• Communications of the Korean Mathematical Society
• /
• v.22 no.3
• /
• pp.419-428
• /
• 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 ${\mid}{\det}\;DdF\mid=1$.

• Journal of IKEEE
• /
• v.23 no.4
• /
• pp.1302-1308
• /
• 2019

This paper presents an approach for classifying image made by acquired position data from a 2D Lidar sensor with a convolutional neural network (CNN). Lidar sensor has been widely used for unmanned devices owing to advantages in term of data accuracy, robustness against geometry distortion and light variations. A CNN algorithm consists of one or more convolutional and pooling layers and has shown a satisfactory performance for image classification. In this paper, different types of CNN architectures based on training methods, Gradient Descent(GD) and Levenberg-arquardt(LM), are implemented. The LM method has two types based on the frequency of approximating Hessian matrix, one of the factors to update training parameters. Simulation results of the LM algorithms show better classification performance of the image data than that of the GD algorithm. In addition, the LM algorithm with more frequent Hessian matrix approximation shows a smaller error than the other type of LM algorithm.

• Coupled systems mechanics
• /
• v.11 no.2
• /
• pp.133-149
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.421-437
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.12
• /
• pp.3804-3821
• /
• 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.