• Industrial Engineering and Management Systems
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• 제12권1호
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• Structural Engineering and Mechanics
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• 제23권6호
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Coupled systems mechanics
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• 제7권6호
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• 한국지능시스템학회논문지
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• 제5권2호
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• pp.86-96
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• 1995

본 논문은 퍼지이론을 이용한 고전적인 역학문제의 확장에 관한 연구이다. 자중 및 휨강성 등 불확실한 매체를 갖는 기둥의 좌굴하중을 지배하는 미분방정식을 유도하였다. 수치해석예에서는 일단은 전형적인 자유, 회전, 고정단이고, 타단은 애매한 상수로 정의되는 회전스프링으로 지지된 기둥을 택하였다. 퍼지함수의 연산을 위하여 vertex method를 이용하였으며, 지배미분방정식의 수치적분과좌굴하중 결정을 위해 Runge-Kutta method와 행렬값탐사법을 각각 이용하였다. 좌굴하중의 소속함수를 산출하였으며,애매성의 흐름을 정량적으로 판단하기 위하여 퍼지지수를 정의 하였다. 지배인자의 애매성 변화에 따른 좌굴하중의 퍼지지수 변화를 분석하였으며, 단부 조건에 따른 감도를 고찰하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제27권2호
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• pp.218-228
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• 2003

A hydraulic system is modeled as the second order differential equation with uncertain system parameters and disturbance composed of modeling errors. To Position the load of the hydraulic system to a desired point. the servo valve of the hydraulic system is controlled. As a control scheme. a global sliding mode control(GSMC) is Proposed Since the servo valve has a torque limit. the GSMC is designed to coordinate the position of the load along the minimum time trajectory within the torque limit. The Proposed control scheme can be designed with ranges of parametric uncertainties and specified torque limits. By the proposed control scheme, the closed form solution of the arriving time at the desired position can be estimated.

• Structural Engineering and Mechanics
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• 제50권5호
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• pp.697-708
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• 2014

The intentional buckling design of micro-films has various potential applications in engineering. The buckling amplitude and critical strain of micro-films are the crucial parameters for the buckling design. In the reported studies, the film parameters were regarded as deterministic. However, the geometrical and physical parameters uncertainty of micro-films due to manufacturing becomes prominent and needs to be considered. In the present paper, the probabilistic nonlinear buckling analysis of micro-films with uncertain parameters is proposed for design accuracy and reliability. The nonlinear differential equation and its asymptotic solution for the buckling micro-film with nominal parameters are firstly established. The mean values, standard deviations and variation coefficients of the buckling amplitude and critical strain are calculated by using the probability densities of uncertain parameters such as the film span length, thickness, elastic modulus and compressive force, to reveal the effects of the film parameter uncertainty on the buckling deformation. The results obtained illustrate the probabilistic relation between buckling deformation and uncertain parameters, and are useful for accurate and reliable buckling design in terms of probability.

• 한국지능시스템학회논문지
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• 제5권3호
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• pp.11-35
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• 1995

본 논문에서는 학습/적응능력을 갖는 퍼지제어시스템들이 여러가지 관점에서 고찰되었다. 먼저, 기존에 제안된 다양한 학습/적응 퍼지제어시스템들의 기본적인 구성요소들을 바탕으로하여 이러한 시스템들의 일반적인 구조를 제안하였다. 그리고 제안된 구조의 중요한 구성요소들을 중심으로 고찰기준을 설정하였다. 고찰기준으로는 퍼지제어기나 퍼지모델 등에 사용되는 퍼지추론시스템의 구조, 학습/적응에 사용되는 퍼지추론시스템의 조정계수와 제어성능 평가함수, 그리고 학습/적응알고리즘을 설정하였다. 다음으로, 이러한 고찰기준들을 바탕으로하여 학습/적응 퍼지제어시스템들을 분류하고 각각의 특징들을 고찰하였다. 마지막으로, 사용된 퍼지추론시스템들의 범용 함수근사화 성질에 대하여도 알아 보았다.

• Transactions on Control, Automation and Systems Engineering
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• 제3권1호
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• pp.21-26
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• 2001

In this study, we propose a two degree of freedom robust output tracking control method for a class of nonlinear system. We consider hyperbolically nonminimum phase single-input single-output uncertain nonlinear systems. We also consider the case that the nominal input-state equation is differentially flat. Nominal stable state trajectory is obtained in the flat output space via the flat output. Nominal feedforward control input is also computed from the nominal state trajectory. Due to the nature of the method, the generated flat output trajectory and control input are noncausal. Robust feedback control is designed to stabilize the systems around the nominal trajectory. A numerical example is given is given to demonstrate that robust tracking is achieved.

• Structural Engineering and Mechanics
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• 제28권4호
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.