• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.345-368
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• 2004

A preconditioning algorithm is developed in this paper for the iterative solution of the linear system of equations resulting from the p-version boundary element approximation of the three dimensional integral equation with hypersingular operators. The preconditioner is derived by first making the nodal and side basis functions locally orthogonal to the element internal bases, and then by decoupling the nodal and side bases from the internal bases. Its implementation consists of solving a global problem on the wire-basket and a series of local problems defined on a single element. Moreover, the condition number of the preconditioned system is shown to be of order $O((1＋ln/p)^{7})$. This technique can be applied to discretization with triangular elements and with general basis functions.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.565-576
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• 1997

The material-based homogenization design method generates arbitrary topologies of initial structural design as well as reinforcement structural design by controlling the amount of material available. However, if a small volume constraint is specified in the design of Lightweight structures, thin and slender structures are usually obtained. For these structures stability becomes one of the most important requirements. Thus, to prevent overall buckling (that is, to increase stability), the objective of the design is to maximize the buckling load of a structure. In this paper, the buckling analysis is restricted to the linear buckling behavior of a structure. The global stability requirement is defined as a stiffness constraint, and determined by solving the eigenvalue problem. The optimality conditions to update the design variables are derived based on the sequential convex approximation method and the dual method. Illustrated examples are presented to validate the feasibility of this method in the design of structures.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.367-370
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• 2006

Performances of multiple surrogate models are evaluated in a turbomachinery blade shape optimization. The basic models, i.e., Response Surface Approximation, Kriging and Radial Basis Neural Network models as well as weighted average models are tested for shape optimization. Global data based errors for each surrogates are used to calculate the weights. These weights are multiplied with the respective surrogates to get the final weighted average models. The design points are selected using three level fractional factorial D-optimal designs. The present approach can help address the multi-objective design on a rational basis with quantifiable cost-benefit analysis.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.173-184
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• 2004

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region in $R^2$. We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error in $L_1$ is controlled.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.2
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• pp.186-191
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• 2015

Presently, rapidly changing and unstable global economic environments demand engineers. Products should be designed to increase profits by lowering costs and provide distinguished performance compared with competitors. This study aims to optimize the design of the power-transmission drive shaft. The mass is reduced as an objective function, and the stress is constrained under a constant value. To reduce the number of experiments, CCD (central composite design) and D-Optimal are used for the experimental design. RSM (response surface methodology) is employed to construct a regression model for the objective functions and constraint function. In this problem, there is only one objective function for the mass. The other objective function gives 1; thus, NSGA-II is used.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.73-79
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• 2006

In this paper, we propose a new triangular finite element mesh generation method based on simplification of high-density mesh and adaptive Level-of-Detail (LOD) methods for efficient CAE. In our method, mesh simplification is used to control the mesh properties required for FE mesh, such as the number of triangular elements, element shape quality and size while keeping the specified approximation tolerance. Adaptive LOD methods based on vertex hierarchy according to curvature and region of interest, and global LOD method preserving density distributions are also proposed in order to construct a mesh more appropriate for CAE purpose. These methods enable efficient generation of FE meshes with properties appropriate for analysis purpose from a high-density mesh. Finally, the effectiveness of our approach is shown through evaluations of the FE meshes for practical use.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.5
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• pp.852-857
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• 2008

A new adaptive neuro-control algorithm for a SISO strict-feedback nonlinear system is proposed. All the previous adaptive neural control algorithms for strict-feedback nonlinear systems are based on the backstepping scheme, which makes the control law and stability analysis very complicated. The main contribution of the proposed method is that it demonstrates that the state-feedback control of the strict-feedback system can be viewed as the output-feedback control problem of the system in the normal form. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. Depending heavily on the universal approximation property of the neural network (NN), only one NN is employed to approximate the lumped uncertain system nonlinearity. The Lyapunov stability of the NN weights and filtered tracking error is guaranteed in the semi-global sense.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.401-414
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• 2020

It is computationally expensive to compute principal components from scratch at every update or downdate when new data arrive and existing data are truncated from the data matrix frequently. To overcome this limitations, incremental principal component analysis is considered. Specifically, we present a sliding window based efficient incremental principal component computation from a covariance matrix which comprises of two procedures; simultaneous update and downdate of principal components, followed by the rank-one matrix update. Additionally we track the accurate decomposition error and the adaptive numerical rank. Experiments show that the proposed algorithm enables a faster execution speed and no-meaningful decomposition error differences compared to typical incremental principal component analysis algorithms, thereby maintaining a good approximation for the principal components.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.585-592
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• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.647-671
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• 2020

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.