Markov envelope as a theoretical solution of the parabolic wave equation with Markov approximation for the von Kármán type random medium is studied and approximated with the convolution of two probability density functions (pdf) of normal and gamma distributions considering the previous studies on the applications of Radiative Transfer Theory (RTT) and the analysis results of earthquake records. Through the approximation with gamma pdf, the constant shape parameter of 2 was determined regardless of the source distance ro. This finding means that the scattering process has the property of an inhomogeneous single-scattering Poisson process, unlike the previous studies, which resulted in a homogeneous multiple-scattering Poisson process. Approximated Markov envelope can be treated as the normalized mean square (MS) envelope for ground acceleration because of the flat source Fourier spectrum. Based on such characteristics, the path duration is estimated from the approximated MS envelope and compared to the empirical formula derived by Boore and Thompson. The results clearly show that the path duration increases proportionately to ro 1/2-ro 2, and the peak value of the RMS envelope is attenuated by exp (-0.0033ro), excluding the geometrical attenuation. The attenuation slope for ro≤100 km is quite similar to that of effective attenuation for shallow crustal earthquakes, and it may be difficult to distinguish the contribution of intrinsic attenuation from effective attenuation. Slowly varying dispersive delay, also called the medium effect, represented by regular pdf, governs the path duration for the source distance shorter than 100 km. Moreover, the diffraction term, also called the distance effect because of scattering, fully controls the path duration beyond the source distance of 300 km and has a steep gradient compared to the medium effect. Source distance 100-300 km is a transition range of the path duration governing effect from random medium to distance. This means that the scattering may not be the prime cause of peak attenuation and envelope broadening for the source distance of less than 200 km. Furthermore, it is also shown that normal distribution is appropriate for the probability distribution of phase difference, as asserted in the previous studies.

본 연구는 국내 냉동보관창고 보관온도에 대한 조사자료를 활용하여, 온도분포를 추정하였고 이를 미생물 위해 평가(microbial risk assessment; MRA)의 입력변수로 활용 할 수 있도록 적정 확률분포 모델을 제시하였다. 조사에 참여한 8곳의 냉동보관창고에서 측정된 공간상의 온도는 최저 -25.8oC, 최고 -10.3oC, 평균 -20.48 ± 3.08oC이었으며, - 18oC이상의 냉동창고 비율은 20.4%로 조사되었다. 공간별 온도분포는 자연대류를 이용하는 냉동창고의 경우 상단 (2.4~4 m) -22.57 ± 0.84oC, 중단(1.5~2.4 m) -22.49 ± 1.05oC, 하단(0.7~1.5 m) -22.68 ± 1.03oC, 최고온도차이는 1.78oC이 었으며, 강제대류를 이용하는 냉동창고의 온도분포는 상단 (2.4~4 m) -17.81 ± 1.47oC, 중단(1.5~2.4 m) -17.94 ± 1.44oC, 하단(0.7~1.5 m) -18.08 ± 1.42oC, 최고온도차이는 0.94oC로 조사되었다. 보관온도는 냉동창고 모든 공간에서 온도가 일정하게 유지되는 것이 아니라 편차가 존재하는 것으로 나타났다. 이상의 수집된 온도자료는 @RISK를 이용, 적합성 검정(GOF: A-D, K-S test)을 수행하여, MRA에서 활용할 수 있는 국내 냉동보관창고 온도분포에 대한 가장 적합한 확률분포모델로 Lognormal [5.9731,3.3483, shift(-26.4281)] 이 선정하였다.

이 연구에서는 입력변수의 확률분포로부터 비선형 구조응답의 확률분포 추정방법을 제안한다. 응답함수를 확률변수들의 평균점과 응답의 꼬리부분 상위 0.01%값에 기여하는 확률변수조합에서 각각 1차 테일러급수로 근사한다. 두 응답함수에 대해 모멘트법을 적용한 후 이를 가우시안 분포로 추정한다. 추정된 두 분포를 결합하기 위해 연결함수를 도입하고, 분포의 연속조건을 적용하여 연결함수의 미정계수를 결정한다. 제안된 방법을 케이블 교량 예제에 적용하고, 카이제곱 검증을 이용하여 추정된 분포의 적합성을 확인한다. 기존의 모멘트법과 제안된 방법의 결과를 비교, 분석한다.

Analysis of water quality distribution is very important for river water quality management. Recently, various studies have been conducted on the analysis of water quality distribution according to reduction methods of nonpoint pollutant. The objective of this study was to select the probability distributions of water quality constituents (T-N, T-P, COD, SS) according to the farming forms (control, slow release fertilizer, water depth control) during non-storm period in the paddy fields. The field monitoring was conducted monitoring site located in Baeksan-myun, Buan-gun, Jeollabuk-do, Korea during non-storm period from May to September in 2016. Our results showed that there were no differences in water quality among three different farming forms, except for SS of control and water depth control. K-S method was used to analyzed the probability distributions of T-N, T-P, COD and SS concentrations discharged from paddy fields. As a results of the fitness analysis, T-N was not suitable for the normal probability distribution in the slow release fertilizer treatment, and the log-normal probability distribution was not suitable for the T-P in control treatment. The gamma probability distribution showed that T-N and T-P in control and slow release fertilizer treatment were not suitable. The Weibull probability distribution was found to be suitable for all water quality constituents of control, slow release fertilizer, and water depth control treatments. However, our results presented some differences from previous studies. Therefore, it is necessary to analyze the characteristics of pollutants flowing out in difference periods according to various farming types. The result of this study can help to understand the water quality characteristics of the river.

In engineering problems, many random variables have correlation, and the correlation of input random variables has a great influence on reliability analysis results of the mechanical systems. However, correlated variables are often treated as independent variables or modeled by specific parametric joint distributions due to difficulty in modeling joint distributions. Especially, when there are insufficient correlated data, it becomes more difficult to correctly model the joint distribution. In this study, multivariate kernel density estimation with bounded data is proposed to estimate various types of joint distributions with highly nonlinearity. Since it combines given data with bounded data, which are generated from confidence intervals of uniform distribution parameters for given data, it is less sensitive to data quality and number of data. Thus, it yields conservative statistical modeling and reliability analysis results, and its performance is verified through statistical simulation and engineering examples.

There always exist nonzero inspection errors whether inspectors are humans or automatic inspection machines. Inspection errors can be categorized by two types, type I error and type II error, and they can be regarded as either a constant or a random variable. Under the assumption that two types of random inspection errors are distributed with the “uniform” distribution on a half-open interval starting from zero, it was proved that inspectors overestimate any given fraction defective with the probability more than 50%, if and only if the given fraction defective is smaller than a critical value, which depends upon only the ratio of a type II error over a type I error. In addition, it was also proved that the probability of overestimation approaches one hundred percent as a given fraction defective approaches zero. If these critical phenomena hold true for any error distribution, then it might have great economic impact on commercial inspection plans due to the unfair overestimation and the recent trend of decreasing fraction defectives in industry. In this paper, we deal with the same overestimation problem, but assume a “symmetrical triangular” distribution expecting better results since our triangular distribution is closer to a normal distribution than the uniform distribution. It turns out that the overestimation phenomenon still holds true even for the triangular error distribution.

백두산 분화의 전조현상 및 일본 화산의 지속적인 활동으로 인하여 화산재 확산으로 인하여 발생할 수 있는 재난에 대한 위협이 지속적으로 제기되고 있다. 이에 대한 대응을 위하여 국내에서도 화산재해대응시스템을 개발하여 활용하고 있는 실정이며 이에 대응하기 위한 연구의 일환으로 화산재 확산에 대한 확률적 공간 분포 분석이 연구된 바가 있다. 본 논문의 part1이라 할 수 있는 ‘백두산과 아소산 화산재 대기 확산의 확률적 공간 분포 분석’에서는 백두산과 아소산 두 개의 화산에 대하여 FALL3D 수치해석을 수행 하고 그 결과를 이용하여 대기 중 화산재 농도 및 퇴적 두께에 대한 분석을 수행한 바 있다. 본 논문에서는 백두산과 아소산 외에도 국내에 영향을 미칠 수 있는 총 5개의 화산에 대하여 해석기간 및 분석 범위를 확장하여 추가 연구를 진행하였다.

최근 백두산 화산분화의 전조현상 증가로 인해 백두산 분화의 가능성이 지속적으로 제기되고 있으며 주변국인 일본의 화산 활동 또한 활발한 추세이다. 일본 화산 및 백두산으로부터 500km 이상의 거리에 위치한 우리나라의 경우 화산 분화로부터 근접 재해의 직접적인 위험은 없으나 화산재 확산에 의한 영향을 받을 가능성이 있어 이에 대한 대책 및 대응 방안 마련이 요구되고 있는 실정 이며 이에 대한 대응 방안 중 하나로, 화산재 확산 모델을 이용하여 화산재 입자의 공간분포 예측 및 대기 중 화산재 농도와 지표면의 화산재 퇴적 두께를 예측하는 방법이 있다. 본 연구에서는 화산재 확산 예측 모형에 의해 도출된 대기 중의 화산재 농도와 낙하 화산재 퇴적 두께를 이용하여 한반도 근역에 대하여 화산재 공간 확산 확률 및 낙하 확률 분석 기법을 제시하고 우리나라 17개 광역지자체에 대한 분석을 수행하였다.

This study aimed to estimate the odor emission rate from swine nursery facilities (naturally and mechanically ventilated) using probability distribution. Odor occurrence trends in the study facilities were very different; odor concentration and gas flow had a lognormal distribution. Monte Carlo simulation was used to carry out the uncertainty analysis. Odor emission rate was found to range from 18.05 OU/sec (10th percentile) to 621.88 OU/ sec (90th percentile), and odor emission rate per head ranged from 0.02 OU/sec · head (10th percentile) to 0.64 OU/ sec · head (90th percentile).

It was confirmed that the extreme value distribution model applies to probability of exceeding more than once a day monthly the facility capacities using data of daily maximum inflow rate for 7 wastewater treatment plant. The result of applying the extreme value model, A, D, E wastewater treatment plant has a problem compared to B, C, F, G wastewater treatment plant. but all the wastewater treatment plant has a problem except C, F wastewater treatment plant based 80% of facility capacity. In conclusion, if you make a standard in statistical aspects probability exceeding more than once a day monthly can be ‘exceed day is less than a few times annually’ or ‘probability of exceeding more than once a day monthly is less than what percent’.

This study was to present the proper probability distribution models that based on the data for surveys of food cold storage temperatures as the input variables to the further MRA (Microbial risk assessment). The temperature was measured by directly visiting 7 food plants. The overall mean temperature for food cold storages in the survey was 2.55 ± 3.55oC, with 2.5% of above 10oC, −3.2oC and 14.9oC as a minimum and maximum. Temperature distributions by space-locations was 0.80 ± 1.69oC, 0.59 ± 1.68oC, and 0.65 ± 1.46oC as an upper (2.4~4 m), middle (1.5~2.4 m), and lower (0.7~1.5 m), respectively. Probability distributions were also created using @RISK program based on the measured temperature data. Statistical ranking was determined by the goodness of fit (GOF) to determine the proper probability distribution model. This result showed that the LogLogistic (−4.189, 5.9098, 3.2565) distribution models was found to be the most appropriate for relative MRA conduction.