• Title/Summary/Keyword: Lognormal Distribution

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Particle Size Distribution Analysis of Mineral Dust in Polar Snow Using a Coulter Counter (쿨터카운터(Coulter Counter)를 이용한 극지 눈시료 중 광물성 먼지의 입자크기분포 분석)

  • Kang, Jung-Ho;Hwang, Heejin;Hong, Sang Bum;Hur, Soon Do
    • Ocean and Polar Research
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    • v.36 no.4
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    • pp.319-326
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    • 2014
  • Mineral dust in the polar snow plays an important role both in the climate system of the Earth and in global biogeochemical cycles. Analysis of the concentration and the particle size distribution of mineral dust has been carried out in the snow from the Antarctic surface snow and the Greenland snowpit. Among the various particle size determination techniques, a Multisizer 3 Coulter Counter in a class 100 clean bench counted all particles between 1.1 and $30.0{\mu}m$ with a $50{\mu}m$ aperture tube. The aperture tube size, the concentration of electrolytes and the accuracy of the particle size distribution were determined in this study. The number concentrations from the Antarctic surface snow were 81,843 particles $mL^{-1}$, but those from the Greenland snowpit were 10,666 particles $mL^{-1}$. In the volume distribution, the distributions of mineral dust in both the Antarctic surface snow and the Greenland snowpit showed lognormal distribution in the size interval 1.1 to $6.0{\mu}m$ with the mode, 3.562 and $3.836{\mu}m$, respectively. The analysis technique using a coulter counter for mineral dust could be used for reconstructing paleoclimates from polar ice cores.

Statistical Characteristics of Deepwater Waves along the Korean Coast (한국 연안 심해파의 통계적 특성)

  • Suh, Kyung-Duck;Kwon, Hyuk-Dong;Lee, Dong-Young
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.20 no.4
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    • pp.342-354
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    • 2008
  • Some statistical characteristics of deepwater waves along the Korean coast have been investigated using various sources of wave measurement and hindcasting data. For very large waves comparable to design waves, it is recommended to use the average value of the empirical formulas proposed by Shore Protection Manual in 1977 and by Goda in 2003 for the relation between significant wave height and period. The standard deviation of significant wave periods non-dimensionalized with respect to the mean value for a certain significant wave height varies between 0.04 and 0.21 with a typical value of 0.1 depending upon different regions and different ranges of significant wave heights. The mean and standard deviation of the principal deepwater wave direction are presented at the 106 coastal grid points along the Korean coast. For relatively large waves, the probability density function of the directional spreading parameter $s_{max}$ is expressed as a lognormal distribution. The most suitable frequency spectrum in the Korean coast is the TMA spectrum. The probability density function of the peak enhancement factor $\gamma$ is also expressed as a lognormal distribution, with its mean value of 2.94, which is close to the value in the North Sea.

A Study Evalucation of Worker Exposure to Diatomaceous Earth Dust and Engineering Control in a Diatomite Factory (모 규조토 가공업체의 규조토 분진 폭로평가 및 개선방향에 관한 연구)

  • Cheong, Hoe Kyeong;Kim, Ji Yong;Cheong, Hae Kwan;Lim, Hyun Sul
    • Journal of Korean Society of Occupational and Environmental Hygiene
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    • v.4 no.1
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    • pp.81-95
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    • 1994
  • This study was performed in a diatomite factory where silicosis had been found at October, 1993. The major objectives were to evaluate worker exposure to diatomaceous earth and to present engineering control methods for workplace management. Total and respirable dust of diatomaceous earth were measured. Size distribution of dust was analyzed by applying the multiple diffraction method. Also crystalline silica in respirable dust samples was analyzed qualitatively by X-ray diffraction. The suitable Local Exhaust Ventilation systems for that factory were recommended. The results were as follows. The airborne total and respirable dust concentrations by exposure groups showed approximate normal distribution. The means of total dust exposures at flour maufacturing, fire brick grinding and packaging, ceramic raws packaging processes exceeded Korean and ACGIH standards, $10mg/m^3$. The means of total and respirable dust concentrations to high exposure groups were 6.8 and 3.9 times higher than those of low expousre groups, respectively. The size distribution of diatomaceous earth dust was lognormal with a median diameter of $7.07{\mu}m$(range, $0.10-60.0{\mu}m$) and with a geometric standard deviation of 1.43. The crystalline silica in respirable dust samples was identified to quartz and cristobalite and/or tridymite. Above results suggest that engineering controls and periodic environmental and medical surveillances will be important for preventing silicosis in the diatomite factory.

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Reliability Analysis for Fatigue Damage of Steel Bridge Details (강교 부재의 피로손상에 대한 신뢰성 해석)

  • Park, Yeon Soo;Han, Suk Yeol;Suh, Byoung Chal
    • Journal of Korean Society of Steel Construction
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    • v.15 no.5 s.66
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    • pp.475-487
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    • 2003
  • This study developed an analysis model of estimating fatigue damage using the linear elastic fracture mechanics method. Stress history occurring to an element when a truck passed over a bridge was defined as block loading and crack closure theory explaining load interaction effect was applied. Stress range frequency analysis considering dead load stress and crack opening was done. Probability of stress range frequency distribution was applied and the probability distribution parameters were estimated. The Monte Carlo simulation of generating the probability various of distribution was performed. The probability distribution of failure block numbers was obtained. With this the fatigue reliability of an element not occurring in failure could be calculated. The failure block number divided by average daily truck traffic remains the life of a day. Fatigue reliability analysis model was carried out for the welding member of cross beam flange and vertical stiffener of steel box bridge using the proposed model. Consequently, a 3.8% difference was observed between the remaining life in the peak analysis method and in the proposed analysis model. The proposed analysis model considered crack closure phase and crack retard.

Stochastic Simulation of Groundwater Flow in Heterogeneous Formations: a Virtual Setting via Realizations of Random Field (불균질지층내 지하수 유동의 확률론적 분석 : 무작위성 분포 재생을 통한 가상적 수리시험)

  • Lee, Kang-Kun
    • Journal of the Korean Society of Groundwater Environment
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    • v.1 no.2
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    • pp.90-99
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    • 1994
  • Heterogeneous hydraulic conductivity in a flow domain is generated under the assumption that it is a random variable with a lognormal, spatially-correlated distribution. The hydraulic head and the conductivity in a groundwater flow system are represented as a stochastic process. The method of Monte Carlo Simulation (MCS) and the finite element method (FEM) are used to determine the statistics of the head and the logconductivity. The second moments of the head and the logconductivity indicate that the cross-covariance of the logconductivity with the head has characteristic distribution patterns depending on the properties of sources, boundary conditions, head gradients, and correlation scales. The negative cross-correlation outlines a weak-response zone where the flow system is weakly responding to a stress change in the flow domain. The stochastic approach has a potential to quantitatively delineate the zone of influence through computations of the cross-covariance distribution.

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Establishment of Effluent Limitation based on Wastewater Characteristics and Treatment Technology (폐수특성 및 처리기술에 근거한 산업폐수 배출허용기준 설정체계 연구)

  • Kwon, Ohsang;Jung, Jinyoung;Heo, Teayoung;Jun, Hangbae;Lee, Younhee;Park, Sangmin
    • Journal of Korean Society on Water Environment
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    • v.28 no.6
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    • pp.804-812
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    • 2012
  • This study contemplated domestic and other country's effluent limitation standards and suggested a methodology to establish technology-base limitation value. Current effluent limitation regulates industrial point sources discriminated by discharge flow rate and by regional distinction in Korea. Discharged $BOD_5$ load from large-scale plants(flow rate above $2,000\;m^3/day)$ exceeds 50% of overall industrial wastewater, which present rationale for discrimination based on plant size. However, regional distinction and pollutant- specific regulation might be insufficient to meet practical effectiveness of wastewater management policy, due to the nearly same limitation. Water quality data and treatment methods were investigated in hospital industry. And their distribution of effluent $BOD_5$ concentrations was statistically analyzed to suggest limitation value. Effluent $BOD_5$ concentrations showed lognormal distribution and $95^{th}$ percentile was corresponded to 87.9 mg/L, which could be suggested as tentative effluent limitation in hospital industry. The $95^{th}$ percentile of log-transformed distribution showed similar value of 86.5 mg/L. This study demonstrated reasonable methodology for establishing effluent limitation reflecting wastewater characteristic and treatment technology in separately categorized industry.

Statistical Analysis for Fatigue Life Evaluation of Vehicle Muffler (자동차용 머플러의 피로수명평가를 위한 통계적 분석)

  • Choi, Ji-Hun;Lee, Yong-Jun;Yoon, Jin-Ho;Kang, Sung-Su
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.37 no.3
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    • pp.365-372
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    • 2013
  • In this study, a statistical method for evaluating the fatigue life of a vehicle muffler was used to obtain reliable fatigue data using a limited number of specimens. Cyclic bending tests were conducted using specimens manufactured to be exactly the same as the mufflers installed in cars that are currently in use. To estimate the fatigue life by comparing the data obtained during the fatigue tests, the most suitable probability density function for the normal, lognormal, and Weibull distributions was selected. A goodness-of-fit test was performed on the probability distributions, and then a Weibull distribution using the least square method was selected. By using the selected Weibull distribution, the probability-moment-life curves (P-M-N curve) reflecting the fatigue characteristics were suggested as the data for the reliable design of a muffler.

Statistical analysis and probabilistic modeling of WIM monitoring data of an instrumented arch bridge

  • Ye, X.W.;Su, Y.H.;Xi, P.S.;Chen, B.;Han, J.P.
    • Smart Structures and Systems
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    • v.17 no.6
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    • pp.1087-1105
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    • 2016
  • Traffic load and volume is one of the most important physical quantities for bridge safety evaluation and maintenance strategies formulation. This paper aims to conduct the statistical analysis of traffic volume information and the multimodal modeling of gross vehicle weight (GVW) based on the monitoring data obtained from the weigh-in-motion (WIM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. A genetic algorithm (GA)-based mixture parameter estimation approach is developed for derivation of the unknown mixture parameters in mixed distribution models. The statistical analysis of one-year WIM data is firstly performed according to the vehicle type, single axle weight, and GVW. The probability density function (PDF) and cumulative distribution function (CDF) of the GVW data of selected vehicle types are then formulated by use of three kinds of finite mixed distributions (normal, lognormal and Weibull). The mixture parameters are determined by use of the proposed GA-based method. The results indicate that the stochastic properties of the GVW data acquired from the field-instrumented WIM sensors are effectively characterized by the method of finite mixture distributions in conjunction with the proposed GA-based mixture parameter identification algorithm. Moreover, it is revealed that the Weibull mixture distribution is relatively superior in modeling of the WIM data on the basis of the calculated Akaike's information criterion (AIC) values.

Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels

  • Wang, Qian;Lin, Hai;Kam, Pooi-Yuen
    • Journal of Communications and Networks
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    • v.18 no.2
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    • pp.182-189
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    • 2016
  • The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

Estimation on Physical Microhabitat Suitability for Species of the Mayfly Genus Ephemera (Ephemeroptera: Ephemeridae) Using Probability Distribution Models (확률분포모형을 이용한 하루살이속(Ephemera) 종들의 물리적 미소서식처 적합도 평가)

  • Dongsoo Kong;Jeaha Song
    • Journal of Korean Society on Water Environment
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    • v.39 no.5
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    • pp.396-412
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    • 2023
  • Species from the mayfly genus Ephemera (Order Ephemeroptera) was assessed for their physical microhabitat suitability (namely E. strigata, E. separigata, and E. orientalis-sachalinensis). Probability distribution models (Exponential, Normal, Lognormal, Logistic, Weibull, Gamma, Beta, and Gumbel) based on the data collected from 23,957 sampling units of 6,787 sites in Korea from 2010 to 2021 were used. Mode and standard deviation calculated from the best-fitting models to species distribution along a water depth gradient were 265 cm and 159 cm in E. orientalis-sachalinensis; 10 cm and 83 cm in E. strigata; 20 cm and 15 cm in E. separigata, respectively. The current velocity gradient was 22 cm/s and 40 cm/s in E. orientalis-sachalinensis; 60 cm/s and 53 cm/s in E. strigata; 82 cm/s and 25 cm/s in E. separigata, respectively. The mean diameter (phi scale) of substrate grains were -3.6 and 2.2 in E. orientalis-sachalinensis; -7.4 and 1.5 in E. strigata; -5.8 and 0.9 in E. separigata, respectively. Habitat suitability range of E. orientalis-sachalinensis was estimated to be 161~369 cm (water depth), 5~44 cm/s (current velocity), -5.2~-2.0 (mean diameter); 3~34 cm (water depth), 36~94 cm/s (current velocity), -8.1~-6.3 (mean diameter) for E. strigata; 12~32 cm (water depth), 63~96 cm/s (current velocity), -6.3~-5.2 (mean diameter) for E. separigata. In relative comparison, E. orientalis-sachalinensis was estimated to be rheophobic, eurybathophilic, and eurypsephophilic; E. strigata to be euryrheophilic, bathophobic, and lithophilic; E. separigata to be stenomesorheophilic, stenobathophobic, stenolithophilic.