• East Asian mathematical journal
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• v.19 no.1
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• pp.17-26
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• 2003

This paper demonstrates the CAS technique of analyzing the nature and the structure of the numerical error for education and research purposes. This also illustrates the CAS approach in experimenting with the numerical operations in an arbitrary computer number system and also in doing error analysis in a visual manner.

• Journal of the Society of Naval Architects of Korea
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• v.40 no.5
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• pp.1-9
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• 2003

To predict the powering performance of full scale ships from the towing tank tests, resistance, propeller open water and self-propulsion tests are conducted. Model tests inevitably include the experimental error defined as the sum of two types of uncertainties, bias and precision errors. The induced errors in each element of model test are propagated through various routes and correlated with one another. The correlation coefficients are very important in the uncertainty analysis. The coefficient gives a direction(increase or decrease) for a value of error in individual elements. If the coefficient is not used accurately, the error bounds of the individual elements are overestimated or underestimated. In this study, the new methodology is applied to the uncertainty analysis of HMRI's towing tank tests, thus error bounds of each element is suggested and verified by several repetitive experiments.

• Transactions of Materials Processing
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• v.20 no.2
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• pp.124-131
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• 2011

A flexible stretch forming process is useful for small quantity batch production because various shape changes of the flexible die can be achieved conveniently. In this study, the design variables, namely, the punch size, curvature radius and elastic pad thickness, were quantitatively evaluated to understand their influence on sheet formability using statistical methods such as the correlation and regression analyses. Forming simulations were designed and conducted by a three-way factorial design to obtain numerical values of a shape error. Linear relationships between the design variables and the shape error resulted from the Pearson correlation analysis. Subsequently, a regression analysis was also conducted between the design variables and the shape error. A regression equation was derived and used in the flexible die design stage to estimate the shape error.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.3
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• pp.17-24
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• 2003

One of the most important performance criteria related to the gain tuning of controller for CNC machining center is the contour error. This study analyzed circular error by the axis-matched and mismatched cases. To reduce ellipse and radius error, it is necessary to set the gain for each axis to be same bandwidth and high response. Based on the analysis in the frequency domain, we simulate feed system by mathematical model and then predict bandwidth of each axis. For analysis of structure vibration while the each axis is moving, we try the various of measuring method and position loop is improved by jerk limit.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.3
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• pp.300-306
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• 2006

In this paper an error analysis of 3-dimensional GNSS attitude determination system is given. The attitude error covariance matrix is derived and analyzed. It implies that attitude errors are affected by the baseline length and configuration, the satellites numbers and geometry, receiver measurement noises and the nominal attitude of the vehicle. By defining Euler Angle Dilution Of Precision (EADOP) which is analogous to GDOP, roll, pitch and yaw errors can be efficiently analyzed. However the expression of the attitude error is too complex to get some intuitions. Therefore with a commonly adopted assumption, new expressions for attitude error are derived. The formulas are easy to compute and represent the attitude error as a function of the nominal attitude of a vehicle, the baseline configuration and the receiver noise. Using the formula, the accuracy of the attitude can be analytically predicted without the computer simulations. Applications to some widely used configurations reveal the effectiveness of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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• pp.995-1006
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• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation is evaluated by a dynamic analysis. Large eddy simulation of isotropic turbulence is performed with various dissipative and non-dissipative schemes to investigate the effect of numerical dissipation on the resolved solutions. It is shown by the present dynamic analysis that upwind schemes reduce the aliasing error and increase the finite differencing error. The existence of optimal upwind scheme that minimizes total numerical error is verified. It is also shown that the finite differencing error from numerical dissipation is the leading source of numerical errors by upwind schemes. Simulations of a turbulent channel flow are conducted to show the existence of the optimal upwind scheme.

• Journal of the Korean Society for Precision Engineering
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• v.30 no.7
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• pp.754-761
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• 2013

Thermal displacement is an important issue in machine tool systems. During the last several decades, thermal error compensation technology has significantly reduced thermal distortion error; this success has been attributed to the development of a precise, robust thermal error model. A major advantage of using the thermal error model is instant compensation for the control variables during the modeling process. However, successful application of thermal error modeling requires correct determination of the temperature sensor placement. In this paper, a procedure for predicting thermal-mode-based thermal error is introduced. Based on this thermal analysis, temperature sensors were positioned for multiple heat-source models. The performance of the sensors based on thermal-mode error analysis, was compared with conventional methods through simulation and experiments, for the case of a slide table in a transient state. Our results show that for predicting thermal error the proposed thermal model is more accurate than the conventional model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.850-858
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• 1997

A new a posteriori error estimator is introduced and applied to variational inequalities occurring in problems of flow through porous media. In order to construct element-wise a posteriori error estimates the global error is localized by a special mixed formulation in which continuity conditions at interfaces are treated as constraints. This approach leads to error indicators which provide rigorous upper bounds of the element errors. A discussion of a compatibility condition for the well-posedness of the local error analysis problem is given. Two numerical examples are solved to check the compatibility of the local problems and convergence of the effectivity index both in a local and a global sense with respect to local refinements.

• Transactions of Materials Processing
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• v.13 no.7
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• pp.594-599
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• 2004

In the sheet metal forming operations, the strain measurement of sheet panel is an essential work which provides the formability information needed in die design, process design, and product inspection. To measure efficiently complex geometry strains, the 3-dimensional automative strain measurement system, which theoretically has a high accuracy but practically has about 3～5％ strain error, is often used. For eliminating the strain error resulted in measuring the strains of formed panels using an automated strain measurement system, the position error calibration method is suggested, which computes accurate strains using the grids with accurate nodal coordinates. The accurate nodal coordinates are calculated by adding the nodal coordinates measured by the measurement system and the position error found using the multiple regression method as a function of the main error parameters obtained from the analysis of strain error in a standard cube. For the verification, the strain distributions of square and dome cups obtained from the position error calibration method are compared with those provided by the finite element analysis and ASAME.

• Bulletin of the Korean Space Science Society
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• 1995.04a
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• pp.39-39
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• 1995

No Abstract. See Full-text