• Korean Journal of Computational Design and Engineering
• /
• v.15 no.3
• /
• pp.178-188
• /
• 2010

This paper addresses the problem of determining if two surfaces intersect tangentially or transversally in a mathematically consistent manner and approximating an intersection curve. When floating point arithmetic is used in the computation, due to the limited precision, it often happens that the decision for tangential and transversal intersection is not clear cut. To handle this problem, in this paper, interval arithmetic is proposed to use, which provides a mathematically consistent way for such decision. After the decision, the intersection is traced using the validated ODE solver, which runs in interval arithmetic. Then an iterative method is used for computing the accurate intersection point at a given arc-length of the intersection curve. The computed intersection points are then approximated by using a B-spline curve, which is provided as one instance of intersection curve for further geometric processing. Examples are provided to demonstrate the proposed method.

• Coupled systems mechanics
• /
• v.1 no.4
• /
• pp.345-360
• /
• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Proceedings of the IEEK Conference
• /
• 2002.07b
• /
• pp.1153-1156
• /
• 2002

In this parer, a high quality mesh generation method by using interval arithmetic is proposed. In the proposed method, the variance of a tangent vector at the point is considered by the automatic differentiation. From the variance, sampling points on the surface are judged whether it is adequate or not, which is calculated by the interval arithmetic. Then Delaunay triangulation is performed to the obtained sampling points, and a set of meshes is generated. The proposed method is hard to overlook the local variation of surfaces.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.2
• /
• pp.208-211
• /
• 2007

In a recently proposed method of model reduction for discrete interval systems, the denominator polynomial of a reduced model is computed by applying interval arithmetic to dominant poles of the original system. However, the denominator polynomial obtained via interval arithmetic usually has poles with larger intervals than desired ones. Hence an unstable polynomial can be derived from the stable polynomial. In this paper a simple technique is presented to partially overcome such a stability problem by accurately preserving desired real dominant poles.

• Smart Structures and Systems
• /
• v.26 no.3
• /
• pp.311-318
• /
• 2020

The goal of this study is to analytically and non-stochastically generate structural uncertainty behaviors of isotropic beams and laminated composite plates under plane stress conditions by using an interval finite element method. Uncertainty parameters of structural properties considering resistance and load effect are formulated by interval arithmetic and then linked to the finite element method. Under plane stress state, the isotropic cantilever beam is modeled and the laminated composite plate is cross-ply lay-up [0/90]. Triangular shape with a clamped-free boundary condition is given as geometry. Through uncertainties of both Young's modulus for resistance and applied forces for load effect, the change of structural maximum deflection and maximum von-Mises stress are analyzed. Numerical applications verify the effective generation of structural behavior uncertainties through the non-stochastic approach using interval arithmetic and immediately the feasibility of the present method.

• Structural Engineering and Mechanics
• /
• v.29 no.5
• /
• pp.469-488
• /
• 2008

Finite element methods have often been used for structural analyses of various mechanical problems. When finite element analyses are utilized to resolve mechanical systems, numerical uncertainties in the initial data such as structural parameters and loading conditions may result in uncertainties in the structural responses. Therefore the initial data have to be as accurate as possible in order to obtain reliable structural analysis results. The typical finite element method may not properly represent discrete systems when using uncertain data, since all input data of material properties and applied loads are defined by nominal values. An interval finite element analysis, which uses the interval arithmetic as introduced by Moore (1966) is proposed as a non-stochastic method in this study and serves a new numerical tool for evaluating the uncertainties of the initial data in structural analyses. According to this method, the element stiffness matrix includes interval terms of the lower and upper bounds of the structural parameters, and interval change functions are devised. Numerical uncertainties in the initial data are described as a tolerance error and tree graphs of uncertain data are constructed by numerical uncertainty combinations of each parameter. The structural responses calculated by all uncertainty cases can be easily estimated so that structural safety can be included in the design. Numerical applications of truss and frame structures demonstrate the efficiency of the present method with respect to numerical analyses of structural uncertainties.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2020.11a
• /
• pp.793-795
• /
• 2020

본 논문에서는 스파이킹 뉴론(Spiking Neuron)들이 쿨롱에너지 포텐셜 (Coulomb Energy Potential)을 가지는 스파이킹 신경회로망에서의 학습알고리즘을 일반화하여 구간연산(Interval Arithmetic)의 학습이 가능한 학습알고리즘을 제안한다. 제안하는 학습알고리즘은 입력 데이터로서 구간(Interval) 데이터와 포인트(Point) 데이터를 모두 학습 할 수 있는 일반화된 학습알고리즘으로서 간단한 컴퓨터 시뮬레이션을 통하여 범위(Lower bound & Upper bound)를 가지는 구간데이터와 포인트데이터의 통합적인 학습이 가능하고 전문가시스템(expert system)에서의 "don't care attributes"의 학습 등에도 활용이 가능함을 보인다.

• Journal of Preventive Medicine and Public Health
• /
• v.41 no.2
• /
• pp.128-134
• /
• 2008

Objectives : This study was conducted to determine the reference interval of serum thyroid hormones(TSH, $FT_3$, $FT_4$) in healthy Korean adults. Methods : Health examination data from 1,591 healthy Korean adults who visited an university hospital were analyzed. Patients with specific health conditions capable of altering laboratory results were excluded from the study. Serum thyroid hormones were measured using IMMULITE 2000 (DPC, USA, 2002). Subjects were 18-65 years old; 911 were male, and 690 were female. Results : The arithmetic means of TSH, $FT_3$, and $FT_4$ values for male subjects were $1.28{\pm}1.84\;{\mu}IU/ml$, $3.23{\pm}0.57\;pg/ml$, and $1.42{\pm}0.22\;ng/dl$, respectively. In female subjects, the arithmetic means of TSH, FT3, and FT4 values were $1.49{\pm}2.08\;{\mu}IU/ml$, $3.08{\pm}0.54\;pg/ml$, and $1.29{\pm}0.24\;ng/dl$, respectively. The arithmetic mean $FT_4$ value for males decreased with age (p<0.01). The arithmetic mean $FT_3$ value for females increased with age (p<0.01). The arithmetic mean thyroid hormone values of all study subjects differed significantly based on season. The arithmetic mean of male $FT_4$ decreased with increasing BMI (p<0.01). The arithmetic mean of female $FT_3$ increased with increasing BMI (p<0.01). The reference intervals recommended by the IMMULITE 2000 manufacturer are $0.40-4.00\;{\mu}IU/ml$ for TSH, 1.80-4.20 pg/ml for $FT_3$, and 0.80-1.90 ng/dl for $FT_4$ (same values for both genders). Conclusions : There was a significant difference in the interval of thyroid hormones between males and females, but the reference interval of IMMULITE 2000 was not established by gender. There is a need to reestablish the reference interval for thyroid hormones in Korean healthy adults.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.21 no.11
• /
• pp.2750-2767
• /
• 1996

In this papr, a new lossless compression method is presented based on the Binary Adaptive Arithmetic Coder(BAAC). A simple unbalanced binary tree is created by recursively dividing the BAAC unit interval into two probability sub-inervals. On the tree the More Probable Predicted Value(MPPV) and Less Probable Predicated Value(LPPV) estimated by local statistics of the image pixels are arranged in decreasing order. The BAAC or Huffman coder is thus applied to the branches of the tree. The proposed method allows the coder be directly applied to the full bit-plane medical image without a decomposition of the full bit-planes into a series of binary bit-planes. The use of the full bit model template improves the compresion ratio. In addition, a fast computation for adjusting the interval is possible since a simple arithmetic operation based on probability interval estimation state machine is used for interval sub-division within the BAAC unit interval.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.2
• /
• pp.428-431
• /
• 2007

A floating-point number system is used to represent a wide range of real numbers using finite number of bits. The standard the IEEE adopted in 1987 divides the range of real numbers into intervals of [$2^E,2^{E+1}$), where E is an Integer represented with finite bits, and defines equally spaced equal counts of discrete numbers in each interval. Since the numbers are defined discretely, not only the number representation itself includes errors but in floating-point arithmetic some strange behaviors are observed which cannot be agreed with the real world arithmetic. In this paper errors with floating-point number representation, those with arithmetic operations, and those due to order of arithmetic operations are analyzed theoretically with help of and verification with the results of some MATLAB program executions.