• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2004년도 ICCAS
• /
• pp.658-662
• /
• 2004

This paper develops a stability analysis and controller synthesis methodology for a continuous-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties. Affine T-S fuzzy system can be an advantage because it may be able to approximate nonlinear functions to high accuracy with fewer rules than the homogeneous T-S fuzzy systems with linear consequents only. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of bilinear matrix inequalities (BMIs). A simulation example is given to illustrate the application of the proposed method.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.681-692
• /
• 2022

Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al. [15]. Some examples are also discussed for the sake of better understanding of this article.

• 대한수학회보
• /
• 제61권4호
• /
• pp.1033-1051
• /
• 2024

In this paper, we define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions, linear and quadratic parametric Euler sums. Furthermore, we also give an explicit evaluation of alternating double zeta values ${\zeta}({\bar{2j}};\,2m+1)$ in terms of a combination of alternating Riemann zeta values by using the parametric Euler sums.

• Structural Engineering and Mechanics
• /
• 제29권3호
• /
• pp.289-300
• /
• 2008

The use of metric trial functions to represent the real stress field in what is called the unsymmetric finite element formulation is an effective way to improve predictions from distorted finite elements. This approach works surprisingly well because the use of parametric functions for the test functions satisfies the continuity conditions while the use of metric (Cartesian) shape functions for the trial functions attempts to ensure that the stress representation during finite element computation can retrieve in a best-fit manner, the actual variation of stress in the metric space. However, the issue of how to handle situations where there is locking along with mesh distortion has never been addressed. In this paper, we show that the use of a consistent definition of the constrained strain field in the metric space can ensure a lock-free solution even when there is mesh distortion. The three-noded Timoshenko beam element is used to illustrate the principles. Some significant conclusions are drawn regarding the optimal strategy for finite element modelling where distortion effects and field-consistency requirements have to be reconciled simultaneously.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
• /
• pp.133-136
• /
• 2004

This paper proposes a stability condition in affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).

• International Journal of CAD/CAM
• /
• 제6권1호
• /
• pp.59-64
• /
• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• 한국CDE학회논문집
• /
• 제7권4호
• /
• pp.240-247
• /
• 2002

Most commercial CAD systems provide parametric modeling functions, and by using these capabilities designers can edit a CAD model in order to create design variants. It is necessary to transfer parametric information during a CAD model exchange to modify the model inside the receiving system. However, it is not possible to exchange parametric information of CAD models based on the cur-rent version of STEP. The designer intents which are contained in the parametric information can be lost during the STEP transfer of CAD models. This paper introduces a hybrid CAB model translator, which also uses the feature tree of commercial CAD systems in addition to the macro file to allow transfer of parametric information. The macro-parametric approach is to exchange CAD models by using the macro file, which contains the history of user commands. To exchange CAD models using the macro-parametric approach, the modeling commands of several commercial CAD systems are analyzed. Those commands are classified and a set of standard modeling commands has been defined. As a neutral fie format, a set of standard modeling commands has been defined. Mapping relations between the standard modeling commands set and the native modeling commands set of commercial CAD systems are defined. The scope of the current version is limited to parts modeling and assemblies are excluded.

• 한국CDE학회논문집
• /
• 제6권4호
• /
• pp.271-276
• /
• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.

• 정보처리학회논문지:소프트웨어 및 데이터공학
• /
• 제10권10호
• /
• pp.407-420
• /
• 2021

심층신경망은 다양한 문제를 해결하는데 널리 사용되고 있다. 하지만 은닉층이 깊은 심층신경망을 학습하는 동안 빈번히 발생하는 기울기 소실 또는 폭주 문제는 심층신경망 학습의 큰 걸림돌이 되고 있다. 본 연구에서는 기울기 소실이 발생하는 원인 중 비선형활성함수에 의해 발생할 수 있는 기울기 소실 문제를 완화하기 위해 파라메트릭 활성함수를 제안한다. 제안된 파라메트릭 활성함수는 입력 데이터의 특성에 따라 활성함수의 크기 및 위치를 변환시킬 수 있는 파라미터를 적용하여 얻을 수 있으며 역전파과정을 통해 활성함수의 미분 크기에 제한이 없는 손실함수를 최소화되도록 학습시킬 수 있다. 은닉층 수가 10개인 XOR문제와 은닉층 수가 8개인 MNIST 분류문제를 통하여 기존 비선형활성함수와 파라메트릭활성함수의 성능을 비교하였고 제안한 파라메트릭 활성함수가 기울기 소실 완화에 우월한 성능을 가짐을 확인하였다.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제7권1호
• /
• pp.100-114
• /
• 2015

This paper deploys optimization techniques to obtain the optimum hull form of KSUEZMAX at the conditions of full-load draft and design speed. The processes have been carried out using a RaPID-HOP program. The bow and the stern hull-forms are optimized separately without altering neither, and the resulting versions of the two are then combined. Objective functions are the minimum values of wave-making and viscous pressure resistance coefficients for the bow and stern. Parametric modification functions for the bow hull-form variation are SAC shape, section shape (U-V type, DLWL type), bulb shape (bulb height and size); and those for the stern are SAC and section shape (U-V type, DLWL type). WAVIS version 1.3 code is used for the potential and the viscous-flow solver. Prior to the optimization, a parametric study has been conducted to observe the effects of design parameters on the objective functions. SQP has been applied for the optimization algorithm. The model tests have been conducted at a towing tank to evaluate the resistance performance of the optimized hull-form. It has been noted that the optimized hull-form brings 2.4% and 6.8% reduction in total and residual resistance coefficients compared to those of the original hull-form. The propulsive efficiency increases by 2.0% and the delivered power is reduced 3.7%, whereas the propeller rotating speed increases slightly by 0.41 rpm.