• Title/Summary/Keyword: Gaussian Distribution

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Analysis of Sodium Spray Fire Using Gaussian Droplet Size Distribution (Gaussian 액적 크기 분포 함수를 이용한 분무형 화재 현상 해석)

  • Kim, B.H.;Hahn, D.H.;Suh, S.H.
    • Transactions of the Korean hydrogen and new energy society
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    • v.15 no.1
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    • pp.72-81
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    • 2004
  • Study on the analysis of sodium spray fire using Gaussian drop size distribution, which redistributes a droplet spectrum with given mean diameter if its size classes with critical diameter(D>8mm) occur, was carried out. In this case, the oversized droplets were reduced to a stable diameter. Results calculated by the code using Gaussian drop size distribution were in better agreement with AI experimental results than those of NACOM and SPRAY code. The effect of variance on pressure in the test cell appeared greatly by introducing Gaussian function, which could represent various sodium droplet size distribution. The increase of the variance with mean droplet size resulted had an important effect upon the pressure in the test cell.

Non-Gaussian feature of fluctuating wind pressures on rectangular high-rise buildings with different side ratios

  • Jia-hui Yuan;Shui-fu Chen;Yi Liu
    • Wind and Structures
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    • v.37 no.3
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    • pp.211-227
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    • 2023
  • To investigate the non-Gaussian feature of fluctuating wind pressures on rectangular high-rise buildings, wind tunnel tests were conducted on scale models with side ratios ranging from 1/9~9 in an open exposure for various wind directions. The high-order statistical moments, time histories, probability density distributions, and peak factors of pressure fluctuations are analyzed. The mixed normal-Weibull distribution, Gumbel-Weibull distribution, and lognormal-Weibull distribution are adopted to fit the probability density distribution of different non-Gaussian wind pressures. Zones of Gaussian and non-Gaussian are classified for rectangular buildings with various side ratios. The results indicate that on the side wall, the non-Gaussian wind pressures are related to the distance from the leading edge. Apart from the non-Gaussianity in the separated flow regions noted by some literature, wind pressures behind the area where reattachment happens present non-Gaussian nature as well. There is a new probability density distribution type of non-Gaussian wind pressure which has both long positive and negative tail found behind the reattachment regions. The correlation coefficient of wind pressures is proved to reflect the non-Gaussianity and a new method to estimate the mean reattachment length of rectangular high-rise building side wall is proposed by evaluating the correlation coefficient. For rectangular high-rise buildings, the mean reattachment length calculated by the correlation coefficient method along the height changes in a parabolic shape. Distributions of Gaussian and non-Gaussian wind pressures vary with side ratios. It is inappropriate to estimate the extreme loads of wind pressures using a fixed peak factor. The trend of the peak factor with side ratios on different walls is given.

Determination of Degraded Fiber Properties of Laminated CFRP Flat Plates Using the Bivariate Gaussian Distribution Function (이변량 Gaussian 분포함수를 적용한 CFRP 적층 평판의 보강섬유 물성저하 규명)

  • Kim, Gyu-Dong;Lee, Sang-Youl
    • Composites Research
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    • v.29 no.5
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    • pp.299-305
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    • 2016
  • This paper presents a method to detect the fiber property variation of laminated CFRP plates using the bivariate Gaussian distribution function. Five unknown parameters are considered to determine the fiber damage distribution, which is a modified form of the bivariate Gaussian distribution function. To solve the inverse problem using the combined computational method, this study uses several natural frequencies and mode shapes in a structure as the measured data. The numerical examples show that the proposed technique is a feasible and practical method which can prove the location of a damaged region as well as inspect the distribution of deteriorated stiffness of CFRP plates for different fiber angles and layup sequences.

OPTIMAL APPROXIMATION BY ONE GAUSSIAN FUNCTION TO PROBABILITY DENSITY FUNCTIONS

  • Gwang Il Kim;Seung Yeon Cho;Doobae Jun
    • East Asian mathematical journal
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    • v.39 no.5
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    • pp.537-547
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    • 2023
  • In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

Simulated Annealing Algorithm Using Cauchy-Gaussian Probability Distributions (Cauchy와 Gaussian 확률 분포를 이용한 Simulated Annealing 알고리즘)

  • Lee, Dong-Ju;Lee, Chang-Yong
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.33 no.3
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    • pp.130-136
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    • 2010
  • In this study, we propose a new method for generating candidate solutions based on both the Cauchy and the Gaussian probability distributions in order to use the merit of the solutions generated by these distributions. The Cauchy probability distribution has larger probability in the tail region than the Gaussian distribution. Thus, the Cauchy distribution can yield higher probabilities of generating candidate solutions of large-varied variables, which in turn has an advantage of searching wider area of variable space. On the contrary, the Gaussian distribution can yield higher probabilities of generating candidate solutions of small-varied variables, which in turn has an advantage of searching deeply smaller area of variable space. In order to compare and analyze the performance of the proposed method against the conventional method, we carried out experiments using benchmarking problems of real valued functions. From the result of the experiment, we found that the proposed method based on the Cauchy and the Gaussian distributions outperformed the conventional one for most of benchmarking problems, and verified its superiority by the statistical hypothesis test.

Vessel traffic geometric probability approaches with AIS data in active shipping lane for subsea pipeline quantitative risk assessment against third-party impact

  • Tanujaya, Vincent Alvin;Tawekal, Ricky Lukman;Ilman, Eko Charnius
    • Ocean Systems Engineering
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    • v.12 no.3
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    • pp.267-284
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    • 2022
  • A subsea pipeline designed across active shipping lane prones to failure against external interferences such as anchorage activities, hence risk assessment is essential. It requires quantifying the geometric probability derived from ship traffic distribution based on Automatic Identification System (AIS) data. The actual probability density function from historical vessel traffic data is ideal, as for rapid assessment, conceptual study, when the AIS data is scarce or when the local vessels traffic are not utilised with AIS. Recommended practices suggest the probability distribution is assumed as a single peak Gaussian. This study compares several fitted Gaussian distributions and Monte Carlo simulation based on actual ship traffic data in main ship direction in an active shipping lane across a subsea pipeline. The results shows that a Gaussian distribution with five peaks is required to represent the ship traffic data, providing an error of 0.23%, while a single peak Gaussian distribution and the Monte Carlo simulation with one hundred million realisation provide an error of 1.32% and 0.79% respectively. Thus, it can be concluded that the multi-peak Gaussian distribution can represent the actual ship traffic distribution in the main direction, but it is less representative for ship traffic distribution in other direction. The geometric probability is utilised in a quantitative risk assessment (QRA) for subsea pipeline against vessel anchor dropping and dragging and vessel sinking.

Shrinkage Estimator of Dispersion of an Inverse Gaussian Distribution

  • Lee, In-Suk;Park, Young-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.3
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    • pp.805-809
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    • 2006
  • In this paper a shrinkage estimator for the measure of dispersion of the inverse Gaussian distribution with known mean is proposed. Also we compare the relative bias and relative efficiency of the proposed estimator with respect to minimum variance unbiased estimator.

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A Gaussian Beam Light Distribution Model of the Biological Tissue (생체의 가우스빔 광분포모델)

  • 조진호;하영호;이건일
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.25 no.6
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    • pp.654-662
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    • 1988
  • A simple and useful model of light distribution for the biologhical tissue to the Gaussian beam is proposed. This model assumes that the incident Gaussian beam broadens into two Gaussian beams, travelling in the opposite directions as the result of both isotropic scattering and absorption in the tissue. With this assumption, two-dimensional light intensity of each flux as well as the equations of both absorption and scattering have been derived, and the validity of modeling has been confirmed experimentally. Consequently, the results paved a way for easy evaluation of the light distribution in the biological tissue.

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