• 대한수학회논문집
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• 제22권3호
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• pp.419-428
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• 2007

In this paper, we will investigate the Hessian geometry of the homogeneous domain over the hypersurface given by a function F : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with ${\mid}{\det}\;DdF\mid=1$.

• 전기전자학회논문지
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• 제23권4호
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• pp.1302-1308
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• 2019

본 논문은 CNN (Convolutional Neural Network)와 2D Lidar 센서에서 획득한 위치 데이터를 이용하여 이미지를 분류하는 방법을 제시한다. Lidar 센서는 데이터 정확도, 형상 왜곡 및 광 변화에 대한 강인성 측면에서의 이점으로 인해 무인 장치에 널리 사용되어 왔다. CNN 알고리즘은 하나 이상의 컨볼루션 및 풀링 레이어로 구성되며 이미지 분류에 만족스러운 성능을 보여 왔다. 본 논문에서는 학습 방법에 따라 다른 유형의 CNN 아키텍처들인 Gradient Descent (GD) 및 Levenberg-arquardt (LM)를 구현하였다. LM 방법에는 학습 파라메터를 업데이트하는 요소 중 하나인 Hessian 행렬 근사 빈도에 따라 두 가지 유형이 있다. LM 알고리즘의 시뮬레이션 결과는 GD 알고리즘보다 이미지 데이터의 분류 성능이 우수하였다. 또한 Hessian 행렬 근사가 더 빈번한 LM 알고리즘은 다른 유형의 LM 알고리즘보다 작은 오류를 보여주었다.

• Coupled systems mechanics
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• 제11권2호
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• pp.133-149
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• 2022

The accurate prediction of elastoplasticity under prescribed workloads is essential in the optimization of engineering structures. Mechanical experiments are carried out with the goal of obtaining reliable sets of material parameters for a chosen constitutive law via inverse identification. In this work, two sample geometries made of high strength steel plates were evaluated to determine the optimal configuration for the identification of Ludwik's nonlinear isotropic hardening law. Finite element model updating(FEMU) was used to calibrate the material parameters. FEMU computes the parameter changes based on the Hessian matrix, and the sensitivity fields that report changes of computed fields with respect to material parameter changes. A sensitivity analysis was performed to determine the influence of the sample geometry on parameter identifiability. It was concluded that the sample with thinned gauge region with a large curvature radius provided more reliable material parameters.

• 대한수학회지
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• 제56권2호
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• 대한기계학회논문집A
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• 제20권12호
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• pp.3804-3821
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• 1996

The configuration optimization is a structural optimization method which includes the coordinates of a structure as well as the sectional properties in the design variable set. Effective reduction of the weight of discrete structures can be obrained by changing the geometry while satisfying stress, Ei;er bickling, displacement, and frequency constraints, etc. However, the nonlinearity due to the configuration variables may cause the difficulties of the convergence and expensive computational cost. An efficient approximation method for the configuration optimization has been developed to overcome the difficulties. The method approximates the constraint functions based onthe second-order Taylor series expansion with reciprocal design variables. The Hessian matrix is approzimated from the information on previous design points. The developed algotithms are coded and the examples are solved.