and its derivative, and are used to assess the control effect of various damping devices quantitatively. The accuracy of the proposed procedure is confirmed by applying it to a structure with nonlinear as well as linear passive/active control systems.