• Title/Summary/Keyword: 2-parameter weibull distribution

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Fatigue Properties of Rail Steel Under Constant Amplitude Loading and Variable Amplitude Loading (일정 및 변동하중하의 레일강의 피로특성)

  • Kim, Cheol-Su;Kim, Jeong-Gyu
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.4
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    • pp.654-661
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    • 2001
  • In this study, fatigue growth behavior of the transverse crack, which was the most dangerous damage among the various types of rail defects, was investigated using the notched keyhole specimen under constant amplitude loadings. Fatigue limit of smooth specimen in rail steel at R=0 was 110MPa, and the fatigue crack initiation life in the region of the low stress amplitude (ie. long life) occupied the major portion of the total fatigue life. The fatigue strength under variable amplitude loading was converted to the equivalent fatigue strength based upon. Miners rule, which was estimated approximately 9% lower than that under constant amplitude loading. Also, in the low ΔK(sub)rms region ($\leq$21MPa√m), fatigue crack growth rate (da/dN) under constant amplitude loading was higher than that under variable amplitude loading, whereas the tendency was reversed in the high ΔK(sub)rms region. It is believed that this behavior is due to the transition of fracture appearance.

Influence of overload on the fatigue crack growth retardation and the statistical variation (강의 피로균열지연거동에 미치는 과대하중의 영향과 통계적 변동에 관한 연구)

  • 김선진;남기우;김종훈;이창용;박은희;서상하
    • Journal of Ocean Engineering and Technology
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    • v.11 no.3
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    • pp.76-88
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    • 1997
  • Constant .DELTA.K fatigue crack growth rate experiments were performed by applying an intermediate single and multiple overload for structural steel, SM45C. The purpose of the present study is to investigate the influence of multiple overloads at various stress intensity factor ranges and the effect of statistical variability of crack retardation behavior. The normalized delayed load cycle, delayed crack length and the minimum crack growth rate are increased with increasing baseline stress intensity factor range when the overload ratio and the number of overload application were constant. The crack retardation under low baseline stress intensity factor range increases by increasing the number of overload application, but the minimum crack growth rate decreases by increasing the number of overload application. A strong linear correlation exists between the minimum crack growth rate and the number of overload applications. And, it was observed that the variability in the crack growth retardation behavior are presented, the probability distribution functions of delayed load cycle, delayed crack length and crack growth life are 2-parameter Weibull. The coefficient of variation of delayed load cycle and delayed crack length for the number of 10 overload applications data are 14.8 and 9.2%, respectively.

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PD Signal Time-Frequency Map and PRPD Pattern Analysis of Nano SiO2 Modified Palm Oil for Transformer Insulation Applications

  • Arvind Shriram, R.K.;Chandrasekar, S.;Karthik, B.
    • Journal of Electrical Engineering and Technology
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    • v.13 no.2
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    • pp.902-910
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    • 2018
  • In recent times, development of nanofluid insulation for power transformers is a hot research topic. Many researchers reported the enhancement in dielectric characteristics of nano modified mineral oils. Considering the drawbacks of petroleum based mineral oil, it is necessary to understand the dielectric characteristics of nanofluids developed with natural ester based oils. Palm oil has better insulation characteristics comparable to mineral oil. However very few research reports is available in the area of nanofluids based on palm oil. Partial discharge (PD) is one of the major sources of insulation performance degradation of transformer oil. It is essential to understand the partial discharge(PD) characteristics by collecting huge data base of PD performance of nano modified palm oil which will increase its confidence level for power transformer application. Knowing these facts, in the present work, certain laboratory experiments have been performed on PD characteristics of nano $SiO_2$ modified palm oil at different electrode configurations. Influence of concentration of nano filler material on the PD characteristics is also studied. Partial discharge inception voltage, Phase resolved partial discharge (PRPD) pattern, PD signal time-frequency domain characteristics, PD signal equivalent timelength-bandwidth mapping, Weibull distribution statistical parameters of PRPD pattern, skewness, repetition rate and phase angle variations are evaluated at different test conditions. From the results of the experiments conducted, we came to understand that PD performance of palm oil is considerably enhanced with the addition of $nano-SiO_2$ filler at 0.01%wt and 0.05%wt concentration. Significant reduction in PD inception voltage, repetition rate, Weibull shape parameter and PD magnitude are noticed with addition of $SiO_2$ nanofillers in palm oil. These results will be useful for recommending nano modified palm oil for power transformer applications.

The Extreme Value Analysis of Deepwater Design Wave Height and Wind Velocity off the Southwest Coast (남서 해역 심해 설계 파고 및 풍속의 극치분석)

  • Kim, Kamg-Min;Lee, Joong-Woo;Lee, Hun;Yang, Sang-Yong;Jeong, Young-Hwan
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • v.29 no.1
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    • pp.245-251
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    • 2005
  • When we design coastal and harbol facilities deepwater design wave and wind speed are the important design parameters. Especially, the analysis of these informations is a vital step for the point of disaster prevention. In this study, we made and an extreme value analysis using a series of deep water significant wave data arranged in the 16 direction and supplied by KORDI real-time wave information system ,and the wind data gained from Wan-Do whether Station 1978-2003. The probability distributions considered in this characteristic analysis were the Weibull, the Gumbel, the Log-Pearson Type III, the Normal, the Lognormal, and the Gamma distribution. The parameter for each distribution was estimated by three methods, i.e. the method of moments, the maximum likelihood, and the method of probability weight moments. Furthermore, probability distributions for the extreme data had been selected by using Chi-square and Kolmogorov-Smirnov test within significant level of 5%, i,e. 95% reliance level. From this study we found that Gumbel distribution is the most proper model for the deep water design wave height off the southwest coast of Korea. However the result shows that the proper distribution made for the selected site is varied in each extreme data set.

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A Simulation Model for the Intermittent Hydrologic Process(I) - Alternate Renewal Process (ARP) and Continuous Probability Distribution - (간헐(間歇) 수문과정(水文過程)의 모의발생(模擬發生) 모형(模型)(I) - 교대재생과정(交代再生過程)(ARP)과 연속확률분포(連續確率分布) -)

  • Lee, Jae Joon;Lee, Jung Sik
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.3
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    • pp.509-521
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    • 1994
  • This study is an effort to develop computer simulation model that produce precipitation patterns from stochastic model. A stochastic model is formulated for the process of daily precipitation with considering the sequences of wet and dry days and the precipitation amounts on wet days. This study consists of 2 papers and the process of precipitation occurrence is modelled by an alternate renewal process (ARP) in paper (I). In the ARP model for the precipitation occurrence, four discrete distributions, used to fit the wet and dry spells, were as follows; truncated binomial distribution (TBD), truncated Poisson distribution (TPD), truncated negative binomial distribution (TNBD), logarithmic series distribution (LSD). In companion paper (II) the process of occurrence is developed by Markov chain. The amounts of precipitation, given that precipitation has occurred, are described by a Gamma. Pearson Type-III, Extremal Type-III, and 3 parameter Weibull distribution. Daily precipitation series model consists of two models, A-Wand A-G model, by combining the process of precipitation occurrence and a continuous probability distribution on the precipitation of wet days. To evaluate the performance of the simulation model, output from the model was compared with historical data of 7 stations in the Nakdong and Seomjin river basin. The results of paper (1) show that it is possible to design a model for the synthetic generation of IX)int precipitation patterns.

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Statistical Analysis for Creep Crack Growth Behavior of Modified 9Cr-1Mo Steel (Modified 9Cr-1Mo 강의 크리프 균열성장 거동에 관한 통계적 해석)

  • Jung, Ik-Hee;Kim, Woo-Gon;Yin, Song-Nan;Ryu, Woo-Seog;Kim, Seon-Jin
    • Korean Journal of Metals and Materials
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    • v.47 no.5
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    • pp.283-289
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    • 2009
  • This paper dealt with a statistical analysis for evaluating the creep crack growth rate (CCGR) for Modified 9Cr-1Mo (ASTM Grade 91) steel. The CCGR data was obtained by the creep crack growth (CCG) tests conducted under various applied loads at $600^{\circ}C$. To obtain logically the B and q values used in the CCGR equation, three methods such as the least square fitting method (LSFM), the mean value method (MVM) and the probabilistic distribution method (PDM) were adopted and their CCGR lines were compared, respectively. In addition, a number of random variables were generated by using the Monte Carlo simulation (MCS), and the CCGR lines were predicted probabilistically. It was found that both the B and q coefficients followed a 2-parameter Weibull distribution well. In the case of the ranges of 10-90% for the probability variables, P(B, q), the CCGR lines were predicted. Fractographic study was conducted from the specimen after the CCG tests.

Reliability-Based Design Optimization for a Vertical-Type Breakwater with an Emphasis on Sliding, Overturn, and Collapse Failure (직립식 방파제 신뢰성 기반 최적 설계: 활동, 전도, 지반 훼손으로 인한 붕괴 파괴를 중심으로)

  • Yong Jun Cho
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.36 no.2
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    • pp.50-60
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    • 2024
  • To promote the application of reliability-based design within the Korean coastal engineering community, the author conducted reliability analyses and optimized the design of a vertical-type breakwater, considering multiple limit states in the seas off of Pusan and Gunsan - two representative ports in Korea. In this process, rather than relying on design waves of a specific return period, the author intentionally avoided such constraints. Instead, the author characterized the uncertainties associated with wave force, lift force, and overturning moment - key factors significantly influencing the integrity of a vertical-type breakwater. This characterization was achieved by employing a probabilistic model derived from the frequency analysis results of long-term in-situ wave data. The limit state of the vertical-type breakwater encompassed sliding, overturning, and collapse failure, with the close interrelation between wave force, lift force, and moment described using the Nataf joint probability distribution. Simulation results indicate, as expected, that considering only sliding failure underestimates the failure probability. Furthermore, it was shown that the failure probability of vertical-type breakwaters cannot be consistently secured using design waves with a specific return period. In contrast, breakwaters optimally designed to meet the reliability index requirement of 𝛽-3.5 to 4 consistently achieve a consistent failure probability across all sea areas.

Analysis and probabilistic modeling of wind characteristics of an arch bridge using structural health monitoring data during typhoons

  • Ye, X.W.;Xi, P.S.;Su, Y.H.;Chen, B.
    • Structural Engineering and Mechanics
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    • v.63 no.6
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    • pp.809-824
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    • 2017
  • The accurate evaluation of wind characteristics and wind-induced structural responses during a typhoon is of significant importance for bridge design and safety assessment. This paper presents an expectation maximization (EM) algorithm-based angular-linear approach for probabilistic modeling of field-measured wind characteristics. The proposed method has been applied to model the wind speed and direction data during typhoons recorded by the structural health monitoring (SHM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. In the summer of 2015, three typhoons, i.e., Typhoon Chan-hom, Typhoon Soudelor and Typhoon Goni, made landfall in the east of China and then struck the Jiubao Bridge. By analyzing the wind monitoring data such as the wind speed and direction measured by three anemometers during typhoons, the wind characteristics during typhoons are derived, including the average wind speed and direction, turbulence intensity, gust factor, turbulence integral scale, and power spectral density (PSD). An EM algorithm-based angular-linear modeling approach is proposed for modeling the joint distribution of the wind speed and direction. For the marginal distribution of the wind speed, the finite mixture of two-parameter Weibull distribution is employed, and the finite mixture of von Mises distribution is used to represent the wind direction. The parameters of each distribution model are estimated by use of the EM algorithm, and the optimal model is determined by the values of $R^2$ statistic and the Akaike's information criterion (AIC). The results indicate that the stochastic properties of the wind field around the bridge site during typhoons are effectively characterized by the proposed EM algorithm-based angular-linear modeling approach. The formulated joint distribution of the wind speed and direction can serve as a solid foundation for the purpose of accurately evaluating the typhoon-induced fatigue damage of long-span bridges.

The Comparative Study for Property of Learning Effect based on Software Reliability Model using Doubly Bounded Power Law Distribution (이중 결합 파우어 분포 특성을 이용한 유한고장 NHPP모형에 근거한 소프트웨어 학습효과 비교 연구)

  • Kim, Hee Cheul;Kim, Kyung-Soo
    • Convergence Security Journal
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    • v.13 no.1
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    • pp.71-78
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    • 2013
  • In this study, software products developed in the course of testing, software managers in the process of testing software test and test tools for effective learning effects perspective has been studied using the NHPP software. The doubly bounded power law distribution model makeup Weibull distribution applied to distribution was based on finite failure NHPP. Software error detection techniques known in advance, but influencing factors for considering the errors found automatically and learning factors, by prior experience, to find precisely the error factor setting up the testing manager are presented comparing the problem. As a result, the learning factor is greater than automatic error that is generally efficient model could be confirmed. This paper, a numerical example of applying using time between failures and parameter estimation using maximum likelihood estimation method, after the efficiency of the data through trend analysis model selection were efficient using the mean square error and $R^2$.

Evaluation of the Fracture Toughness Transition Characteristics of RPV Steels Based on the ASTM Master Curve Method Using Small Specimens (소형시험편의 Master Curve 방법을 이용한 원자로 압력용기강의 파괴인성 천이특성평가)

  • Yang, Won-Jon;Heo, Mu-Yeong;Kim, Ju-Hak;Lee, Bong-Sang;Hong, Jun-Hwa
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.2 s.173
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    • pp.303-310
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    • 2000
  • Fracture toughness of five different reactor pressure vessel steels was characterized in the transition temperature region by the ASTM E1921-97 standard method using Charpy-sized small specimens. T he predominant fracture mode of the tested steels was transgranular cleavage in the test conditions. A statistical analysis based on the Weibull distribution was applied to the interpretation of the scattered fracture toughness data. The size-dependence of the measured fracture toughness values was also well predicted by means of the Weibull probabilistic analysis. The measured fracture toughness transition curves followed the temperature-dependence of the ASTM master curve within the expected scatter bands. Therefore, the fracture toughness characteristics in the transition region could be described by a single parameter, so-called the reference temperature (T。), for a given steel. The determined reference temperatures of the tested materials could not be correlated with the conventional index temperatures from Charpy impact tests.