• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.589-601
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• 1996

Geometric approach to extend the classical two-set theory of canonical correlation analysis to three or more sets is considered. It provides statistical graphs to represent the data in a low dimensional space. Procedures are developed for computing the canonical variables and the corresponding properties are investigated. The solution is equivalent to that of the usual problem in the case of two sets. Goodness-of-fit of the proposed plots is studied and a numerical example is included.

• Fibers and Polymers
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• v.7 no.1
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• pp.57-61
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• 2006

A study has been made on the quantification and evaluation of fabric pilling using two-dimensional and three-dimensional hybrid imaging methods. Two-dimensional imaging method was good for some samples while three-dimensional measurement method for others, according to the properties of their base fabric. Various image processing techniques as well as three-dimensional data processing algorithms were applied for the extraction of pills from measured data and a series of shape parameters have been defined for the objective evaluation of fabric pilling. An evaluation criterion that is compatible with the conventional evaluation method has been proposed by applying the new evaluation method to the current photographic standards.

• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.3
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• pp.1-8
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• 2001

The flow field inside a cylinder of four-valve Sl engine was investigated quantitatively using a three-dimensional Laser Doppler Velocimetry system, to determine how stroke changes affect the flow field. The purpose of this work was to develop quantitative methods which correlate in-cylinder flows to engine performance. For this study, the sane intake manifold, engine head, cylinder, and the piston were used to examine the flow characteristics in different strokes. Quantification of the flow field was done by calculating three major parameters which are believed to adequately characterize in cylinder motion. These quantities were TKE, tumble and swirl ratios. The LDV results reveal that flow patterns are similar, the flow velocities scale with piston speed but another parameters such as TKE, and tumble and swirl numbers are not the same for different stroke systems.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.1-13
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• 2005

Fluid flows within microchannels are characterized by low Reynolds numbers. Therefore the effect of mixing is a crucial factor in design of the channels. Since the action of the electro-osmotic or magnetic forces used in the mixing enhancement is usually periodic in the three-dimensional channel configuration, use of the various concepts of chaotic advection is reasonable in the quantification of the stirring effect. In this paper, the details of the method of material-stretching mapping is explained. The actual application of the method to the screw extruder is also presented.

• Maxillofacial Plastic and Reconstructive Surgery
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• v.42
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• pp.17.1-17.11
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• 2020

Background: To evaluate the facial asymmetry, three-dimensional computed tomography (3D-CT) has been used widely. This study proposed a method to quantify facial asymmetry based on 3D-CT. Methods: The normal standard group consisted of twenty-five male subjects who had a balanced face and normal occlusion. Five anatomical landmarks were selected as reference points and ten anatomical landmarks were selected as measurement points to evaluate facial asymmetry. The formula of facial asymmetry index was designed by using the distances between the landmarks. The index value on a specific landmark indicated zero when the landmarks were located on the three-dimensional symmetric position. As the asymmetry of landmarks increased, the value of facial asymmetry index increased. For ten anatomical landmarks, the mean value of facial asymmetry index on each landmark was obtained in the normal standard group. Facial asymmetry index was applied to the patients who had undergone orthognathic surgery. Preoperative facial asymmetry and postoperative improvement were evaluated. Results: The reference facial asymmetry index on each landmark in the normal standard group was from 1.77 to 3.38. A polygonal chart was drawn to visualize the degree of asymmetry. In three patients who had undergone orthognathic surgery, it was checked that the method of facial asymmetry index showed the preoperative facial asymmetry and the postoperative improvement well. Conclusions: The current new facial asymmetry index could efficiently quantify the degree of facial asymmetry from 3D-CT. This method could be used as an evaluation standard for facial asymmetry analysis.

• Tunnel and Underground Space
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• v.22 no.2
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• pp.106-119
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• 2012

Roughness of rock joint has generally been characterized based upon geometrical aspects of a two-dimensional surface profile. The appropriate description of joint roughness, however, should consider the features of roughness mobilization at contact areas under normal and shear loads. In this study, direct shear tests were conducted on the replicas of tensile fractured gneiss joints and the influence of the shear direction on the shear behavior and effective roughness was examined. In this procedure, a joint surface was represented as a group of triangular planes, and the steepness of each plane was characterized using the concepts of the active and inactive micro-slope angles. The contact areas at peak strength which were estimated by a numerical method showed that the locations of the contact areas were mainly dependent on the distribution of the micro-slope angle and the shear behavior of joint was dominated by only the fractions with active micro-slope angles. Therefore, a three-dimensional coefficient for the quantification of rock joint roughness is proposed based on the distribution of active micro-slope angle: active roughness coefficient, $C_r$. Comparison of the active roughness coefficient and the peak shear strength obtained from the experiment suggests that the active roughness coefficient is the effective parameter to quantify the surface roughness and estimate the shear behavior of rock joint.

• Tunnel and Underground Space
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• v.13 no.4
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• pp.245-259
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• 2003

Refering to the articles "Squeezing rocks in tunnels(Barla, 1995)" and "Tunnelling under squeezing rock conditions(Barla 2002)" this article deals with technologies for design, stability analysis and construction of the tunnel being driven in the squeezing rock mass. The definition of this type of behavior was proposed by ISRM(1994). The identification and quantification of squeezing is given according to both the empirical and semi-empirical methods available to anticipate the potential of squeezing problems in tunnelling. Based on the experiences and lessons learned in recent years, the state of the art in modem construction methods was reported, when dealing with squeezing rock masses by either conventional or mechanical excavation methods. The closed-form solutions available for the analysis of the rock mass response during tunnel excavation are described in terms of the ground characteristic line and with reference to some elasto-plastic models for the given rock mass. Finally numerical methods were used for the simulation of different models and for design analysis of complex excavation and support systems, including three-dimensional conditions in order to quantify the influence of the advancing tunnel face to the deformation behavior of the tunnel.

• Journal of computational fluids engineering
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• v.9 no.4
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• pp.55-63
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• 2004

The three-dimensional Stokes flow within a staggered screw channel is obtained by using a finite volume method. The geometry is intended to mimic the single screw extruder having staggered arrangement of flights. The flow solution is then subjected to the analysis of the stirring performance. In the analysis of the stirring performance, the stretching-mapping method developed by the author is employed for calculating the materials' stretching exponents, which are to be used in quantification of the mixing effect. The numerical results Indicate that the staggered geometry gives indeed far much better stirring-performance than the standard (nonstaggered) flight geometry. It was also shown that care must be given to the selection of the basis planes for evaluating the local stretching rate, and it turns out that the best method (H-method) has its basis plane just on the half way between the past and future evolution of fluid particles subjected to the defromation. In evaluating the stretching exponent, the expansion ratio must be considered which is one of the characteristic differences of the actual three-dimensional flows from the two-dimensionmal counterparts. The larger axial pressure-difference causes in general the smaller stirring performance while the flow rate is increased. The smaller channel length also increases the stirring performance.

• Smart Structures and Systems
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• v.29 no.2
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• pp.321-336
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• 2022

Model uncertainty is a key factor that could influence the accuracy and reliability of numerical model-based analysis. It is necessary to acquire an appropriate updating approach which could search and determine the realistic model parameter values from measurements. In this paper, the Bayesian model updating theory combined with the transitional Markov chain Monte Carlo (TMCMC) method and K-means cluster analysis is utilized in the updating of the structural model parameters. Kriging and polynomial chaos expansion (PCE) are employed to generate surrogate models to reduce the computational burden in TMCMC. The selected updating approaches are applied to three structural examples with different complexity, including a two-storey frame, a ten-storey frame, and the national stadium model. These models stand for the low-dimensional linear model, the high-dimensional linear model, and the nonlinear model, respectively. The performances of updating in these three models are assessed in terms of the prediction uncertainty, numerical efforts, and prior information. This study also investigates the updating scenarios using the analytical approach and surrogate models. The uncertainty quantification in the Bayesian approach is further discussed to verify the validity and accuracy of the surrogate models. Finally, the advantages and limitations of the surrogate model-based updating approaches are discussed for different structural complexity. The possibility of utilizing the boosting algorithm as an ensemble learning method for improving the surrogate models is also presented.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.8
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• pp.126-131
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• 2009

Acetabular dysplasia is a condition defined by inadequate development of an individual's acetabulum. Individual diversity of the symptoms in this disease needs safe and accurate preoperative planning. Technologies that utilize multidimensional image information are thus important. The assessment method by Janzen et al. was suggested a coefficient method in evaluation of acetabular dysplasia. In this study, we applied it, using a three-dimensional computed tomography (3D CT) on the koreans. 19 cases of the normal hips and 4 cases of the acetabular dysplasia were investigated to evaluate the proved method; 3D CT was used to define the geometric center of the femoral head and to measure center edge angles at $10^{\circ}$ rotational increments around the acetabular rim. Mean and standard deviation in CEAs (Center Edge Angle) of normal 19 hips at $10^{\circ}$ rotational increments from anterior to posterior rim were determined, and termed as a 'normal curve'. Then this normal values were compared with the CEA data measured from 4 cases of acetabular dysplasia patiens. Quantative comparison of the CEA values between the normal cases and dysplasia cases was successfully demonstrated, and thus, we claim that this simple CT method of assessing acetabular dysplasia can be well applicable to diagnosis, quantification and surgical planning for adult acetabular dysplasia patients.