• 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.

• 센서학회지
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• 제26권4호
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• pp.251-258
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• 2017

According to recent studies by scientists about how to search for food, homes and the mates, it is found that the gradient information plays a key role. From cells to insects and large animals, they mostly either have special sensing organism or use a strategy to measure the gradient. Use of a perturbation as an additional input is introduced for sensor signal processing in order to get the gradient information. Different from typical approach, which calculates the gradient from differentiation, the proposed processing is done by a form of integration, thus it is very robust to noise. Discrete time domain analyses are given for one, two and three input functions for the estimation of the gradients. The amplitude and the frequency of the perturbation are two important parameters for this approach. A quantitative index to measure the effects of the amplitude is developed based on the linear regression analysis. The frequency of the perturbation is to be selected high enough to finish one period of the perturbation before the property is changed significantly with respect to time. Another quantitative index is proposed for guiding the selection of the frequency.

• 센서학회지
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• 제29권3호
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• pp.141-148
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• 2020

To find food, homes, and mates, some animals have adapted special sensing capabilities. Rather than using a passive method, they discharge a signal and then extract the necessary information from the response. More importantly, they use the slope of the detected signal to find the destination of an object. In this paper, similar strategy is mathematically formulated. A perturbation and correlation-based gradient estimation method is developed and used as a sensing strategy. This method allows us to adaptively sense an object in a given environment effectively. The proposed strategy is based on the use of gradient values; rather than instantaneous measurements. Considering the gradient value, the sampling frequency is planned adaptively, i.e., sparse sampling is performed in slowly varying regions, while dense sampling is conducted in rapidly changing regions. Using a temperature sensor, the proposed strategy is verified and its effectiveness is demonstrated.

• 로봇학회논문지
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• 제14권4호
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• pp.258-263
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• 2019

Some animals have special sensing functions in order to find foods, home and mates. Instead of passively sensing, they discharge signals and then extract necessary information from the response. More importantly, they utilize the gradients of the sensed signal in order to find the destination or objects. In this paper this special strategy is formulated mathematically, i.e., the perturbation and the correlation based gradient estimation is developed. A stereo sensor system using temperature sensors mounted on motors is developed for verification. The proposed method can estimate the gradient of the measured value accurately. Using this method, the direction in the maximum measured value can be estimated accurately, and the position of the heat source can be estimated from the intersection of the directions estimated from both sensors.

• 한국전자파학회논문지
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• 제27권9호
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• pp.808-816
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• 2016

본 논문에서는 단일포트시스템으로 설계된 배열안테나에서 수신신호의 스펙트럼 분포로부터 목표신호와 재밍신호를 분리하여 목표신호 방향의 주빔 왜곡을 최소화 하며, 재밍신호 방향으로 패턴 널(null)을 형성하는 새로운 기법 및 비용함수를 제안한다. 제안한 비용함수는 최적화 알고리즘의 한 종류인 PSO(Particle Swam Optimization) 알고리즘과 gradient-based 섭동 알고리즘을 혼합한 적응형 알고리즘에 적용하여 시간에 따라 재밍신호의 입사방향이 변화하는 이동형 재밍환경에서도 적응적으로 안정적인 널링 성능을 가진다.

• Structural Engineering and Mechanics
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• 제69권2호
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• pp.205-219
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• 2019

This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

• Structural Engineering and Mechanics
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• 제4권4호
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• pp.425-436
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• 1996

An application of the perturbation method to optimum structural design with random parameters is presented. It is formulated on the basis of the first-order stochastic finite element perturbation method. It also takes into full account the stress, displacement and eigenvalue constraints, together with the rates of change of the random variables. A method for calculating the sensitivity coefficients in regard to the governing equation and the first-order perturbed equation has been derived, by using a direct differentiation approach. A gradient-based nonlinear programming technique is used to solve the problem. The numerical results are specifically noted, where the stiffness parameter and external load are treated as random variables.

• 대한기계학회논문집
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• 제19권8호
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• pp.1822-1831
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• 1995

A general formulation of the design optimization problem with the random parameters is presented here. The formulation is based on the stochastic finite element second-order perturbation method ; it takes into full account of the stress and displacement constraints together with the rates of change of the random variables. A method of direct differentiation for calculating the sensitivity coefficients in regard to the governing equation and the second-order perturbed equation is derived. A gradient-based nonlinear programming technique is used to solve the problem. The numerical results are specifically noted, where the stiffness parameter and external load are treated as random variables.

• Steel and Composite Structures
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• 제33권2호
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• pp.261-275
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• 2019

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

• Steel and Composite Structures
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• 제47권6호
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• pp.795-811
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• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.