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.

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.

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).

선박의 접안과정 중 발생하는 접안에너지는 접안속도와 밀접한 관계가 있다. 접안속도가 과다할 경우 선박 및 부두에 손상이 발생 하는 접안사고로 이어질 수 있으므로 적절한 접안속도를 설계하는 것이 중요하다. 선박접안속도의 경우, 일반적으로 대수정규분포를 따른다 고 가정하고 있으나 국내에서는 이에 대한 검증이나 연구가 없어 해외의 사례를 바탕으로 설계접안속도를 설정하고 있는 상황이다. 이에 본 연구에서는 부두의 선박접안속도 분석을 통계학적으로 접근하여 실측데이터와 확률분포를 비교하여 가장 적합한 확률분포를 찾고자 하였다. 적합도 검정으로는 K-S(Kolmogorov-Smirnov) 검정, A-D(Anderson-Darling) 검정, Q-Q(Quantile-Quantile) 플롯 등을 이용하여 접안속도 실측치 분포에 적합한 확률분포를 확인하였다. 분석 결과, 접안속도의 빈도분포는 선박의 재화상태에 따라 만재 시, 대수정규분포, 경하 시에 는 와이블분포와 적합함을 확인하였다. 또한 적합도 검정 결과를 이용하여 초과확률에 해당하는 접안속도 예측치를 산출하였다. 이 예측값과 해당 부두의 설계접안속도와 비교 해본 결과, 예측값이 설계값을 크게 초과함을 확인하였다. 이를 통해 설계 시의 접안속도가 현실과 맞지 않게 다소 낮게 설정되어 있음을 알 수 있으며, 이 결과를 바탕으로 적정 설계접안속도 산정법 개선에 기여할 수 있을 것으로 기대된다.

해양사고를 야기한 선원의 행동오류를 식별하는 것은 해양사고의 예방 또는 저감에 관한 연구의 기초가 된다. 본 연구의 목적은 선원들의 행동오류를 세 가지 행동(즉, Skill, Rule, Knowledge)으로 모델링하는데 필요한 최적의 확률분포함수를 추정하는데 있다. 본 저자들 의 사전 연구에서 획득한 해양사고 종류별 행동오류 데이터를 이용하여 세 가지 행동오류에 최적인 확률분포함수를 추정하고, 확률분포함수에서 도출한 확률 값들 사이의 유의성을 검증하였다. 확률분포함수 추정에는 최우추정법(Maximum Likelihood Estimation, MLE)을 적용하고, 유의성 검증에는 분산분석(ANOVA)를 이용하였다. 실험결과 여덟 가지 해양사고 종류별 세 가지 행동으로 각각에 대해서 최소의 오차를 갖는 확률분포함수를 추정할 수 있었다. 이를 이용하여 계산한 여덟 가지의 해양사고 종류에 대한 세 가지 행동오류들의 확률 값들은 통계적인 유의성이 관측 되었다. 또한, 행동오류가 해양사고에 영향을 미치는 것으로 관측되었다.

This study investigates the performance of four Bayesian methods, Random Walk Metropolis (RWM), Hit-And-Run Metropolis (HARM), Adaptive Mixture Metropolis (AMM), and Population Monte Carlo (PMC), for estimating the parameters and uncertainties of probability rainfall distribution, and the results are compared with those of conventional parameter estimation methods; namely, the Method Of Moment (MOM), Maximum Likelihood Method (MLM), and Probability Weighted Method (PWM). As a result, Bayesian methods yield similar or slightly better results in parameter estimations compared with conventional methods. In particular, PMC can reduce parameter uncertainty greatly compared with RWM, HARM, and AMM methods although the Bayesian methods produce similar results in parameter estimations. Overall, the Bayesian methods produce better accuracy for scale parameters compared with the conventional methods and this characteristic improves the accuracy of probability rainfall. Therefore, Bayesian methods can be effective tools for estimating the parameters and uncertainties of probability rainfall distribution in hydrological practices, flood risk assessment, and decision-making support.

This study applied the Bayesian method for the quantification of the parameter uncertainty of spatial linear mixed model in the estimation of the spatial distribution of probability rainfall. In the application of Bayesian method, the prior sensitivity analysis was implemented by using the priors normally selected in the existing studies which applied the Bayesian method for the puppose of assessing the influence which the selection of the priors of model parameters had on posteriors. As a result, the posteriors of parameters were differently estimated which priors were selected, and then in the case of the prior combination, F-S-E, the sizes of uncertainty intervals were minimum and the modes, means and medians of the posteriors were similar to the estimates using the existing classical methods. From the comparitive analysis between Bayesian and plug-in spatial predictions, we could find that the uncertainty of plug-in prediction could be slightly underestimated than that of Bayesian prediction.

Bootstrap methods is the computer-based resampling method that estimates the standard errors and confidence intervals of summary statistics using the plug-in principle for assessing the accuracy or uncertainty of statistical estimates, and the BCa method among the Bootstrap methods is known much superior to other Bootstrap methods in respect of the standards of statistical validation. Therefore this study suggests the method of the representation and treatment of uncertainty in flood risk assessment and water resources planning from the construction and application of rainfall frequency analysis model considersing the uncertainty based on the nonparametric BCa method among the Bootstrap methods for the assessement of the estimation of probability rainfall and the effect of uncertainty considering the uncertainty of the parameter estimation of probability in the rainfall frequency analysis that is the most fundamental in flood risk assessement and water resources planning.

본 연구는 확률강우량에 대한 공간분포 추정시 신뢰도를 향상시키는데 있어서 외부변수 사용의 유효성을 평가하기 위하여 확률강우량과 단일 보조변수로서 지형특성인자들과의 상관관계를 고려한 KED 기법을 적용하였으며, 그 결과 강우공간분포 및 유역평균강우량의 추정에 있어서 확정론적 공간보간기법 및 크리징 기법과 대체로 비슷한 결과를 나타내는 것으로 분석되었으며, KED 및 크리징 기법에 대한 교차검증 결과 보조변수로서 표고를 사용한 KED 기법이 가장 좋은 결과