• Structural Engineering and Mechanics
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• v.34 no.6
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• pp.779-799
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• 2010

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.

• Journal of Soil and Groundwater Environment
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• v.24 no.5
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• pp.11-16
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• 2019

In this study, a reliable number of soil samples for TPH fractionation was investigated in order to perform risk assessment. TPH was fractionated into volatile petroleum hydrocarbons (VPH) with three subgroups and extractable petroleum hydrocarbons (EPH) with four subgroups. At the study site, concentrations of each fraction were determined at 18 sampling points, and the 95% upper confidence limit (UCL) value was used as an exposure concentration of each fraction. And then, 5 sampling points were randomly selected out of the 18 points, and an exposure concentration was calculated. This process was repeated 30 times, and the results were compared statistically. Exposure concentrations of EPH obtained from 18 points were 99.9, 339.1, 27.3, and 85.9 mg/kg for aliphatic $C_9-C_{18}$, $C_{19}-C_{36}$, $C_{37}-C_{40}$, and aromatic $C_{11}-C_{22}$, respectively. The corresponding exposure concentrations obtained from 5 points were 139.8, 462.8, 35.1 and 119.4 mg/kg, which were significantly higher than those from 18 points results (p <0.05). Our results suggest that limited number of samples for TPH fractionation may bias estimation of exposure concentration of TPH fractions. Also, it is recommended that more than 30 samples need to be analyzed for TPH fractionation in performing risk assessment.

• The Journal of Engineering Geology
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• v.33 no.2
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• pp.229-240
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• 2023

Instruments are installed in soft ground improvement projects to manage economic and safe construction. When analyzing data, the amount of settlement data over time can be used to understand the overall ground settlement behavior, but it is difficult to analyze the interrelatedness between measurement points. Therefore, to analyze the relative compressive settlement behavior between measurement points, the settlement amount and velocity were processed and defined as the mean settlement difference index (AS_i,j) and the slope difference index (SDI_i,j). Plotted in the mean settlement difference index - slope difference index (AS_i,j-SDI_i,j) coordinate system. As a result of the analysis of the relative compaction subsidence behavior between the measuring points, the relationship between the measuring points in the average subsidence difference index - slope difference index coordinate system moved to area 1 as the compaction was completed. By continuously plotting the movement path of the observation point in the corresponding coordinate system, the relative settlement behavior between the measurement points was analyzed, and it was possible to check whether the settlement behavior of the two measurement points was stable or unstable depending on the direction of the path.

• Journal of the Korea Society of Computer and Information
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• v.17 no.6
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• pp.37-48
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• 2012

Image registration is a process to establish the spatial correspondence between the images of same scene, which are acquired at different view points, at different times, or by different sensors. In this paper, we propose an effective registration method for images acquired by multi-sensors, such as EO (electro-optic) and IR (infrared) sensors. Image registration is achieved by extracting features and finding the correspondence between features in each input images. In the recent research, the multi-sensor image registration method that finds corresponding features by exploiting NMI (Normalized Mutual Information) was proposed. Conventional NMI-based image registration methods assume that the statistical correlation between two images should be global, however images from EO and IR sensors often cannot satisfy this assumption. Therefore the registration performance of conventional method may not be sufficient for some practical applications because of the low accuracy of corresponding feature points. The proposed method improves the accuracy of corresponding feature points by combining the gradient orientation as spatial information along with NMI attributes and provides more accurate and robust registration performance. Representative experimental results prove the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.752-757
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• 2003

Recently, 3D structure recovery through self-calibration of camera has been actively researched. Traditional calibration algorithm requires known 3D coordinates of the control points while self-calibration only requires the corresponding points of images, thus it has more flexibility in real application. In general, self-calibration algorithm results in the nonlinear optimization problem using constraints from the intrinsic parameters of the camera. Thus, it requires initial value for the nonlinear minimization. Traditional approaches get the initial values assuming they have the same intrinsic parameters while they are dealing with the situation where the intrinsic parameters of the camera may change. In this paper, we propose new initialization method using the minimum 2 images. Proposed method is based on the assumption that the least violation of the camera’s intrinsic parameter gives more stable initial value. Synthetic and real experiment shows this result.

• East Asian mathematical journal
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• v.27 no.1
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• pp.35-49
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• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.4.2-4
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• 2003

In this paper, we describe how to approximate the solutions of partial differential equations by bicubic spline functions whose interpolation errors at non-grid points are smaller in general than those by linear interpolations of the original solution at grid points. We show that the bicubic spline function can be represented exactly or approximately by a fuzzy system, and that the resulting fuzzy rule table shows the contours of the solution function. Thus, the fuzzy rule table is identified as a digital image and the contours in the rule table provide approximate contours of the solution of partial differential equations. Several illustrative examples are included.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.59-68
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• 2009

In this paper we present an iterative scheme for finding a common element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscosity approximation methods and under suitable conditions, some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.669-684
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• 1999

We are interested in the problem of fitting a curve to a set of points in the plane in such a way that the sum of the squares of the orthogonal distances to given data points ins minimized. In[1] the prob-lem of fitting circles and ellipses was considered and numerically solved with general purpose methods. Especially in [2] H. Spath proposed a special purpose algorithm (Spath's ODF) for parabolas y-b=$c($\chi$-a)^2$ and for rotated ones. In this paper we present another parabola fitting algorithm which is slightly different from Spath's ODF. Our algorithm is mainly based on the steepest descent provedure with the view of en-suring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.661-670
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• 2005

In this paper, we deal with approximations of com­mon fixed points of the iterative sequences with errors for three asymptotically nonexpansive mappings in a uniformly convex Banach space. Our results generalize and improve the corresponding results of Khan and Takahashi, Schu, Takahashi and Tamura, and others.