• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.339-355
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• 2008

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.39-46
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• 2007

One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form G(X)=$A_0X^m+A_1X^{m-1}+{\cdots}+A_m$ where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ real matrices. We show how the minimization methods can be used to solve the matrix polynomial G(X) and give some numerical experiments. We also compare Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version of conjugate gradient method.

• Advances in aircraft and spacecraft science
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• v.7 no.2
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• pp.169-186
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• 2020

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.

• The Journal of Korea Robotics Society
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• v.14 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.913-918
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• 2007

Human motion analysis is an important research subject in human-robot interaction (HRI). However, before analyzing the human motion, silhouette of human body should be extracted from sequential images obtained by CCD camera. The intelligent robot system requires more robust silhouette extraction method because it has internal vibration and low resolution. In this paper, we discuss the hybrid silhouette extraction method for detecting and tracking the human motion. The proposed method is to combine and optimize the temporal and spatial gradient information. Also, we propose some compensation methods so as not to miss silhouette information due to poor images. Finally, we have shown the effectiveness and feasibility of the proposed method through some experiments.

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.339-356
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• 2020

In this article, a developed bond-based peridynamic model for functionally graded materials (FGMs) is proposed to simulate the dynamic fracture behaviors in FGMs. In the developed bond-based peridynamic model for FGMs, bonds are categorized into three different types, including transverse directionally peridynamic bond, gradient directionally peridynamic bond and arbitrary directionally peridynamic bond, according to the geometrical relationship between directions of peridynamic bonds and gradient bonds in FGMs. The peridynamic micromodulus in the gradient directionally and arbitrary directionally peridynamic bonds can be determined using the weighted projection method. Firstly, the standard bond-based peridynamic simulations of crack propagation and branching in the homogeneous PMMA plate are performed for validations, and the results are in good agreement with the previous experimental observations and the previous phase-field numerical results. Then, the numerical study of crack initiation, propagation and branching in FGMs are conducted using the developed bond-based peridynamic model, and the influence of gradient direction on the dynamic fracture behaviors, such as crack patterns and crack tip propagation speed, in FGMs is systematically studied. Finally, numerical results reveal that crack branching in FGMs under dynamic loading conditions is easier to occur as the gradient angle decreases, which is measured by the gradient direction and direction of the initial crack.

• IEMEK Journal of Embedded Systems and Applications
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• v.15 no.1
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• pp.1-8
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• 2020

A derivation method for a quantized gradient for machine learning on an embedded system is proposed, in this paper. The proposed differentiation method induces the quantized gradient vector to an objective function and provides that the validation of the directional derivation. Moreover, mathematical analysis shows that the sequence yielded by the learning equation based on the proposed quantization converges to the optimal point of the quantized objective function when the quantized parameter is sufficiently large. The simulation result shows that the optimization solver based on the proposed quantized method represents sufficient performance in comparison to the conventional method based on the floating-point system.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.27-46
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• 1998

We are concerned with an optimal control problem governed by a Poisson equation in which body force acts like a control parameter. The cost functional to be optimized is taken to represent the error from the desired observation and the cost due to the control. We recast the problem into the mixed formulation to take advantage of the minimax principle for the duality method. The existence of a saddle point for the Lagrangian shall be shown and the optimality system will be derived therein. Finally, to attain an optimal control, we combine the optimality system with an operational technique. By achieving the gradient of the cost functional, a convergent algorithm based on the projected gradient method is established.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.1
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• pp.180-186
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• 2001

PID control is widely used in industrial areas, but it is not easy to tune PID gains for an optimal control. The proposed learning method is to tune PID gains using the gradient approach. We use two estimation functions in this method : one is an error function for tuning of PID gains, and the other is a performance measuring function for a completion of learning. This paper shows that optimal PID controllers can be acquired when this learning method is applied to 10 systems with different natural frequencies and damping ratios.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.6
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• pp.169-174
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• 2001

Optimization of the collocated piezoceramic sensor/actuator placement is investigated numerically and verified experimentally for vibration control of laminated composite plates. The finite element method is used for the analysis of dynamic characteristics of the laminated composite plates with the piezoceramic sensor/actuator. The structural damping index(SDI) is defined from the modal damping(2$\omega$ζ) . It is chosen as the objective function for optimization. Weights for each vibrational mode are taken into account in the SDI calculation. The gradient method is used for the optimization. Optimum location of the piezoceramic sensor/actuator is determined by maximizing the SDI. Numerical simulation and experimental results show that the optimum location of the piezoceramic sensor/actuator is dependent upon the outer layer fiber orientations of the plate, and location and size of the piezoceramic sensor/actuator.