• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.73-93
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• 2005

In this paper, we attempt to present a new numerical approach to solve non-linear backward stochastic differential equations. First, we present some definitions and theorems to obtain the conditions, from which we can approximate the non-linear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE correspond with the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems, to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original non-linear BSDE in two different cases.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.93-106
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• 1999

In this paper we consider estimation of a real valued parameter in the drift coefficient of a Hilbert space valued Ito stochastic differential equation. First we consider observation of the corresponding diffusion in a fixed time interval [0, T] and prove the Bernstein - von Mises theorem concerning the convergence of posterior distribution of the parameter given the observation, suitably normalised and centered at the MLE, to the normal distribution as Tlongrightarrow$\infty$. As a consequence, the Bayes estimator of the drift parameter becomes asymptotically efficient and asymptotically equivalent to the MLE as Tlongrightarrow$\infty$. Next, we consider observation in a random time interval where the random time is determined by a predetermined level of precision. We show that the sequential MLE is better than the ordinary MLE in the sense that the former is unbiased, uniformly normally distributed and efficient but is latter is not so.

• Particle and aerosol research
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• v.10 no.1
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• pp.33-43
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• 2014

A differential mobility analyzer (DMA) has been widely used as a standard tool for classifying nanoparticles with a certain size. More recently, several new types of DMA have been tested in an attempt to produce size-monodisperse nanoparticles. It is a bit surprise to see how simple the working theory of the DMA is. Although the theory was demonstrated quite successful, no one can guarantee whether the theory still works in another geometry of the DMA. In this regard, we first investigated the validity of the theory under various working conditions and then moved to check the validity upon minor change in its design. For the valid test, we compared the results with those obtained from a computational fluid dynamics.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.3
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• pp.158-164
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• 2003

This paper proposes a percentage current differential relaying algorithm for bus protection using an advanced compensating algorithm of the secondary current of current transformers (CTs). The compensating algorithm estimates the core flux at the start of the first saturation based on the value of the second-difference of the secondary current. Then, it calculates the core flux and compensates distorted currents using the magnetization curve. The algorithm Is unaffected by a remanent flux. The simulation results indicate that the proposed algorithm can discriminate internal faults from external faults when the CT saturates. This paper concludes by implementing the algorithm into a TMS320C6701 digital signal processor. The results of hardware implementation are also satisfactory. The proposed algorithm can improve not only stability of the relay in the case of an external fault but sensitivity of the relay in the case of an internal fault.

• Smart Structures and Systems
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• v.17 no.2
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• pp.347-361
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• 2016

A two-stage method for damage detection in truss systems is proposed. In the first stage, a modal residual vector based indicator (MRVBI) is introduced to locate the potentially damaged elements and reduce the damage variables of a truss structure. Then, in the second stage, a differential evolution (DE) based optimization method is implemented to find the actual site and extent of damage in the structure. In order to assess the efficiency of the proposed damage detection method, two numerical examples including a 2D-truss and 3D-truss are considered. Simulation results reveal the high performance of the method for accurately identifying the damage location and severity of trusses with considering the measurement noise.

• Proceedings of the KSR Conference
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• 2005.11a
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• pp.1165-1170
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• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.725-740
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• 2015

This study presents critical buckling load optimization of the axially graded layered uniform columns. In the first place, characteristic equations for the critical buckling loads for all boundary conditions are obtained using the transfer matrix method. Then, for each case, square of this equation is taken as a fitness function together with constraints. Due to explicitly unavailable objective function for the critical buckling loads as a function of segment length and volume fraction of the materials, especially for the column structures with higher segment numbers, initially, prescribed value is assumed for it and then the design variables satisfying constraints are searched using Differential Evolution (DE) optimization method coupled with eigen-value routine. For constraint handling, Exterior Penalty Function formulation is adapted to the optimization cycle. Different boundary conditions are considered. The results reveal that maximum increments in the critical buckling loads are attained about 20% for cantilevered and pinned-pinned end conditions and 18% for clamped-clamped case. Finally, the strongest column structure configurations will be determined. The scientific and statistical results confirmed efficiency, reliability and robustness of the Differential Evolution optimization method and it can be used in the similar problems which especially include transcendental functions.

• Journal of information and communication convergence engineering
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• v.17 no.4
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• pp.261-266
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• 2019

Differential evolution (DE) is an uncomplicated and serviceable developmental algorithm. Nevertheless, its execution depends on strategies and regulating structures. The combination of several strategies between subpopulations helps to stabilize the probing on DE. In this paper, we propose a unique k-mean soft island model DE(KSDE) algorithm which maintains population diversity through soft island model (SIM). A combination of various approaches, called KSDE, intended for migrating the subpopulation information through SIM is developed in this study. First, the population is divided into k subpopulations using the k-means clustering algorithm. Second, the mutation pattern is singled randomly from a strategy pool. Third, the subpopulation information is migrated using SIM. The performance of KSDE was analyzed using 13 benchmark indices and compared with those of high-technology DE variants. The results demonstrate the efficiency and suitability of the KSDE system, and confirm that KSDE is a cost-effective algorithm compared with four other DE algorithms.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.6
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• pp.47-54
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• 2010

In this paper, the purpose is to study a method for detection of crack in clamped-clamped beams using the vibration characteristics. The natural frequency of beam is obtained by FEM and experiment. The governing differential equations of a Timoshenko beam are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The differences between the actual and predicted crack positions and sizes are less than 9.8% and 28%, respectively.

• Journal of Advanced Navigation Technology
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• v.17 no.5
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• pp.568-573
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• 2013

In this paper, we propose a differential fault analysis on symmetry structured SPN block cipher proposed in 2008. The target algorithm has the SPN structure and a symmetric structure in encryption and decryption process. To recover the 128-bit secret key of the target algorithm, this attack requires only one random byte fault and an exhaustive search of $2^8$. This is the first known cryptanalytic result on the target algorithm.