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In this study, the effectiveness of six numerical methods is evaluated to determine the shape ( k ) and scale ( c ) parameters of Weibull distribution function for the purpose of calculating the wind power density. The selected methods are graphical method (GP), empirical method of Justus (EMJ), empirical method of Lysen (EML), energy pattern factor method (EPF), maximum likelihood method (ML) and modified maximum likelihood method (MML). The purpose of this study is to identify the more appropriate method for computing the wind power density in four stations distributed in Alberta province of Canada namely Edmonton City Center Awos, Grande Prairie A, Lethbridge A and Waterton Park Gate. To provide a complete analysis, the evaluations are performed on both daily and monthly scales. The results indicate that the precision of computed wind power density values change when different parameters estimation methods are used to determine the k and c parameters. Four methods of EMJ, EML, EPF and ML present very favorable efficiency while the GP method shows weak ability for all stations. However, it is found that the more effective method is not similar among stations owing to the difference in the wind characteristics. [ABSTRACT FROM AUTHOR]

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With the development of urbanization, pervious concrete has been increasingly used in urban road pavement structures. The objective of this paper was to investigate the effect of stress levels and modifier (ground tire rubber and silica fume) on the fatigue life of pervious concrete and establish the fatigue equations with different survival probabilities. In order to improve the deformability of pervious concrete without sacrificing its strength, ground tire rubber and silica fume were added into pervious concrete. Two kinds of pervious concrete, control pervious concrete and ground tire rubber and silica fume modified pervious concrete, were made in the laboratory. The pervious concrete beam specimens of 100 × 100 × 400 mm were casted, and the static flexural strength and flexural strain of the two kinds of pervious concrete were tested. The fatigue lives of two pervious concretes were tested using MTS fatigue testing machine under four different stress levels (0.85, 0.80, 0.75, and 0.70). The fatigue life was analyzed by two-parameter Weibull distribution. The parameters of Weibull distribution were determined by graphical method, maximum likelihood method and moment method. The Kolmogorov–Smirnov test was used to test the Weibull distribution and the fatigue equations under different survival probabilities were established. The results showed that ground tire rubber and silica fume modified pervious concrete had better deformability while ensuring strength compared to control pervious concrete. The addition of ground tire rubber and silica fume improved the fatigue life of pervious concrete. The two-parameter Weibull distribution was suitable to characterize the fatigue characteristics and predict the fatigue life of pervious concrete. Fatigue equations with different survival probabilities were a good guide for pervious concrete design. [ABSTRACT FROM AUTHOR]

In this article, a new method was practiced to form a model by using twofold Weibull mixture distribution in right-censored reliability data. The method depends on estimating the parameters of right-censored twofold Weibull mixture distribution in a most appropriate way to the data by using genetic algorithm techniques. The best model was tried to be found by using MSE, MAE and MAPE metrics, respectively, as fitness function in the method. To test the model, failure data of aircraft planes' windshield, which is often used in the literature, was used and the results were compared with other methods in the literature. Furthermore, the performance of the method was compared for the sample sizes, censorship ratios and mixture proportions by conducting Monte Carlo simulation study. [ABSTRACT FROM AUTHOR]

Probabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by Kaniadakis. The deformed exponential transform can be used to generate skewed data from normal variates. We apply this transform to a censored autoregressive model for the generation of precipitation time series. We also highlight the connection between the heavy-tailed κ -Weibull distribution and weakest-link scaling theory, which makes the κ -Weibull suitable for modeling the mechanical strength distribution of materials. Finally, we introduce the κ -lognormal probability distribution and calculate the generalized (power) mean of κ -lognormal variables. The κ -lognormal distribution is a suitable candidate for the permeability of random porous media. In summary, the κ -deformations allow for the modification of tails of classical distribution models (e.g., Weibull, lognormal), thus enabling new directions of research in the analysis of spatiotemporal data with skewed distributions. [ABSTRACT FROM AUTHOR]

The need to deliver accurate predictions of renewable energy generation has long been recognized by stakeholders in the field and has propelled recent improvements in more precise wind speed prediction (WSP) methods. Models such as Weibull-probability-density-based WSP (WEB), Rayleigh-probability-density-based WSP (RYM), autoregressive integrated moving average (ARIMA), Kalman filter and support vector machines (SVR), artificial neural network (ANN), and hybrid models have been used for accurate prediction of wind speed with various forecast horizons. This study intends to incorporate all these methods to achieve a higher WSP accuracy as, thus far, hybrid wind speed predictions are mainly made by using multivariate time series data. To do so, an error correction algorithm for the probability-density-based wind speed prediction model is introduced. Moreover, a comparative analysis of the performance of each method for accurately predicting wind speed for each time step of short-term forecast horizons is performed. All the models studied are used to form the prediction model by optimizing the weight function for each time step of a forecast horizon for each model that contributed to forming the proposed hybrid prediction model. The National Oceanic and Atmospheric Administration (NOAA) and System Advisory Module (SAM) databases were used to demonstrate the accuracy of the proposed models and conduct a comparative analysis. The results of the study show the significant improvement on the performance of wind speed prediction models through the development of a proposed hybrid prediction model. [ABSTRACT FROM AUTHOR]

This work experimentally investigates the quasi‐static crush response and energy absorption of glass‐reinforced epoxy thin‐walled crash box filled with nano‐aluminum oxide (Al2O3). The effect of the triggering (45 ° edge chamfering) and the weight percentage (wt%) of Al2O3 on the crushing performance have been studied. Field emission scanning electron microscope (FE‐SEM) and energy‐dispersive X‐ray spectroscopy (EDX) were adapted to show the elemental composition of the fabricated samples' surfaces. To follow the fracture mechanism, visual inspection, and scanning electron microscope (SEM) were performed. Two‐parameter Weibull distribution function was employed to statistically analyze the experimental results. Failure probability curves were established to help the designers in selecting the suitable material for energy‐absorbing applications. Results indicated that for untriggered glass/epoxy composite crash boxes, the inclusion of 1, 2, and 3 wt% of nano‐Al2O3 leads to an increase of, respectively, 16.34%, 48.46%, and 68.70% in the absorbed energy (U). While there is a decrease of 32.72% in (U) when adding 4 wt% of nano‐Al2O3. An enrichment of 9.00%, 18.04%, 31.53%, and 11.30% in crush force efficiency (CFE) was reached by the inclusion of, respectively, 1, 2, 3, and 4 wt% of nano‐Al2O3. Triggering has a considerable effect on the crashworthiness parameters of the fabricated composite crash boxes. A decrease of 6.56%, 10.11%, 4.01%, 4.76%, and 11.62% in the initial peak load (Pip), an enrichment of 34.10%, 26.06%, 26.77%, 18.08%, and 28.97% in (CFE) and an improvement of 36.43%, 31.32%, 29.27%, 12.99%, and 52.47% in (U) were reported for composite crash boxes filled with 0, 1, 2, 3, and 4 wt% of nano‐Al2O3. It is obvious that glass/epoxy triggered composite crash boxes filled with 3 wt% of nano‐Al2O3 are appropriate to be used as energy absorbing device employed in vehicles due to their enhanced energy absorbing capabilities. [ABSTRACT FROM AUTHOR]

Background: In general, the individual patient-level data (IPD) collected in clinical trials are not available to independent researchers to conduct economic evaluations; researchers only have access to published survival curves and summary statistics. Thus, methods that use published survival curves and summary statistics to reproduce statistics for economic evaluations are essential. Four methods have been identified: two traditional methods 1) least squares method, 2) graphical method; and two recently proposed methods by 3) Hoyle and Henley, 4) Guyot et al. The four methods were first individually reviewed and subsequently assessed regarding their abilities to estimate mean survival through a simulation study. Methods: A number of different scenarios were developed that comprised combinations of various sample sizes, censoring rates and parametric survival distributions. One thousand simulated survival datasets were generated for each scenario, and all methods were applied to actual IPD. The uncertainty in the estimate of mean survival time was also captured. Results: All methods provided accurate estimates of the mean survival time when the sample size was 500 and a Weibull distribution was used. When the sample size was 100 and the Weibull distribution was used, the Guyot et al. method was almost as accurate as the Hoyle and Henley method; however, more biases were identified in the traditional methods. When a lognormal distribution was used, the Guyot et al. method generated noticeably less bias and a more accurate uncertainty compared with the Hoyle and Henley method. Conclusions: The traditional methods should not be preferred because of their remarkable overestimation. When the Weibull distribution was used for a fitted model, the Guyot et al. method was almost as accurate as the Hoyle and Henley method. However, if the lognormal distribution was used, the Guyot et al. method was less biased compared with the Hoyle and Henley method. [ABSTRACT FROM AUTHOR]

To install a wind energy conversion system to a region, the wind speed characteristics of that region must be identified. The two-parameter Weibull distribution is highly efficient in modeling wind speed characteristics. In this study, the wind speed data of 32 cities in three different regions of Turkey have been comparatively analysed to estimate Weibull distribution function parameters by the use of three well-known methods (Graphical Method (GM), Maximum Likelihood Method (MLM), Justus Moment Method (JMM)) and three new parameter estimation methods (Energy Pattern Factor Method (EPFM), Wind Energy Intensification Method (WEIM), Power Density Method (PD)) which have been proposed in recent years. Three years of hourly wind speed data of the specified regions have been used. The performance metrics of these analyses have been compared using Wind Energy Error (WEE), Root Mean Square Error (RMSE), and Coefficient of Determination (R2). The results have shown that while the PD method has high model performance, the JMM is closely competitive with the MLM. Besides, the wind energy densities that were estimated by using actual data have been compared with the resulting Weibull distribution. It has been clear that the method that has the closest estimation to the actual values is the PD method.

In the literature of model selection, Vuong's test and Akaike information criterion aim to find the best statistical model. Both of them are related to the expectation of the log-likelihood function of the rival models, but they are not sensitive to the small difference between rival models. The goal of this study is to develop a simple model selection approach which does not assume a true distribution for data. We have introduced a nonparametric tracking interval in the context of model selection. We have shown that this interval is compatibale with the known Vuong's test results, but here we let the magnitude of the data enhance the performance of statistical inference. Simulation study provide this method works well. It is shown that this interval has acceptable results for classical densities, autoregressive models and finite mixture models. This tracking interval is illustrated on a real data. The strength(mechanics) of brittle materials in various applications is characterized by Weibull distribution. These kind of data are usually skewed and platykurtic or leptokurtic. Thus, their median is more precise than their mean. Using the proposed interval, it is shown that, sometimes the Gamma and Log-normal distributions are suitable alternative to Weibull distribution. [ABSTRACT FROM AUTHOR]

The change of the wind speed is strictly related to several natural factors such as local topographical and the ground cover variations, then any adjustment has to take into account the statistical variation for each specific region under study. Unlike the Weibull distribution, which is most used in wind speed modeling, we investigate two alternative distribution functions for wind speed by using the extreme value theory. The generalized Champernowne distribution function and the mixture Log-normal-Pareto distribution function are considered. We demonstrate that the proper generalized extreme value distribution gives a good fit for wind speed in the North Moroccan. In order to validate the models, a comparison of the produced aggregate wind energy in the aeolian wind turbine was being established. The empirical study shows that the generalized extreme value distribution reflects better the intensity of the wind power energy. [ABSTRACT FROM AUTHOR]

Wind energy is the second largest source of renewable energy, across the world. For designing and construction of wind farms, most critical information is consistent wind resource assessment forecasts and appropriate models of wind speed distribution for a particular site. The purpose of this study is to provide the wind characteristics and wind potential evaluation of offshore locations, in Gujarat in India, using the wind Weibull density function. The Weibull shape k and scale c parameters are computed using six distinct numerical approaches at two different heights, to determine wind power density. The LiDAR sensor was used to capture the time series wind data. The goodness of fit test, which includes the RMSE, R2, MAPE, and χ2 is considered to evaluate the performance of the selected methods. Wind power densities are calculated from the acquired results with the help of estimated parameter values, all the methods used in this study were found to be appropriate for Weibull distribution parameters estimation. The MLM has been determined to offer the most accurate evaluation of wind potential. The WPD computed from observed wind data was compared to the obtained power densities of the specified region. The evaluated data is a considered as preliminary characteristic of wind potential that aids in the wind energy conversion and determining the actual wind potential of a specific site. [ABSTRACT FROM AUTHOR]

The present paper proposes a model of the specimen size effect on the critical flaw strength distribution in fiber tows for composite reinforcement. The model is based on the basic assumption of brittle fracture that the failure probability at a given strength increases with specimen size in the p-quantile vs. strength relation and on the normal distribution. Empirical results derived from force–strain curves determined on tows made of 1000 and 500 Nicalon SiC filaments and with various gauge lengths show some discrepancy with predictions using the model. The empirical p-quantile diagrams and cumulative distributions of critical flaw strengths exhibited excellent reproducibility at longer gauge lengths, which suggests the absence of a size effect above a critical tow size. The reproducibility of flaw strength distributions at gauge lengths above 60 mm and the higher strengths obtained at lower gauge lengths despite structural effects were related to the features of the critical flaw distribution in tows of parallel fibers. [ABSTRACT FROM AUTHOR]

Home energy retrofit has recurred in public policy throughout recent decades. However, the savings in energy usage attributable to home retrofit have remained difficult to accurately predict. Occupants cause prediction inaccuracies by varying different factors, especially heating setpoints temperatures and heating patterns. Acting together, such occupant factors result in distributions — not single values — of heat-energy usage, even among similar homes. Datasets of heat-energy distributions can be found by building performance simulation using modern grey-box models. This study presents a methodology to simulate grey-box models of home heating through ranges of heating setpoints and patterns. An entire process to calibrate, validate and simulate at a large scale is described, and then demonstrated using case studies. Grey-box models, written in Modelica language, can conveniently simulate through large ranges of occupant factors. The case studies exploited this advantage of grey-box models to simulate empirical data on occupant factors. (For instance, empirical data found that home heating setpoints shifted before and after home energy retrofit.) In doing so, the datasets of simulation results enabled the exploration of home heat-energy usage with the normal and Weibull statistical distributions. Additionally, the heat-energy distributions of case-study homes were statistically tested, first for retrofit savings, second for equality to each other and third for equality to an official heat-energy estimate. Results demonstrate that home heat-energy usage, at a large scale, is best expressed as a Weibull distribution not normality. After home energy retrofit, heat-energy usage displays less variation (in general), less skewness, and thus becomes closer to normality. Occupant factors were found to vary home heat-energy usage into distinct distributions, even within similar homes. Therefore, in most case-study homes, heat-energy usage did not equal an official estimate. Finally, shallow retrofit of a modern home in Ireland fails to save heat-energy usage by most occupants. [ABSTRACT FROM AUTHOR]

The article presents a study on the effect of mineral additives on the flexural fatigue performance of concrete. Mineral additives were applied to replace cement in different proportions. Distribution parameters were determined using the graphical method and the method of moments. The study found that the improved multi-powder particle size distribution, particle effect, and pozzolanic effect of mineral additives cause synergistic effect.

In this study, the Weibull distribution with various numerical estimation methods is utilized for the assessment of wind energy potential in Mersing and Port Dickson, Malaysia, by considering different monsoon seasons, i.e., northeast and southwest monsoons. This assessment is conducted based on hourly wind speed data obtained from the Malaysian Meteorological Department and the Department of Environment, Malaysia. A total of 28 numerical estimation methods are presented, and their performances are first investigated through a Monte Carlo simulation. The results of the Monte Carlo simulation indicate that no particular method outperforms all other methods. In different settings, i.e., different sample sizes and shape parameters, certain methods are more efficient than others in estimating the Weibull parameters. Based on the simulation results, 24 out of 28 numerical estimation methods are utilized for wind energy potential assessment in Mersing and Port Dickson. The performance efficiency of all the considered methods is evaluated using an integrated approach comprising four goodness of fit criteria, the modified Kolmogorov − Smirnov, modified Anderson − Darling, modified Cramér–von Mises, and power density error. Using this integrated approach allow us to obtain a single-value goodness of fit measure known as the global score to determine the best method. Based on the best fitted Weibull model, the wind characteristics in both sites are investigated. The wind characteristics during northeast monsoon is found to be favorable for wind energy generation in Mersing with the northeast (0 − 40°) as the prominent wind direction. However, small-scale wind energy is the best option for wind energy development in Mersing. On the other hand, the Port Dickson site demonstrates poor wind characteristics, indicating that this area is not favorable for wind energy development. [ABSTRACT FROM AUTHOR]

The Weibull distribution is regarded as among the finest in the family of failure distributions. One of the most commonly used parameters of the Weibull distribution (WD) is the ordinary least squares (OLS) technique, which is useful in reliability and lifetime modeling. In this study, we propose an approach based on the ordinary least squares and the multilayer perceptron (MLP) neural network called the OLSMLP that is based on the resilience of the OLS method. The MLP solves the problem of heteroscedasticity that distorts the estimation of the parameters of the WD due to the presence of outliers, and eases the difficulty of determining weights in case of the weighted least square (WLS). Another method is proposed by incorporating a weight into the general entropy (GE) loss function to estimate the parameters of the WD to obtain a modified loss function (WGE). Furthermore, a Monte Carlo simulation is performed to examine the performance of the proposed OLSMLP method in comparison with approximate Bayesian estimation (BLWGE) by using a weighted GE loss function. The results of the simulation showed that the two proposed methods produced good estimates even for small sample sizes. In addition, the techniques proposed here are typically the preferred options when estimating parameters compared with other available methods, in terms of the mean squared error and requirements related to time. [ABSTRACT FROM AUTHOR]

As the onshore wind farm technology matures, offshore wind energy has attracted increasing attention. Zhejiang has coastal areas with massive potential for wind resources because of its geographical location. Therefore, understanding the wind resources in these areas can lay a foundation for future development and utilization. On this basis, this study used the measured wind field data of a wind farm along the coast of Zhejiang from March 2014 to February 2015 and from March 2016 to February 2018 to investigate and compare the characteristics of wind energy resources, including average wind speed, Weibull shape and scale factors, wind direction variation, and wind energy density. Then, the capacity coefficient of a wind turbine predicted using the wind farm data was compared with the actual capacity coefficients of two wind turbines in the wind farm in 2019. Results revealed the following observations: The overall variations in the evaluation indicators followed clear patterns over the 3 years. For example, the main wind direction in the same season was the same, and the variations in the monthly average wind speed, the monthly wind power density, and the theoretical capacity factors were highly similar. The time-series data indicated that the difference in the indicators between summer and autumn was significantly larger than that between other seasons, with the maximum difference in monthly average wind speed of 1.46 times and the maximum difference in monthly wind power density of 1.5 times. The comparison results of the capacity coefficient showed that the theoretical and actual capacity coefficients were extremely close when the monthly average wind speed was less than 6 m/s, with the average difference being less than 9%. When the monthly average wind speed was greater than 6 m/s, the proximity between the theoretical and actual capacity coefficients was reduced, with an average difference of more than 9% and a maximum value of 28%. In general, the overall characteristics of wind resources in coastal areas of Zhejiang exhibited similar trends but fluctuated considerably in some months. Wind energy forecasts had significant discrepancies from the actual operation indicators of the wind farm when the wind speed was high. [ABSTRACT FROM AUTHOR]

Wind energy (WE), which is one of the renewable energy (RE) sources for generating electricity, has been making a significant contribution to obtaining clean and green energy in recent years. Fitting an appropriate statistical distribution to the wind speed (WS) data is crucial in analyzing and estimating WE potential. Once the best suitable statistical distribution for WS data is determined, WE potential and potential yield could be estimated with high accuracy. The main objective of this paper is to propose a novel approach for calculating wind energy potential. For this purpose, the Efficient Global Optimization (EGO) technique was proposed for fitting a statistical distribution to WS data and the performance of the technique was compared with genetic algorithm (GA), simulated annealing (SA), and differential evolution (DE). Performance metrics showed that EGO is providing better estimations compared with GA, SA, and DE. Based on Weibull parameters obtained by using EGO, potential WE and potential annual revenue were estimated for Gdańsk, which is the capital of Pomerania Voivodeship in Poland, in the case of having city-type wind turbines in the city center. Estimations for Gdańsk showed that city-type wind turbines might be helpful for producing electricity from WE in the city without being limited by constraints such as having a long distance between wind turbines and buildings. If such wind turbines were erected on the roofs of residential buildings, malls, or office buildings, there is a possibility that part of the electric energy needed for such buildings could be generated using WE. However, this topic should be further investigated from technical and financial perspectives. [ABSTRACT FROM AUTHOR]

This research examines the modified drop-mass impact performance on functionally graded preplaced aggregate fibrous concrete (FPAFC) against repeated low-velocity impacts. Three-layered FPAFCs were prepared with the outer layers reinforced with steel and polypropylene fibers to evaluate the impact resistance. For comparison, both one- and two-layered concretes were cast simultaneously. The modified version of the impact test was suggested to the ACI 544 drop-mass impact test to decrease the scattered test data. The modification was a replacement of the steel ball with a steel bar to apply a line impact instead of the single-point impact. This modification distributes the impact energy over a broader area and reduces the scattering of results. The study parameters for the tests were impact numbers, which cause first cracking and failure; ductility index; and mode of failure. In addition, three methods of the two-parameter Weibull distribution were used to examine the dispersed test results, which were presented in terms of reliability. Results revealed that the specimens comprising 3.6% steel fibers at the top layer and no fiber at the middle layer exhibited the highest percentage improvements of 633% and 2732% recorded for the cracking and failure impact number, respectively. The percentage difference in impact strength results between these two methods ranged from −14% to 75% for cracking impact number and from 6.8% to 57.2% for failure impact number. The coefficient of variation value calculated from the modified impact test was reduced and ranged from 20.3% to 56.1% for cracking impact number and from 15.2% to 65.3% for failure impact number, compared with the same mixtures from the ACI 544 test method. This phenomenon indicates that the modified impact test delivered a lower scattering of results by introducing a line of impact using a steel bar rather than a single-point impact. [ABSTRACT FROM AUTHOR]

Electromagnetic wave logging-while-drilling (LWD) tool plays an important role in unconventional oil and gas exploitation and deep-sea oil and gas resource exploration process. The reliability such as reliable life and durability of the tool can control drilling efficiency and production cost in extreme environmental conditions. In this paper, main faults of the electromagnetic wave LWD tool have been analyzed when it working to the drilling site. Failure time of antenna coils, circuit boards, and power supply have been recorded. Therefore, failure mode and failure mechanism can be analyzed of the tool. Secondly, a fault analysis model of electromagnetic wave LWD tool based on Weibull distribution model has been built up, and by using this fault analysis model the reliable life and the remaining useful life of antenna system can be calculated. The last, the goodness-of-fit test can be operated to Weibull distribution model by using Kolmogorov–Smirnov test. Study results show that the reliability and the law of fault occurrence of electromagnetic wave LWD tool can be directly reflected. And it has practical significance to reliability evaluation of the instrument system and joint optimization of safe operation and maintenance of the tool. [ABSTRACT FROM AUTHOR]

In order to reduce the estimation uncertainty for the wind energy output, the accurate assessment of the wind speed distribution plays an important role. Due to the influence of the complex terrain, the wind speed data in mountainous area may show the heavy tail. The tail has an important effect on the annual energy production of the wind turbine because of the power output being the cubic of the wind speed. Hence the heavy tail should be highlighted before choosing the proper distributions. To characterize the heavy tail, the box plot, QQ plot and conditional mean exceedance are used. In addition, the wind climate in the mountainous area is very complicated and typically mixed by local storms and large-scale wind flows. The distribution of the wind speed is prone to exhibit bimodal or even multi-modal nature. The conventional unimodal distributions such as Weibull may not well portray these distributions. The mixture distribution has more flexibilities to handle this challenge. Both generalized extreme value distribution and generalized Pareto distribution are considered to formulate the mixture distribution in modeling the tail. The maximum likelihood method and the constrained maximum likelihood method are used to estimate distribution parameters. The comprehensive evaluation criteria are adopted to determine the most appropriate distribution of four sets of wind speed in the mountainous area of Yunnan, China. Graphical tools, such as histogram density curve and QQ plot, are also used for evaluation. Results show that heavy tail distribution should be considered for the wind data in mountainous areas and the proposed mixture model with the constrained maximum likelihood method for the parameter estimation will be superior for the wind energy potential estimation. [ABSTRACT FROM AUTHOR]

A complex and varied terrain has a great impact on the distribution of wind energy resources, resulting in uncertainty in accurately assessing wind energy resources. In this study, three wind speed distributions of kernel, Weibull, and Rayleigh type for estimating average wind power density were first compared by using meteorological tower data from 2018 to 2020 under varied desert steppe terrain contexts in northern China. Then three key parameters of scale factor (c) and shape factor (k) from the Weibull model and surface roughness (z0) were investigated for estimating wind energy resource. The results show that the Weibull distribution is the most suitable wind speed distribution over that terrain. The scale factor (c) in the Weibull distribution model increases with an increase in height, exhibiting an obvious form of power function, while there were two different forms for the relationship between the shape factor (k) and height: i.e., the reciprocal of the quadratic function and the logarithmic function, respectively. The estimated roughness length (z0) varied with the withering period, the growing period, and the lush period, which can be represented by the estimated median value in each period. The maximum and minimum values of surface roughness length over the whole period are 0.15 and 0.12 m, respectively. The power-law model and the logarithmic model are used to estimate the average power density values at six specific heights, which show greater differences in autumn and winter, and smaller differences in spring and summer. The gradient of the increase in average power density values with height is largest in autumn and winter, and smallest in spring and summer. Our findings suggest that dynamic changes in three key parameters (c , k , and z0) should be accurately considered for estimating wind energy resources under varied desert steppe terrain contexts. [ABSTRACT FROM AUTHOR]

Global warming and depletion of fossil fuels have urged the world to control their impacts and find clean and green energy sources. Due to this paradigm shift, renewable energy resources (RESs) have received tremendous attention around the globe and amongst other RESs, wind energy has been proving itself a promising renewable resource. However, still, the proper selection of wind turbines (WTs) and their installation is considered a major challenge. Presently, due to the economic boom of Pakistan as a regional power under the China Pakistan Economic Corridor (CPEC) and increasing energy demand, it needs to meet the energy shortage. This paper aims to conduct a pre-feasibility ainvestigation of wind farm exploitation at Gwadar and Quetta, major cities of Baluchistan province in Pakistan by harnessing the wind energy potential and electricity generation cost through different WT models. The wind speed (WS) data is recorded by a professional wind mast at different measurement heights during F.Y 2016 and analyzed using Five approaches, Modified Maximum Likelihood Method (MMLM), Graphical Method (GM), Empirical Method of Lysen (EML), Empirical Method of Jestus (EMJ) and Energy Pattern Factor Method (EPF) at the proposed site and EPF shows the best performance than other approaches. Different WTs models are also evaluated and out of them, the GW121 WT gives the lowest cost in dollars and lowest payback period at each site so it can be recommended as one of the most feasible WT for electricity generation for powering local communities at the proposed sites.

Wind energy is considered one of the most important alternative energy sources for generating electricity. But the stochastic nature of wind, leads to use the distribution function to present the wind system. The two-parameter Weibull distribution is often used in the wind speed presentation. The two-parameter Weibull distribution has scale and shape parameters that are important in wind energy applications, thus selecting the optimum method for estimation them is important. The unpredictability in wind speed leads to uncertainty in devolved power which leads to difficult system operation. In this study, two novel artificial intelligence (AI) methods called Mayfly algorithm (MA) and Aquila Optimizer (AO) are used for calculating the Weibull distribution parameters. Results are compared with four classical numerical methods called the Maximum likelihood approach, Energy pattern factor method, Graphical method, and Empirical method. The two AI methods prove superiority and robustness for evaluating two-parameter of Weibull distribution as they give lower errors and higher correlation coefficients. Moreover, to prove the accuracy of the MA method in solving the optimal power flow (OPF) problem, single and multi-objective OPF is applied on a standard IEEE-30 bus system to minimize fuel cost, power loss, thermal unit emissions, and voltage security index (VSI), and results are compared with other metaheuristic methods. The results prove the validity and robustness of the MA method in solving the OPF problem. Then, single and multi-objective stochastic optimal power flow (SCOPF) is applied to modified IEEE-30 which contains two wind farms to minimize total generation cost, power loss, thermal unit emission, and VSI. The fuzzy-based Pareto front technique is utilized in multi-objective optimization (MOO) to obtain the best compromise point solution. The objective function of SCOPF considers reserve cost for overestimation and penalty cost for underestimation of wind energy. Finally, this paper studies the effect of changing Weibull parameters, penalty cost coefficient, and reverse cost coefficient in wind energy generation cost. The proposed MA method could be valuable to system operators as a decision-making aid when dealing with hybrid power systems.

Abstract: Turkey is a country that is dependent on foreign energy; the majority of Turkey''s energy needs are supplied through imports. Renewable energy sources are becoming important in Turkey due to both the country''s energy dependency and the disadvantages of using fossil fuels. Turkey has begun to use renewable energy sources, especially wind energy, which has a high potential in the country. Moreover, investigations of and investments in wind power have increased recently. This study investigates the wind energy potential that is a result of the distribution of wind speeds in Osmaniye,which is located east of the Mediterranean Sea in Turkey. The Weibull and Rayleigh distribution methods, which are generally used for this type of wind energy study, are employed. The approximate wind energy potential was obtained and indicates whether the region is suitable for related investments. Wind data, consisting of wind speed, direction and flow time at a height of 10m, were collected by the Turkish State Meteorological Service for a period of 44 months, from January 2008 to August 2011. To determine the Weibull parameters, a graphical method is used; hence, the mean annual value of the shape parameter (k) is between 1.00 and 1.04, while the annual value of the scale parameter (c) is between 1.59 and 1.66m/s. The average wind speed and wind potential energy are 2.23m/s and 24.587W/m2, respectively. [Copyright &y& Elsevier]

Abstract: The wind profile of Letšeng-la-Terae in Lesotho is analyzed using a 2-year data of 10-min averages. Wind velocity distribution data is estimated as a Weibull distribution using the Graphical Method and Method of Moments. The optimal Weibull parameters for the bi-annual data are obtained using the Method of Moments and the values of the dimensionless shape parameter, k = 1.76, and the scale parameter, c = 6.71 m/s at 10 m above ground level. The calculated air density at the site is 0.875 kg/m3 using the temperature and the pressure measurements. The data shows that the wind is prevalently from the West. The daily wind speed trends show that the interval between 5.00 am and 3.00 pm is the windiest for every month of the year. The months with the most and the least wind speeds are August and February, respectively. Letšeng-la-Terae is a class 4 wind energy site with a 95% confidence interval of both the bi-annual mean wind speed given by 5.97 ± 0.07 m/s and the bi-annual mean power density given by 208.56 ± 7.31 W/m2, both calculated at 10 m above the ground level. The typical turbines on the site are expected to operate 82.8 ± 6.7% of the time. The results show that the site is ideal for large-scale electricity generation. [Copyright &y& Elsevier]

Abstract: Two-parameter Weibull function has been widely applied to evaluate wind energy potential. In this paper, six kinds of numerical methods commonly used for estimating Weibull parameters are reviewed; i.e. the moment, empirical, graphical, maximum likelihood, modified maximum likelihood and energy pattern factor method. Their performance is compared through Monte Carlo simulation and analysis of actual wind speed according to the criterions such as Kolmogorov–Smirnov test, parameter error, root mean square error, and wind energy error. The results show that, in simulation test of random variables, the graphical method’s performance in estimating Weibull parameters is the worst one, followed by the empirical and energy pattern factor methods, if data number is smaller. The performance for all the six methods is improved while data number becomes larger; the graphical method is even better than the empirical and energy pattern factor methods. The maximum likelihood, modified maximum likelihood and moment methods present relatively more excellent ability throughout the simulation tests. From analysis of actual data, it is found that if wind speed distribution matches well with Weibull function, the six methods are applicable; but if not, the maximum likelihood method performs best followed by the modified maximum likelihood and moment methods, based on double checks including potential energy and cumulative distribution function. [ABSTRACT FROM AUTHOR]

Wind energy potential of Canakkale region has been analyzed using real time series analysis and Weibull distribution, making use of hourly average wind data of Turkish State Meteorological Service measured in 10 m height between 2001 and 2006. Weibull parameters have been calculated by using graphic, moment, and maximum likelihood methods for 50, 60, 70, 80, 90, and 100 m hub heights. It has been determined that moment method gives better results than other methods according to the R2 and root mean square error (RMSE) analysis. [ABSTRACT FROM AUTHOR]

The paper presents results of an investigation conducted to study the fatigue strength of steel fibre reinforced concrete (SFRC) beams in flexure. An experimental programme was planned in which about two hundred and thirty three flexural fatigue tests were conducted at different stress levels and stress ratios to obtain the fatigue lives of SFRC containing different volume fractions of steel fibres. One hundred and sixty six complimentary static flexural tests were also conducted to obtain the static flexural strength of SFRC beams prior to fatigue testing. The specimens of size 100 × 100 × 500 mm were used for static flexural as well as flexural fatigue tests and incorporated 0.5, 1.0 and 1.5% volume fraction of corrugated steel fibres of size 0.6 × 2.0 × 30 mm. The concept of equivalent fatigue life was then applied to the fatigue life data to incorporate the effects of stress level, stress ratio and survival probability into the fatigue equation. The results indicate that the distribution of equivalent fatigue life of SFRC can approximately be described by the two-parameter Weibull distribution. The material coefficients of the fatigue equation have been determined corresponding to different survival probabilities so that the fatigue equation can be used to predict the flexural fatigue strength of SFRC. [ABSTRACT FROM AUTHOR]

The article describes a study which examined the fatigue strength of steel fiber-reinforced concrete (SFRC) containing mixed fibers. The concrete was incorporated with corrugated mixed steel fibers. Equations were proposed to predict the flexural fatigue strength of SFRC. The results indicated that the distribution of fatigue life of SFRC can be modeled by two-parameter Weibull distribution.

This study strives to present a preliminary assessment of wind characteristics and the regime for Cappadocia Airport in Turkey by in-depth a holistic and precise comparative analysis. For this purpose, the parameters of the well-accepted Weibull distribution, namely shape and scale parameters, are determined by a variety of estimation methods. Furthermore, the distribution of wind direction and speed over a period of 2015 and 2017 is investigated. Several well-known statistical tools, including Root Mean Square Error (RMSE), R-squared (R2) and Chi-squared (X2), are conducted to analyze comparatively the fitting performance and efficiency of the estimation methods to wind data. This study reveals that the wind speed remains equal to or greater than around three (m/s) 61.12% of the time and the prevailing wind direction is between 290o and 335o, consistent with the runway orientation. The value of the shape parameter ranges from 2.4368 to 4.093, while the scale parameter is in the range from 3.4793 to 4.2349. Consequently, in light of the statistical indicators, it is clearly observed that Empirical Method of Justus (EMJ) and Empirical Method of Lysen (EML) with RMSE of 0.0392, R2 of 0.9865, and X2 of 0.0016, respectively, exhibit more excellent ability in estimating the Weibull parameters in comparison with other numerical methods and also are the most suitable methods in determining the wind characteristics and wind profile of the airport. This study may attract the attention of academics, industrial researchers and policymakers intending to establish the runway orientation at an airport. [ABSTRACT FROM AUTHOR]

This study primarily aims at the estimation of mean fatigue lives, design fatigue lives and theoretical fatigue lives of Self Compacting Concrete (SCC) made by 100% coarse fraction of Recycled Concrete Aggregates (RCA). For reference, SCC mix containing 100% Natural Aggregates (NA) was also tested. The Weibull distribution has been found to be suited for description of the fatigue life stats showing higher variance in fatigue life for SCC containing RCA. The mean values of the distribution parameters have been used for determining the mean, design and theoretical fatigue lives of SCC containing RCA and NA separately. Two million cycles endurance limit has also been determined for the SCC containing RCA and NA. It has been found that SCC containing RCA shows inferiority in terms of mean fatigue life, design fatigue life and theoretical fatigue life along with endurance limit and is mainly due to the substandard properties of RCA. [ABSTRACT FROM AUTHOR]

In this study, rotating bending fatigue tests have been conducted for carbon fiber-reinforced epoxy composites. Hollow cylindrical specimens were prepared for two different lay-up sequences, i.e., [± 45°]2 and [± 45°/(90°)2] using filament winding process. These specimens were tested at constant stress levels with zero mean stress using an in-house built rotating bending fatigue testing machine. Several failure modes including matrix cracking, fiber pull-out, and longitudinal splitting of fibers from the matrix and fiber failure have been ascertained using a scanning electron microscope. The probability distribution of fatigue life results of the test specimens is statistically analyzed using the two-parameter Weibull distribution function. Higher shape parameters are witnessed for both the stacking sequences at lower stress levels, indicating less dispersion in the fatigue life during high cycle fatigue. S–N diagrams are drawn for the different probability of failures (Pf = 0.10, Pf = 0.37, Pf = 0.50, and Pf = 0.99) for the benefit of machine designers to identify the first failure time. [ABSTRACT FROM AUTHOR]

Purpose: To investigate the probability of survival of different implant-abutment connection designs in narrow versus standard-diameter implants supporting anterior crowns.Materials and Methods: A total of 108 implants of either 3.5-mm or 4.0-mm diameter (narrow and standard, respectively) (10 mm in length, Implacil de Bortoli) were divided into six groups (n=18 each) as follows: external hexagon 3.5 mm or 4.0 mm (EH3.5 or EH4.0), internal hexagon 3.5 mm or 4.0 mm (IH3.5 or IH4.0), and Morse taper 3.5 mm or 4.0 mm (MT3.5 or MT4.0). The corresponding abutments were screwed to the implants, and standardized maxillary central incisor metal crowns were cemented and subjected to step-stress accelerated life testing in water. Use-level probability Weibull curves and reliability for a mission of 50,000 and 100,000 cycles at 100 N and 150 N (90% 2-sided confidence intervals [CI]) were calculated. Polarized-light and scanning electron microscopes were used to assess the failure modes.Results: The calculated reliability with 90% CI for a mission of 50,000 cycles at 100 N and 150 N showed that cumulative damage from the respective loads would lead to ~93% and ~18% implant-supported restoration survival in group EH3.5, ~99% and ~1% in group IH3.5, ~97% and ~89% in the MT3.5, ~100% and ~99% in the group EH4.0, ~100% and ~100% in group IH4.0, and ~99% and ~99% in group MT4.0. For the 100,000-cycle mission, the probability of survival estimated at 100 N and 150 N was, respectively: 0% for EH3.5 and IH3.5 at both load levels, ~96% and ~87% for the MT3.5, 100% and ~99% for EH4.0, 100% and ~99% for IH4.0, and 98% and ~92% for the MT4.0.Conclusion: A significant decrease in the probability of survival as a function of elapsed fatigue cycles and load increase was observed for narrow implants only with EH and IH implant-abutment connections, but not on Morse taper. [ABSTRACT FROM AUTHOR]

Polypropylene fiber, as a micro-scale reinforcement, can effectively inhabit the continuous micro-crack propagation of concrete during service. This paper aimed at examination of the fatigue life of polypropylene fiber reinforced concrete (PFRC) as subjected to repetitive compressive stress at multiple levels. A total of 18 groups of prismatic specimens were tested for different stress levels and polypropylene fiber parameters (volume fractions and aspect ratios). A two-parameter Weibull distribution was employed to describe the fatigue life probability distribution of PFRC. The shape parameter and characteristic life parameter were derived by averaging the values estimated by graphical method, moment method and maximum likelihood estimation method. The results indicated that the addition of polypropylene fiber into the concrete matrix can remarkably prolong the fatigue strength of concrete. Compared with plain concrete, the fatigue strength of PFRC could be increased by up to 28.1% under the failure probability of 5%. The fatigue life of PFRC was increased with an increase in the polypropylene fiber volume fraction up to 0.15%. However, the fatigue life of PFRC was decreasing with an increase in the fiber aspect ratio. The PFRC specimen with a volume fraction of 0.15% and an aspect ratio of 167 possessed the highest fatigue compressive strength among all the designed specimens. The fatigue life probability distribution of PFRC also obeyed the two-parameter Weibull distribution. Finally, a single-logarithm fatigue equation for PFRC was developed with both fiber parameters and failure probabilities taken into account, which can realistically predict the fatigue life of PFRC. This research outcome provides new knowledge and database that underpin the future development of design specifications for PFRC structures. • Cheap polypropylene fiber can help prolong the fatigue life of concrete. • Fatigue damage mechanism and fiber reinforced mechanism are revealed. • A unified fatigue equation is developed with consideration of failure probability. [ABSTRACT FROM AUTHOR]

The progressive type-II censoring has a wide range of applications in reliability studies and survival analysis. The analysis of the mixture models under progressively type-II censored samples has recently been introduced. The reliability estimation from the mixture model under the optimal progressive censoring schemes is still lacking in the current literature. We have discussed the estimation of parameters and reliability characteristics from the Weibull mixture model when failures are progressively censored. The Weibull mixture is proposed for this case as it is S-shaped, which can appropriately handle the mixture data. We have addressed the problem of determination of optimal censoring schemes and estimation of expected test times using the said mixed model. The optimal censoring schemes were found to be less sensitive hence robust. As the corresponding posterior distributions do not provide explicit solutions, we have considered Lindley's approximation for the approximate numerical solutions. [ABSTRACT FROM AUTHOR]

This work compares the efficiency of historically used Weibull parameters estimation methods with newly developed method. Newly developed method has been termed as Combined Linearized Moment Method (CLMM). Five-year wind data at five locations namely Chaghi, Lehri, Badin, Hyderabad and Nankana Sahib (Pakistan) was used for the calculation of Weibull parameters. Efficiency was assessed and compared using R-Squared(R2), MSE, RMSE, wind error (WE), MAPE and Chi-test ( χ 2 ). Each method was given a rank against each performance evaluation criterion and then an overall ranking was done. The study concluded that CLMM is the most accurate method among all while Empirical Method of Justus (EMJ) is the least accurate. Hence, CLMM can be used to estimate Weibull parameters for wind resource assessment with significant accuracy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to compare three different methods of analysis of results of lightning impulse breakdown voltage measurements of solid materials such as insulating pressboard. These three methods are the series method, the step method and the up-and-down method which are applied to withstand voltage estimation commonly in high voltage engineering. To obtain the data needed for the analysis a series of experimental studies was carried out. It included studies of mineral oil and natural ester impregnating 1 mm of thick cellulose-based pressboard. In order to show the distribution of breakdown voltage the Weibull distribution was additionally applied in data analysis. The results were also assessed from the viewpoint of dielectric liquid used for impregnation. The studies carried out showed that series and step methods give comparable results opposite to the up-and-down method. The latest overstates the results for mineral oil impregnated pressboard and understates for natural ester impregnated pressboard when juxtaposing them with the rest of the methods applied. In addition, there is lack of possibility to assess the withstand voltage for the up-and-down method directly from the vector of random variable. It is possible only as a result of a specially developed equation which always arouses doubt. From the methods applied it seems that the step method can be a great substitution for the series method as intuitive, fast in application and limiting the number of samples in solid insulation material testing. [ABSTRACT FROM AUTHOR]

PURPOSE. The objective of this study was to evaluate the effect of thickness reduction and fatigue on the failure load of monolithic zirconia crowns. MATERIALS AND METHODS. 140 CAD-CAM fabricated crowns (3Y-TZP, inCorisTZI, Dentsply-Sirona) with different ceramic thicknesses (2.0, 1.5, 1.0, 0.8, 0.5 mm, respectively, named G2, G1.5, G1, G0.8, and G0.5) were investigated. Dies of a mandibular first molar were made of composite resin. The zirconia crowns were luted with a resin composite cement (RelyX Unicem 2 Automix, 3M ESPE). Half of the specimens (n = 14 per group) were mouth-motion-fatigued (1.2 million cycles, 1.6 Hz, 200 N/5 - 55°C, groups named G2-F, G1.5-F, G1-F, G0.8-F, and G0.5-F). Single-load to failure was performed using a universal testing-machine. Fracture modes were analyzed. Data were statistically analyzed using a Weibull 2-parameter distribution (90% CI) to determine the characteristic strength and Weibull modulus differences among the groups. RESULTS. Three crowns (21%) of G0.8 and five crowns (36%) of G0.5 showed cracks after fatigue. Characteristic strength was the highest for G2, followed by G1.5. Intermediate values were observed for G1 and G1-F, followed by significantly lower values for G0.8, G0.8-F, and G0.5, and the lowest for G0.5-F. Weibull modulus was the lowest for G0.8, intermediate for G0.8-F and G0.5, and significantly higher for the remaining groups. Fatigue only affected G0.5-F. CONCLUSION. Reduced crown thickness lead to reduced characteristic strength, even under failure loads that exceed physiological chewing forces. Fatigue significantly reduced the failure load of 0.5 mm monolithic 3Y-TZP crowns. [ABSTRACT FROM AUTHOR]

Roselle fibre- and coconut shell powder (CSP)-reinforced vinyl ester composite was studied for analyzing the tensile properties. The fibre particle-reinforced vinyl ester composite (FPRV) specimens were fabricated using hand lay-up technique. It was observed that tensile properties of vinyl ester composite increase upon reinforcement with roselle fibres and CSP particle. The reinforcement of roselle fibres shows a significant effect on the tensile strength and modulus of the composite. The fractographic study was carried out on the surface of fractured composite specimens using scanning electron microscopy. A better interfacial adhesion, fibre dispersion and less fibre pull out on the surface of fractured composite specimens were identified. The tensile strength of FPRV composite has also been statistically analyzed by two-parameter Weibull distribution. Twenty-seven tension tests were carried out. The results obtained vary between 32.11 and 40.12 MPa. Furthermore, the inspection of the developed distribution was examined by Kolmogorov test. The results show that the gained two-parameter Weibull distribution can be used to express the tensile strength and predict its values accurately. [ABSTRACT FROM AUTHOR]

Estimation of wind speed distribution is essential for wind energy resources assessment, design of wind farms, and selection of suitable wind turbines. Two-parameter Weibull distribution function is widely used worldwide for wind energy resources assessment. As a case study, 1one-year field measurements at Gabal Al-Zayt wind farm in Egypt are used to estimate the Weibull parameters and to accurately assess the wind energy resource. In this work, seven statistical methods are adopted to estimate the Weibull parameters and their estimation accuracy is compared based on some common estimation errors. However, the improvement in one estimation error does not necessarily improve other types of errors. Consequently, a multi-objective genetic algorithm (MOGA) is adopted to investigate the tradeoffs among the competing estimation errors and to enhance the assessment of wind energy resources. The results show significant improvement in the estimation accuracy of the Weibull parameters using MOGA as compared to conventional statistical estimation methods. On the other hand, the case study at Gabal Al-Zayt wind farm reveals that the selection of wind turbines does not depend only on wind characteristics of the site but also on its environmental characteristics. [ABSTRACT FROM AUTHOR]

In this paper, a step-stress accelerated life test with two stress variables for Weibull distribution under progressive Type-I censoring is considered. The stress-life relationship is a log-linear function of stress levels, and for each combination of stress levels, a cumulative exposure model is assumed. The maximum likelihood and Bayes estimates of the model parameters are obtained. The optimum test plan is developed using the variance-optimality criterion, which consists of finding out the optimal stress change time by minimizing the asymptotic variance of the maximum likelihood estimates of the log of the scale parameter at the design stress. The proposed study is illustrated by using simulated data. [ABSTRACT FROM AUTHOR]

A mixture of two Weibull distributions (WW) has a variety of usage area from reliability analysis to wind speed modeling. Maximum likelihood (ML) method is the most frequently used method in parameter estimation of WW. Due to the nonlinear nature of the log-likelihood function of WW, usage of iterative techniques is a necessary process. Conventional iterative techniques such as Newton Raphson (NR) require considerable analytical preparatory to work to obtain gradient and may lead to numerical difficulties such as convergence problems. The aim of this paper is to present a genetic algorithm (GA) with an adaptive search space based on the Expectation–Maximization (EM) algorithm to obtain the ML estimators of the parameters of WW. The simulation study is conducted to compare the performances of ML estimators obtained using NR algorithm, EM algorithm, simulated annealing algorithm, and the proposed GA. Furthermore, real data examples are used to compare the efficiency of proposed GA with the existing methods in the literature. Simulation results and real data examples show that the proposed GA has superiority over other techniques in terms of efficiency. [ABSTRACT FROM AUTHOR]

A graphical method is given for the analysis of repairable systems failing according to a Weibull process. The integrated hazard rate is plotted in a logarithmic co-ordinate system. If the process is of Weibull type the observed data will be located around a straight line. The plot provides estimates of the parameters. The graphical procedure is completed by confidence bands and variation bands built either around the observed failure numbers at fixed time or vice versa. [ABSTRACT FROM AUTHOR]

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