• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.2
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• pp.161-165
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• 2014

In this paper, we proposed the fuzzy prototype pattern classifier. In the proposed classifier, each prototype is defined to describe the related sub-space and the weight value is assigned to the prototype. The weight value assigned to the prototype leads to the change of the boundary surface. In order to define the prototypes, we use Fuzzy C-Means Clustering which is the one of fuzzy clustering methods. In order to optimize the weight values assigned to the prototypes, we use the Differential Evolutionary Algorithm. We use Linear Discriminant Analysis to estimate the coefficients of the polynomial which is the structure of the consequent part of a fuzzy rule. Finally, in order to evaluate the classification ability of the proposed pattern classifier, the machine learning data sets are used.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2552-2557
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• 2007

Shape optimization of an internal cooling passage with staggered dimples on single surface is performed and performances of surrogates are evaluated in this paper. Optimizations are performed so that turbulent heat transfer can be enhanced compromising with pressure loss due to friction. The three-dimensional governing differential equations have been solved to find the overall Nusselt number and friction factor which are related to the objective functions of this problem. Three design variables were selected among the dimensionless geometric variables. Basic surrogate models such as second order polynomial response surface approximation (RSA), Kriging meta-modeling technique, radial basis neural network (RBNN), and derived press based averaged (PBA) surrogate model are constructed. The optimal points are searched from the above constructed surrogates by sequential quadratic programming (SQP). It is shown that use of multiple surrogates can increase the robustness in prediction of better design with minimum computational cost.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.455-470
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• 2016

In this paper, we investigate the free vibration of axially loaded non-uniform Rayleigh cantilever beams. The Rayleigh beams account for the rotary inertia effect which is ignored in Euler-Bernoulli beam theory. Using an inverse problem approach we show, that for certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for Rayleigh beams. The derived property variation can serve as test functions for numerical methods. For the rotating beam case, the results have been compared with those derived using the Euler-Bernoulli beam theory.

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.4
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• pp.390-396
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• 1982

The onset of longitudinal vortices in horizontal Blasius flow isothermally heated from below is studied analytically. The assumption that at the onset of thermal instability the thermal disturbances are confined within the thermal boundary layer is employed for the limiting case of large Prandtl number. Polynomial representations for the basic quantities obtained by the integral method of the boundary layer analysis have been used. Then the system of differential equations and boundary conditions for disturbance quantities is reformulated in a convenient form so that the solutions may be constructed as rapidly convergent power series. The critical buoyancy parameter G $r_{x}$ $^{*}$ /R $e^{*1.5}$ falls between 2 and 6, which is about one order of magnitude lower than the existing experimental values. It is also shown that the positions of the onset of instability can be closely predicted by the present theory.y.y.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.569-580
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• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

• Steel and Composite Structures
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• v.9 no.5
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• pp.473-497
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• 2009

For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.8
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• pp.969-976
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• 1999

This paper is concerned with the generation of a balancing trajectory for improving the walking performance. The balancing motion has been determined by solving a second -order differential equation. However, this method caused some difficulties in linearizing and approximating the equation and had restrictions on using various balancing trajectories. The proposed difficulties in linearizing and approximating the equation and had restrictions on using various balancing trajectories. The proposed method i this paper is based on the genetic algorithm for minimizing the motins of balancing joints, whose trajectories are generated by the fifth-order polynomial interpolation after planning leg trajectories. The real walking experiments are made on the biped robot IWR-III, developed by our Automatic Control Laboratory. The system has 8 degrees of freedom and the structure of three pitches in each leg, and one roll and one prismatic joint in the balancing joints. The experimental result shows the validity and applicability of the new proposed algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.827-835
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• 1999

In this paper, a dead reckoning navigation system for differential drive mobile robots is presented. The navigation system consists of two incremental encoders and a gyroscope. We have built a third order polynomial function for compensating the nonlinear scale factor errors of the gyroscope. We utilize an indirect Kalman filter that feeds back estimated errors to the main navigation system. Also, the observability of the filter is analyzed in order to systematically evaluate the filter's performance. Experimental results show that the proposed navigation system provides a reliable position and heading angle by mutually compensating the encoder and the gyroscope errors. The proposed filter also reduces the computational burden and enhances the navigation system's reliability. The observability analysis confirms the characteristics of inevitably unbounded position error growth in dead reckoning navigation systems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.