• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.257-270
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• 2018

An extrapolated Crank-Nicolson characteristic finite element method is introduced for approximate solutions of nonlinear Sobolev equations with a convection term. And we obtain the higher order of convergence for approximate solutions in the temporal and the spatial directions with respect to $L^2$ norm.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.99-112
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• 2012

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.6
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• pp.33-43
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• 2021

A60 class bulkhead penetration piece is a fire resistance system installed on a bulkhead compartment to protect lives and to prevent flame diffusion in a fire accident on a ship and offshore plant. This study focuses on the approximate optimization of the fire resistance design of the A60 class bulkhead penetration piece using a multi-island genetic algorithm. Transient heat transfer analysis was performed to evaluate the fire resistance design of the A60 class bulkhead penetration piece. For approximate optimization, the bulkhead penetration piece length, diameter, material type, and insulation density were considered discrete design variables; moreover, temperature, cost, and productivity were considered constraint functions. The approximate optimum design problem based on the meta-model was formulated by determining the discrete design variables by minimizing the weight of the A60 class bulkhead penetration piece subject to the constraint functions. The meta-models used for the approximate optimization were the Kriging model, response surface method, and radial basis function-based neural network. The results from the approximate optimization were compared to the actual results of the analysis to determine approximate accuracy. We conclude that the radial basis function-based neural network among the meta-models used in the approximate optimization generates the most accurate optimum design results for the fire resistance design of the A60 class bulkhead penetration piece.

• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1143-1155
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• 2001

In order to reduce the expensive CPU time for design sensitivity analysis in dynamic response optimization, this study introduces the design sensitivities approximated within estimated confidence radius in dynamic response optimization with ALM method. The confidence radius is estimated by the linear approximation with Hessian of quasi-Newton formula and qualifies the approximate gradient to be validly used during optimization process. In this study, if the design changes between consecutive iterations are within the estimated confidence radius, then the approximate gradients are accepted. Otherwise, the exact gradients are used such as analytical or finite differenced gradients. This hybrid design sensitivity analysis method is embedded in an in-house ALM based dynamic response optimizer, which solves three typical dynamic response optimization problems and one practical design problem for a tracked vehicle suspension system. The optimization results are compared with those of the conventional method that uses only exact gradients throughout optimization process. These comparisons show that the hybrid method is more efficient than the conventional method. Especially, in the tracked vehicle suspension system design, the proposed method yields 14 percent reduction of the total CPU time and the number of analyses than the conventional method, while giving similar optimum values.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.7
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• pp.4611-4617
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• 2014

This paper proposes an approximate method to estimate member forces of columns in a rigid frame. One of the conventional methods, Cantilever Method assumes the midpoint of a column as a hinge and linear distribution of axial stresses regarding the centroid of the column areas. As a result, it shows erroneous results compared to those of matrix analysis of two frames. In this study, a new method is proposed to estimate the member forces in columns and location of hinges in columns, which can be adopted easily by a practicing engineer, and numerical examples showed improved results compared to conventional methods.

• KIPS Transactions on Software and Data Engineering
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• v.3 no.6
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• pp.215-218
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• 2014

In hashing-based methods for approximate nearest neighbors(ANN) search, by mapping data points to k-bit binary codes, nearest neighbors are searched in a binary embedding space. In this paper, we present a hashing method using a PCA-based clustering method, Principal Direction Divisive Partitioning(PDDP). PDDP is a clustering method which repeatedly partitions the cluster with the largest variance into two clusters by using the first principal direction. The proposed hashing method utilizes the first principal direction as a projective direction for binary coding. Experimental results demonstrate that the proposed method is competitive compared with other hashing methods.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.3
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• pp.259-266
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• 2011

We present a new dual sequential approximate optimization (SAO) algorithm called SD-TDQAO (sequential dual two-point diagonal quadratic approximate optimization). This algorithm solves engineering optimization problems with a nonlinear objective and nonlinear inequality constraints. The two-point diagonal quadratic approximation (TDQA) was originally non-convex and inseparable quadratic approximation in the primal design variable space. To use the dual method, SD-TDQAO uses diagonal quadratic explicit separable approximation; this can easily ensure convexity and separability. An important feature is that the second-derivative terms of the quadratic approximation are approximated by TDQA, which uses only information on the function and the derivative values at two consecutive iteration points. The algorithm will be illustrated using mathematical and topological test problems, and its performance will be compared with that of the MMA algorithm.

• The Journal of Engineering Geology
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• v.11 no.2
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• pp.153-161
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• 2001

The quantitative evaluation of the stereo graphic projection, the limit equilibrium analysis, the finite difference analysis, the distinct element methocI is a analytical evaluation using many variables. Through the reliability analysis by the point estimation technique, uncertainty of other variables that have an effect on the stability of the rock slo~ was considered. The organized evaluation method of the approximate reasoning concept and using a fuzzy language was developed to confer and analysis the failure factors in planning and constructing the rock slope. Considering the result of the an- alysis, it was demonstrated that stability of entire sections can be evaluated through reliability analysis of point estimation technique. The results of stability evaluation by Fuzzy Approximate Reasoning is generally identical with the results of other existirw; analyses. As mentioned above, general and organized evaluation of special qualities of rock slope is possible using RMR Classification, Stereo Graphic Projection, Limit Equilibriwn Analysis, Finite Difference Analysis, Distinct Element Method, Point Estimation Technique, and Fuzzy Approximate Reasoning.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.277-284
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• 1993

The purpose of this paper is to prove the approximate controllability results for the delay Volterra system in the case of trajectories. In method, our paper differs from [5].

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.