• 대한기계학회논문집
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• 제18권4호
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• pp.1039-1049
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• 1994

The intermitternt and transient fuel spray have been investigated from the simultaneous measurement of droplet sizes and velocities by using Phase/Doppler Particle Analyzer(PDPA). Measurement have been done on the spray axis and at the edge of the spray near nozzle at various gas-to-liquid density ratios(.rho./sub g//.rho./sub l/) that ranges from those found in free atmospheric jets to conditions typical of diesel engines. Probability density distributions of the droplet size and velocity were obtained from raw data and mathematical probability density functions which can fit the experimental distribations were extracted using the principle of maximum likelihood. In the near nozzle region on the spray axis, droplet sizes ranged from the lower limit of the measurement system to the order of nozzle diameter for all (.rho./sub g/ /.rho./sub l/) and droplet sizes tended to be small on the spray edge. At the edge of spray, average droplet velocity peaked during needle opening and needle closing. The rms intensity is greatly incresed as the radial distance from the nozzle is increased. The probability density function which can best fit the physical breakage process such as breakup of fuel drops is exponecially decreasing log-hypebolic function with 4 parameters.

• Ocean Systems Engineering
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• 제12권3호
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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.

• 풍력에너지저널
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• 제14권1호
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• pp.37-43
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• 2023

In this study, synthetic time series wind data was generated numerically using a second-order Markov chain. One year of wind data in 2020 measured by the AWS on Wido Island was used to investigate the statistics for measured wind data. Both the transition probability matrix and the cumulative transition probability matrix for annual hourly mean wind speed were obtained through statistical analysis. Probability density distribution along the wind speed and autocorrelation according to time were compared with the first- and the second-order Markov chains with various lengths of time series wind data. Probability density distributions for measured wind data and synthetic wind data using the first- and the second-order Markov chains were also compared to each other. For the case of the second-order Markov chain, some improvement of the autocorrelation was verified. It turns out that the autocorrelation converges to zero according to increasing the wind speed when the data size is sufficiently large. The generation of artificial wind data is expected to be useful as input data for virtual digital twin wind turbines.

• 한국습지학회지
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• 제2권1호
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• pp.49-58
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• 2000

The frequency analysis of annual maximum rainfall data and the derivation of probable rainfall intensity formula at Masan station are performed in this study. Based on the eight different rainfall duration data from 10 minutes to 24 hours, eight types of probability distribution (Gamma, Lognormal, Log-Pearson type III, GEV, Gumbel, Log-Gumbel, Weibull, and Wakeby distributions), three types of parameter estimation scheme (moment, maximum likelihood and probability weighted methods) and three types of goodness-of-fit test (${\chi}^2$, Kolmogorov-Smirnov and Cramer von Mises tests) were considered to find an appropriate probability distribution at Masan station. The Lognormal-2 distribution was selected and the probable rainfall intensity formula was derived by regression analysis. The derived formula can be used for estimating rainfall quantiles of the Masan vicinity areas with convenience and reliability in practice.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.23-45
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• 2015

We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.

• Journal of the Optical Society of Korea
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• 제15권4호
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• pp.407-414
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• 2011

We analyze the cooperative spontaneous emission of optically excited nanocrystals into surface plasmon polaritons propagating on the surface of a cylindrical metallic nanowire. The spontaneous emission probability of the nanocrystals is obtained by perturbative expansions with and without dipole-dipole interaction among nanocrystals in order to see the cooperative effects. The spontaneous emission probability depends on the radial and axial distributions, as well as on the dipolar orientation of nanocrystals. It is shown that the spontaneous emission probability is strongly influenced by dipole-dipole interaction, axial distribution, and dipolar orientation of nanocrystals for closely spaced nanocrystals.

• 한국농공학회:학술대회논문집
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• 한국농공학회 2003년도 학술발표논문집
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• pp.511-514
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• 2003

This study was conducted to estimate the design rainfall by the determination of best fitting order for Higher Probability Weighted Moments of the annual maximum series according to consecutive duration at sixty-five rainfall stations in Korea. Design rainfalls were obtained by generalized extreme value distribution which was selected to be suitable distribution in 4 applied distributions and by L, L1, L2, L3 and L4-moment. The best fitting order for Higher Probability Weighted Moments was determined with the confidence analysis of estimated design rainfall.

• 대한수학회논문집
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• 제14권2호
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• pp.405-423
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• 1999

We consider a statistical multiplexer model with finite buffer capacity and finite number of independent identical 3-state bursty voice sources. The burstiness of the sources is modeled by describing both two different active periods (at the rate of one packet perslot) and the passive periods during which no packets are generated. Assuming a mixture of two geometric distributions for active period and a geometric distribution for passive period and geometric distribution for passive period, we derive the recursive algorithm for the probability mass function of the buffer contents (in packets). We also obtain loss probability and the distribution of packet delay. Numerical results show that the system performance deteriorates considerably as the variance of the active period increases. Also, we see that the loss probability of 2-state Markov models is less than that of 3-state Markov models.

• 한국국방경영분석학회지
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• 제22권1호
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• pp.97-113
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• 1996

Mission effectiveness may be defined as a probability that a system can successfully meet an intended mission demand within a given time when operated under specified conditions. This study deals with the Mission effectiveness of a replenishment ships that is performing several types of missions. The essential attributes and their related factors affecting the replenishment missions are established, and then, a mathematical mission effectiveness model is constructed with a replenishment mission characteristics for a basis. Mission effectiveness for a mission is determined by finding the joint probability measure of the following three attributes : operational readiness of the replenishment ships at the start of a mission ; mission reliability of the replenishment ships ; capability of successfully accomplishing intended objectives given an environmental condition. The model is solved analytically. Operational readiness of the replenishment ships in found by the assumed data. Mission reliability and capability are calculated based on the assumed probability distributions. The model would be a useful tool to evaluate mission effectiveness as it is very a replenishment ships.

• Journal of the Korean Data and Information Science Society
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• 제15권3호
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• pp.523-529
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• 2004

In Korea, mathematics education has been changed according to the 7th national mathematics curriculum renovated by the Ministry of Education and Human Resources Development announcement in 1997. The education of probability and Statistics has been carried out as a part of this curriculum. We analyze and compare 3 kinds of mathematics textbooks for 10-12 grade students. Descriptions of random variable, sample variance and sample standard deviation, distribution of sample mean, and etc. which are on some textbooks, are misleaded in school education. We suggest the unbiased estimator of sample variance in textbooks and distributions of sample means with normal population assumption.