• Advances in concrete construction
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• 제9권5호
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• pp.469-478
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• 2020

This study aims to establish a new methodological framework for the evaluation of the evolution of the reliability of plain concrete for pavement vs number of cycles under flexural fatigue loading. According to the framework, a new method calculating the reliability was proposed through probability simulation in order to describe a random accumulation of fatigue damage, which combines reliability theory, one-to-one probability density functions transformation technique, cumulative fatigue damage theory and Weibull distribution theory. Then the statistical analysis of flexural fatigue performance of cement concrete tested was carried out utilizing Weibull distribution. Ultimately, the reliability for the tested cement concrete was obtained by the proposed method. Results indicate that the stochastic evolution behavior of concrete materials under fatigue loading can be captured by the established framework. The flexural fatigue life data of concrete at different stress levels is well described utilizing the two-parameter Weibull distribution. The evolution of reliability for concrete materials tested in this study develops by three stages and may corresponds to develop stages of cracking. The proposed method may also be available for the analysis of degradation behaviors under non-fatigue conditions.

• 대한의용생체공학회:의공학회지
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• 제37권1호
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• pp.21-30
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• 2016

Weibull distribution with two parameters, shape (k) and scale (s) parameters are used to model the fatigue failure analysis due to periodic vortex shedding of the synovial fluid in knee joints. In order to determine the later parameter, a suitable statistical model is required for velocity distribution of synovial fluid flow. Hence, wide applicability of Weibull distribution in life testing and reliability analysis can be applied to describe the probability distribution of synovial fluid flow velocity. In this work, comparisons of three most widely used methods for estimating Weibull parameters are carried out; i.e. the least square estimation method (LSEM), maximum likelihood estimator (MLE) and the method of moment (MOM), to study fatigue failure of bone joint due to periodic vortex shedding of synovial fluid. The performances of these methods are compared through the analysis of computer generated synovial fluidflow velocity distribution in the physiological range. Significant values for the (k) and (s) parameters are obtained by comparing these methods. The criterions such as root mean square error (RMSE), coefficient of determination ($R^2$), maximum error between the cumulative distribution functions (CDFs) or Kolmogorov-Smirnov (K-S) and the chi square tests are used for the comparison of the suitability of these methods. The results show that maximum likelihood method performs well for most of the cases studied and hence recommended.

• International Journal of Naval Architecture and Ocean Engineering
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• 제11권1호
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• pp.165-177
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• 2019

This paper considers corrosion wastage of two ship hull structure members as a part of investigated fuel oil tanks of 25 aging bulk carriers. Taking into account that many factors which influence corrosion wastage of ship hull structures are of uncertain nature, the related corrosion rate ($c_1$) is considered here as a real-valued continuous distribution, assuming that the corrosion wastage starts after 5, 6 or 7 years. In all considered cases, by using available data and applying three basic statistical tests, it is established that between two-parameter continuous distributions, normal, Weibull and logistic distributions are best fitted distributions for the mentioned corrosion rate ($c_1$). Note that the presented statistical, numerical and graphical results concerning two mentioned ship hull structure members allow to compare and discuss the corresponding probabilistic estimates for the corrosion rate ($c_1$).

• Structural Engineering and Mechanics
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• 제61권4호
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• pp.463-473
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• 2017

Reinforced concrete is a complex material to be modeled in finite element domain. A proper material model is necessary to represent the nonlinear behaviour accurately. Though the nonlinear analysis of RC structures evolved long back, still an accurate and reliable model to predict the realistic behaviour of components are limited. It is observed from literature that there are three well-known models to represent the nonlinear behaviour of concrete. These models include Chu model (1985), Hsu model (1994) and Saenz model (1964).A new stress-strain model based on Weibull distribution has been proposed in the present study. The objective of the present study is to analyze a reinforced concrete beam under flexural loading by employing all the models. Nonlinear behaviour of concrete is considered in terms of stress vs. strain, damage parameter, tension stiffening behaviour etc. The ductility of the RC beams is computed by using deflection based and energy based concepts. Both deflection ductility and energy based ductility is compared and energy based concept is found to be in good correlation with the experiments conducted. The behavior of RC beam predicted using ABAQUS has been compared with the corresponding experimental observations. Comparison between numerical and experimental results confirms that these four constitutive models are reliable in predicting the behaviour of RC structures and any of the models can be employed for analysis.

• 한국신뢰성학회지:신뢰성응용연구
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• 제16권1호
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• pp.32-40
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• 2016

Purpose: The purpose of this study is to analyze the effect of sampling points on accuracy of storage reliability estimation for one-shot systems by assuming a weibull distribution as a storage reliability distribution. Also propose method for determining of sampling points for increase the accuracy of reliability estimation. Methods: Weibull distribution was divided into three sections for confirming the possible to estimate the parameters of the weibull distribution only some section's sample. Generate quantal response data for failure data. And performed parameter estimation with quantal response data. Results: If reduce sample point interval of 1 section, increase the accuracy of reliability estimation although sampling only section 1. Even reduce total number of sampling point, reducing sampling time interval of the 1 zone improve the accuracy of reliability estimation. Conclusion: Method to increase the accuracy of reliability estimation is increasing number of sampling and the sampling points. But apply this method to One-shot system is difficult because test cost of one-shot system is expensive. So propose method of accuracy of storage reliability estimation of one-shot system by adjustment of the sampling point. And by dividing the section it could reduce the total sampling point.

• 한국농공학회논문집
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• 제55권3호
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• pp.105-111
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• 2013

Probability distribution of microbes in wastewater is a crucial factor to be determined for microbial risk assessment associated with its reuse. The objective of this study was to investigate probability distribution of an indicator microorganism in wastewater. Daily total coliform counts measured from nationwide wastewater treatment plants in 2010 by the Ministry of Environment were used for statistical analysis. Basic statistics and probability distributions were estimated in the three different spatial scales using the MS Excel software and FARD2006 model. Overall, wastewater from manure and livestock treatment plants demonstrated greater median coliform counts than from sewage and village treatment plants. Generalized logistic (GLO) and 2-parameter Weibull (WBU2) appeared to be the two probability distributions that fitted best for total coliform numbers in wastewater. The study results of microbial statistics and probability distributions would provide useful data for quantitative assessment of microbial risk from agricultural wastewater reuse.

• 한국해양공학회지
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• 제17권2호
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• pp.54-59
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• 2003

The characteristics of the parameters for the probability distribution of fatigue crack growth life, using the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length equals the number of cycle curves that are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratios of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth life seems to follow the 3-parameter Wiubull,, showing a slight dependence on specimen thickness and stress intensity level. The shape parameter, $\alpha$, does not show the dependency of thickness and stress intensity level, but the scale parameter, $\beta$, and location parameter, ${\gamma}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2002년도 추계학술대회 논문집
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• pp.301-306
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• 2002

The characteristics of parameters for the probability distribution of fatigue crack growth lives by the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length - the number of cycles curves are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratio of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth lives seems to follow the 3-parameter Wiubull and shows a slight dependence on specimen thickness and stress intensity level. The shape parameter, ${\alpha}$, does not show the dependency of thickness and stress intensity level, but the scale parameter, ${\beta}$, and location parameter, ${\upsilon}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• 한국해안해양공학회지
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• 제16권3호
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• pp.130-141
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• 2004

연안 및 항만구조물의 설계에서 심해 설계파는 매우 중요한 환경인자이다. 특히, 심해설계파고의 분포 정보는 최근 부각되고 있는 신뢰성 설계에 필수적인 요소이다. 본 연구에서는 한국해양연구원(2003)에서 제시한 1979년부터 1998년까지의 한국연안 67개 지점의 16방향별 최대 유의파 산출자료를 이용하여 극치분포 분석을 수행하였다. 특성분석에 사용된 극치분포함수는 Weibull, Gumbel, Log-Pearson Type-III, Lognormal 분포이며, 각 분포함수의 매개변수는 모멘트법, 최우도법 그리고 확률가중모멘트법으로 추정하였다. 또한, 극치분포함수의 적합성은 95% 신뢰도 수준으로 $\chi$$^2$및 K-S 검정을 실시하였다. 그 결과, 한국연안의 심해 설계파고는 Gumbel 분포형이 가장 적합한 모형으로 파악되었으며, 최적 추정된 매개변수 및 재현기간 50년에 대한 심해 설계파고 정보를 제시하였다.

• Smart Structures and Systems
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• 제17권6호
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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.