• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.2
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• pp.104-109
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• 2011

I present a method of aspheric surface profile measurement using 2nd derivative of local area profile. This method is based on the principle of curvature sensor which measures the local 2nd derivative under test along a line. The profile is then reconstructed from the data on the each point. Unlike subaperture-stiching method and slope detection method, 2nd derivative method has strong points from a geometric point of view in measuring the aspheric surface profile. The second derivative terms of surface profile is an intrinsic property of the test piece, which is independent of its position and tip-tilt motion. The curvature is measured at every local area with high accuracy and high lateral resolution by using White-light scanning interferometry.

• Journal of the Korean Statistical Society
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• v.35 no.2
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• pp.213-224
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• 2006

We investigate the influence of subjects or observations on regression coefficients of generalized estimating equations using the influence function and the derivative influence measures. The influence function for regression coefficients is derived and its sample versions are used for influence analysis. The derivative influence measures under certain perturbation schemes are derived. It can be seen that the influence function method and the derivative influence measures yield the same influence information. An illustrative example in longitudinal data analysis is given and we compare the results provided by the influence function method and the derivative influence measures.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.387-396
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• 1997

For given discrete derivative data in a rectangular re-gion we propose a method to generate an approximated surface which fits the given derivative data in the region and extends smoothly to a sufficiently large rectangular region. Such an extension in nec-essary in the generation of the surface in NC(numerical control) ma-chine.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1389-1410
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• 2016

This paper proposes a hybrid of topological derivative-based level set method (LSM) and isogeometric analysis (IGA) for structural topology optimization. In topology optimization a significant drawback of the conventional LSM is that it cannot create new holes in the design domain. In this study, the topological derivative approach is used to create new holes in appropriate places of the design domain, and alleviate the strong dependency of the optimal topology on the initial design. Furthermore, the values of the gradient vector in Hamilton-Jacobi equation in the conventional LSM are replaced with a Delta function. In the topology optimization procedure IGA based on Non-Uniform Rational B-Spline (NURBS) functions is utilized to overcome the drawbacks in the conventional finite element method (FEM) based topology optimization approaches. Several numerical examples are provided to confirm the computational efficiency and robustness of the proposed method in comparison with derivative-based LSM and FEM.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.365-372
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• 2006

A new meshfree formulation is developed for material discontinuity problems. A local interfacial jump function which is defined as hyperplane function is embedded in the meshless approximation and the approximation accurately models functions with jumps in the displacement and the derivative fields. Diffuse derivative technique copes with difficulty due to complexity of derivative computation of meshfree approximation. Collocation method with diffuse derivative accelerates computing speed for numerical solution. By solving inclusion and composite material problems, the robustness and effectiveness of the method are verified.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.1
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• pp.272-287
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• 2017

This paper proposes new methods, named Derivative Code (DerivativeCode) and Derivative Code Pattern (DCP), for object recognition. The discriminative derivative code is used to capture the local relationship in the input image by concatenating binary results of the mathematical derivative value. Gabor based DerivativeCode is directly used to solve the palmprint recognition problem, which achieves a much better performance than the state-of-art results on the PolyU palmprint database. A new local pattern method, named Derivative Code Pattern (DCP), is further introduced to calculate the local pattern feature based on Dervativecode for object recognition. Similar to local binary pattern (LBP), DCP can be further combined with Gabor features and modeled by spatial histogram. To evaluate the performance of DCP and Gabor-DCP, we test them on the FERET and PolyU infrared face databases, and experimental results show that the proposed method achieves a better result than LBP and some state-of-the-arts.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.21-28
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• 2005

This paper proposes a new method for accelerating the search speed of genetic algorithms by taking derivative evaluation and conditional random selection into account in their evolution process. Derivative evaluation makes genetic algorithms focus on the individuals whose fitness is rapidly increased. This accelerates the search speed of genetic algorithms by enhancing exploitation like steepest descent methods but also increases the possibility of a premature convergence that means most individuals after a few generations approach to local optima. On the other hand, derivative evaluation under a premature convergence helps genetic algorithms escape the local optima by enhancing exploration. If GAs fall into a premature convergence, random selection is used in order to help escaping local optimum, but its effects are not large. We experimented our method with one combinatorial problem and five complex function optimization problems. Experimental results showed that our method was superior to the simple genetic algorithm especially when the search space is large.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.499-509
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• 2001

We investigate the influence of observations on a test of additional information about discrimination using the influence function and the derivative influence measures. the influence function for the test statistic is derived and this sample versions are used for influence analysis. The derivative influence measures for the test statistic under a perturbation scheme are derived. It will be seen that the influence function method and the derivative influence measures yield the same result. Furthermore, we will derive the relationships between the influence function and the derivative influence measures when the sample size is large. an illustrative example is given and we will compare the results provided by the influence function method and the derivative influence measures.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.819-822
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• 2002

It is necessary for the numerical simulation of 3-dimensional incompressible isotropic decaying turbulence to construct 3-dimensional initial velocity field which resembles the fully developed turbulence. Although the previous velocity field generation method proposed by Rogallo(1981) satisfies continuity equation and 3-dimensional energy spectrum, it has limitation, as indicated in his paper, that it does not produce the higher velocity moments(e. g. velocity derivative skewness) characteristic of real turbulence. In this study, a new velocity field generation method which is able to control velocity derivative skewness of initial velocity field is proposed. Brief descriptions of the new method and a few parameters which is used to control velocity derivative skewness are given. A large eddy simulation(LES) of isotropic decaying turbulence using dynamic subgrid-scale model is carried out to evaluate the performance of the initial velocity field generated by the new method. It was shown that the resolved turbulent kinetic energy decay curve and the resolved enstrophy decay curve from the initial field of new method were more realistic than those from the initial field of Rogallo's method. It was found that the dynamic model coefficient from the former was initially half the stationary value and experienced relatively short transition period, though that from the latter was initially zero and experienced relatively longer transition period.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.583-590
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• 2002

Point collocation method based on the fast derivatives approximation of meshfree shape function is applied to solid mechanics in this study. Enhanced meshfree approximation with approximated derivative of shape function is reviewed, and formulation of linear elastic solid mechanics by point collocation method is presented. It implies that governing equation of solid mechanics with strong form is directly formulated without no numerical integration cells or grid. The regularity of weight function is not required due to a use of approximated derivative, so we propose the exponential type weight function that is discontinuous in first derivative. The convergence and stability of the proposed method is verified by passing the generalized patch test. Also, the efficiency and applicability of the proposed method in solid mechanics is verified by solving types of solid problems. Numerical results show that not only a use of proposed weight function leads lower error and higher convergence rate than that of the conventional weight functions, but also the improved collocation method with derivative approximation enables to compute the derivatives of shape function very fast and accurately enough to replace the classical direct derivative calculation.