Parameter Weibull Distribution Research Articles

The impacts of climate change on rainfall modeling in the Pantanal of Mato Grosso do Sul

The most significant and influential meteorological element in environmental conditions and human activities is precipitation. The objective of this study was to adjust eight probability distributions to monthly, seasonal and annual rainfall data in the Pantanal of Mato Grosso do Sul, Brazil, using a time series of data (1983-2013) by the National Meteorological Water Agency (ANA). The performance evaluation of different probability distribution models was assessed by the quality of fit of the selected probability distributions for precipitation data. Quality tests as chi-square, Kolmogorov-Smirnov (KS) and Anderson-Darling (AD), the information criteria as Akaike (AIC) and the Bayesian criterion (BIC) were used. Then the mean root square error (RMSE) and the coefficient of determination (R2) were applied. The analyzes were made monthly, annually and by seasons. The 3-parameter Lognormal distribution performs the best for all twelve months and provides the best-fit to the monthly rainfall data. Thus characterizing a dry period that runs from May to September and a rainy period between the months of October and April, it was observed that the 3-parameter Lognormal distribution has best adjustment for spring and summer, and for winter and autumn the 2-parameter Gamma and 3-parameter Gamma distribution performed better. For annual observations, the function that best fits is 3-parameter Weibull distribution.

Chloride threshold, modelling of corrosion rate and pore structure of concrete with metakaolin addition

The effect of metakaolin addition on the chloride threshold (Cth) for steel corrosion initiation was investigated. Half-cell potential (Ecorr) and corrosion current density (icorr) were monitored to assess the corrosion condition of the steel. The results indicate that the Cth becomes lower with increasing metakaolin replacement fraction. Variation of the icorr (i.e. corrosion rate) follows a 3-parameter Weibull distribution, with the time parameter implicitly related to the initial corrosion time. The first derivative of the modelled icorr curve, which can be regarded as the rebar depassivation rate, is found to first increase and then decrease. Based on the corrosion rate and depassivation rate, the corrosion initiation phase can be further divided into pitting nucleation, metastable pitting growth and stable pitting growth phases. MIP test demonstrates that adding metakaolin decreases the effective porosity, thus impeding the chloride penetration.

Fatigue life of preloaded injection bolts in a bridge strengthening scenario – sensitivity analysis of fatigue life estimators

AbstractOld metallic bridges are prone to high levels of structural degradation due to their long service life, therefore, it is essential to study strengthening techniques. Implementation of injection bolts to replace riveted joints exposed to fatigue damages has been studied. The mechanical performance of injection bolts has been studied mainly based on quasi‐static or creep tests. The objective of this paper is comparison of fatigue resistance between bolted joints with preloaded injection bolts opposing bolted joints with preloaded high strength bolts. Specimens were defined aiming to reproduce as close as possible a strengthening scenario. Single and double lap joints were tested. The fatigue phenomenon has a stochastic nature and therefore robust models are necessary to estimate parameters of distribution functions. Therefore, different estimation methodologies were implemented to determine the parameters of Weibull distribution. The main goal was to define reliable S‐N design curves. Results showed that the use of preloaded injection bolts contribute to increase the fatigue life and to reduce the scatter, mainly for double lap joints. It is shown that S‐N curves of EN1993‐1‐9 do not represent the fatigue strength of structural details with old metallic materials.

Statistical Analysis of Wind Speed Distribution Based on Five Weibull Methods for Wind Power Evaluation in Maan, Jordan

Due to the increasing environmental and economic cost of fossil fuels, alternative sources of energy are needed. One of these sources is wind energy. The wind-turbines extract kinetic energy from the wind to convert it to mechanical energy and then transfer to electrical energy. Wind speed is the most important parameter for an efficient wind energy system. In this work the Microsoft excel software used to analysis of wind speed data and evaluate the wind speed distribution. the wind speed probability estimated and analyzed by using five methods of Weibull and Rayleigh distributions and evaluated the best methods to represent the actual data based on monthly mean wind speed data of the Ma'an city site, Jordan. furthermore, from the analysis, it has been found that the energy pattern factor method EPFM is the best method to represent the actual data and the EPFM is the best and most accurate and efficient method to determine the Weibull distribution parameters ( k ) and ( c ). In addition, in this work, the annual average shape parameter ( k ) is 3.4 and the annual average scale parameter ( c ) is 4.0 m/s. The most probable wind speed is 4.4 m/s in August and the maximum wind speed carrying maximum energy is 5.2 m/s occurs in October. Meanwhile, the maximum power and energy density are 57.5 W/m 2 , 42.8 kWh/m 2 respectively in August. Moreover, the site has annual power density 39.3W/m 2 and 345.5 kWh/m 2 of energy density. Keywords : Renewable energy, Wind energy, Wind speed, Weibull distributions, Power density, Energy density DOI: 10.7176/JETP/11-4-05 Publication date: September 30th 2021

Rüzgar Hızı Değerlendirmesinde İki Parametreli Weibull Dağılımı İçin Üç Parametre Tahmin Metodunun Karşılaştırmalı Performans Analizi

The two-parameter Weibull distribution is widely used in the estimation of wind speed. In this paper, some recently proposed parameter estimation methods for the two parameter Weibull distribution have been compared using the wind data from two cities in Turkey. The compared methods in this paper are Wind Energy Intensification Method (WEIM), Energy Pattern Factor Method (EPFM), and Power Density Method (PD). These methods have been compared by checking the fit have provided in the probability-density graph. The comparison has also been made by comparing of efficiencies these methods in predicting wind energy density. Lastly, a comparison has been investigated by using the following performance criteria; Wind Energy Error (WEE), Root Mean Square Error (RMSE), Coefficient of Determination (R2), and the results of error analysis have been compared. According to simulation results, while the EPFM and PD methods have shown a very close fit on the graph; when it comes to calculating wind energy densities, the PD method has shown a significant advantage over other methods. Finally, after the examination of error criteria, it was clear that EPFM has shown accurate performance which is the desired result. The main conclusion is that the accurate method for these selected regions is the EPFM.

Wind Speed Profile Statistics from Acoustic Soundings at a Black Sea Coastal Site

More than seven years of remote sensing data with high spatial and temporal resolution were investigated in this study. The 20-min moving averaged wind profiles form the acoustic sounding with Scintec MFAS sodar were derived every 10 min. The profiles covered from 30 to 600 m height with vertical resolution of 10 m. The wind speed probability and the Weibull distribution parameters were calculated by the maximum likelihood method at each level and then the profiles of the Weibull scale and shape parameters were analyzed. Diurnal wind speed at heights above 200 m has shown a well-expressed increase in the averaged values during the night hours, while during the day lower wind speeds were observed. The reversal height was explored from spatially and temporally homogenized diurnal wind speed data with applied quadratic functions for better interpretation of the results. In addition, analyses by type of air masses (land or sea air mass) were performed. One of the outcomes of the study was assessment of the internal boundary layer height, which was estimated to 50–80 m at the location of the sodar. The obtained information forms the basis for climatological insights on the vertical structure of the coastal boundary layer and is unique long-term data set important not only for Bulgaria but for coastal meteorology in general.

Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

The hybrid censoring is a mixture of type-I and type-II censoring schemes. This paper presents the statistical inferences of the inverse Weibull distribution parameters when the data are type-I hybrid censored. First, we consider the maximum likelihood estimates of the unknown parameters. It is observed that the maximum likelihood estimates can not be obtained in closed form. We further obtain the Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimates using Lindley's approximation technique. The performance of the Bayes estimates have been compared with maximum likelihood estimates through the Monte Carlo Markov chain techniques. Finally, a real data set have been analysed for illustration purpose.

Distribution distortion in the statistical analysis of strength data when using multiple specimen batches

The strength distribution of Zerodur® (Schott AG) prepared by grinding and etching is determined through statistical analysis to be best described as normal. Although a 3-parameter Weibull appearance is exhibited when multiple specimen batches are combined and analyzed together, this appearance is the result of mixing of components of variation. As a result of the particular type of flaw population, little effect of scale is exhibited. Caution is advised when assuming a 3-parameter Weibull distribution and associated threshold solely based on distribution shape. Fractography to understand the flaw distribution should be employed.

Digital image contrast assessment based on the Weibull distribution parameters

The goal of the studies described in the paper is to find a quantitative assessment that maximally correlates with the subjective assessment of the contrast image quality in the absence of reference image. As a result of the literature analysis, 16 functions were selected that are used for no-refernce image quality assessment: BEGH, BISH, BREN, CMO, CURV, FUS, HELM, EBCM, KURT, LAPD, LAPL, LAPM, LOCC, LOEN, SHAR, WAVS. They all use the arithmetical mean of the local contrast quality. As an alternative to averaging local estimates (since the mean is one of two parameters of the normal distribution), it is proposed to use one of two parameters of the Weibull distribution of the same data – scale or shape.For the experiments, digital images with nonlinear contrast distortion from the available CCID2014 database were used. It contains 15 original images with a size of 768x512 pixels and 655 versions with modified contrast. This database of images contains the average visual quality assessment (Mean Opinion Score, briefly MOS) of each image. Spearman’s rank correlation coefficient was used to determine the correspondence between the visual MOS scores and the studied quantitative measures.As a result of the research, a new quality assessment measure of contrast images in the absence of references is presented. To obtain the estimate, local quality values are calculated by the BREN measure, their set is described by the Weibull distribution, and the scale parameter of the distribution serves as the best numerical estimate of the quality of contrast images. This conclusion is confirmed experimentally, and the proposed measure correlates better than other variants with the subjective assessments of experts.

Analysis of Probability Distribution of Muzzle Velocity for Chrome Plated Barrel

To confirm the change of muzzle velocity and the most suitable probability distribution model of the 155 mm K9 howitzer barrel with chrome plating and changed rifling. Using a statistical program, the muzzle velocity were plotted on a normal distribution, a 2-parameter and 3-parameter Weibull distribution on a probability paper. Also, statistical parameters were estimated and muzzle velocity fitness test and probability of K676 charge were plotted. In both the chrome-plated with standard rifling and changed rifling for K9 barrel, the 2-parameter and 3-parameter Weibull distribution were skewed to the left compared to the normal distribution. It was confirmed that the muzzle velocity of the K9 barrel with chromium-plated is suitable for the normal distribution and 3-parameter Weibull distribution model.

Technical agave fiber tensile performance: The effects of fiber heat-treatment

Natural fiber composites are a lightweight, sustainable alternative to high-density synthetic fiber composites in semi-structural automotive applications. Heat-treatment of natural fibers prior to compounding has been shown to improve composite thermal and dimensional stability while reducing moisture absorption and odor. Previous investigation into the performance of heat-treated blue-agave fiber composites found that heat treatment of fibers at 180 ℃ increased fiber crystallinity but did not significantly alter the mechanical performance of the resulting agave fiber composites. Therefore, this study seeks to better understand the effects of heat treatment on blue-agave fiber mechanical performance (single-fiber tensile) and morphology (SEM) prior to compounding. Heat-treatment of fibers at 180 ℃ resulted in an increase in fiber secondary modulus by approximately 150 % and a reduction in strain at break by approximately 80 %. Morphological analysis of fiber fracture surfaces showed that heat-treated fibers failed in a more brittle manner than untreated fibers, which is consistent with an increase in fiber crystallinity and stiffness. Additionally, this work evaluated the ability to predict agave fiber behavior using a modified 3-parameter Weibull distribution model. The resulting volume-based model was found to be a suitable predictor for agave fiber strength.

A framework on the investigation of wind characteristics based on Weibull distribution function by comparative scrutiny of estimation methods: application to an airport

ABSTRACT 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.

A Bayesian Inference Approach for Bivariate Weibull Distributions Derived from Roy and Morgenstern Methods

Bivariate lifetime distributions are of great importance in studies related to interdependent components, especially in engineering applications. In this paper, we introduce two bivariate lifetime assuming three- parameter Weibull marginal distributions. Some characteristics of the proposed distributions as the joint survival function, hazard rate function, cross factorial moment and stress-strength parameter are also derived. The inferences for the parameters or even functions of the parameters of the models are obtained under a Bayesian approach. An extensive numerical application using simulated data is carried out to evaluate the accuracy of the obtained estimators to illustrate the usefulness of the proposed methodology. To illustrate the usefulness of the proposed model, we also include an example with real data from which it is possible to see that the proposed model leads to good fits to the data.

Characteristic Value of the Modulus of Elasticity (MOE) for Natural and Planted Larch in Northeast China

The density and modulus of elasticity (MOE) distribution can provide information on the effectiveness of parametric and non-parametric methods in calculating the characteristic value of MOE. In this study, we aim to determine the optimal distribution model of the actual measured data of the lumber. We also estimate the lumber’s MOE characteristic value and compare the difference in density and MOE between natural and planted larch. Approximately 1200 pieces of dimension lumber of 4 m × 140 mm × 40 mm in size, made from larch and planted larch, were obtained, tested, and the corresponding standard MOE value was calculated. Results revealed the 3-parameter Weibull distribution to be optimal in fitting the natural and planted larch distributions. The parametric method proved effective in calculating the characteristic value of both larch groups, with characteristic MOE values of 9.73 kN/mm2 and 8.84 kN/mm2, and characteristic density values of 530 kg/m3 and 460 kg/m3 for natural and planted larch, respectively. Moreover, the MOE and density values followed grades C40 and C35. Thus, the conclusion is that the parametric method should be used to determine these characteristic values for natural and planted larch.

Integration of Multivariate Loss Function Approach in the Hotelling’s Charts under Banerjee-Rahim (1988) Weibull Shock Models

A proper monitoring of stochastic systems is the control charts of statistical process control and drift in characteristics of output may be due to one or several assignable causes. Although many research works have been done on the economic design of control charts with single assignable cause, the economic statistical design of T^2 control chart under Weibull shock model with multiple assignable causes and considering multivariate Taguchi loss function has not been presented yet. Using Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values ??of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with Taguchi loss function has a lower cost than single assignable cause model and integrated model with non-uniform sampling has a lower cost than that with uniform sampling.

Analysis of the Frequency and Onset Time of Hyponatremia/Syndrome of Inappropriate Antidiuretic Hormone Induced by Antidepressants or Antipsychotics

Hyponatremia and syndrome of inappropriate antidiuretic hormone (SIADH) is a potentially fatal adverse effect of antidepressants (ADs) and antipsychotics (APs), although its frequency and onset time have not been well documented. To analyze the frequency and onset time of AD- or AP-induced hyponatremia/SIADH. We used plural data-mining techniques to search the US Food and Drug Administration Adverse Event Reporting System (FAERS) database for reports on hyponatremia/SIADH induced by psychotropic drugs from January 2004 to June 2020. For each item, we assessed the reporting odds ratio, 95% CI, median onset time, and Weibull distribution parameters. We identified 36 422 reports related to hyponatremia/SIADH. Signals were detected for all psychotropic drugs that we analyzed, except for clozapine. The median onset time of total AD-induced hyponatremia/SIADH was shorter than that of AP. For all ADs and APs except clozapine, hazards were considered to be the early failure type. In contrast, the hazard of clozapine was considered to be the random failure type. The limitations of this study included several reporting biases and the presence of confounding variables, particularly age. Most ADs and APs were found to be associated with a risk for hyponatremia/SIADH. In addition, sufficient attention should be paid to signs of hyponatremia/SIADH in the early phase when most ADs and APs are administered. These data are potentially useful for determining AD- or AP-induced hyponatremia/SIADH in the early stage and for preventing its further aggravation into a serious condition.

Potential of wind energy in Medina, Saudi Arabia based on Weibull distribution parameters

This study aims to assess the potential of wind energy in Medina by using Weibull probability distribution to provide an insight concerning the energy production from the selected wind turbine Aventa AV-7. Scale factors c and shape k of Weibull distribution, were determined for wind speed frequency. Significant findings included a wind speed recurrence of 2.9 m/s with a probability of 30% approximately. The average c and k were found to be 3.467 and 2.923 m/s, respectively. The estimated average k is relatively high, which indicates that the spread in wind speeds is small. Aventa AV-7 turbine was chosen to test the power generation of wind in Medina. It was found that this wind turbine can generate 8648 kWh/year in the Medina region, which is only 15.2% of the maximum power production. This turbine is expected to generate the maximum possible power output at a wind speed of 7 m/s.

Offshore Wind Potential of West Central Taiwan: A Case Study

In this study, we present the wind distributions from a long-term offshore met mast and a novel approach based on the measure–correlate–predict (MCP) method from short-term onshore-wind-turbine data. The annual energy production (AEP) and capacity factors (CFs) of one onshore and four offshore wind-turbine generators (WTG) available on the market are evaluated on the basis of wind-distribution analysis from both the real met mast and the MCP method. Here, we also consider the power loss from a 4-month light detection and ranging (LiDAR) power-curve test on an onshore turbine to enhance the accuracy of further AEP and CF evaluations. The achieved Weibull distributions could efficiently represent the probability distribution of wind-speed variation, mean wind speed (MWS), and both the scale and shape parameters of Weibull distribution in Taiwan sites. The power-loss effect is also considered when calculating the AEPs and CFs of different WTGs. Successful offshore wind development requires (1) quick, accurate, and economical harnessing of a wind resource and (2) selection of the most suitable and efficient turbine for a specific offshore site.

Quantification of random pore features of porous concrete mixes prepared with brick aggregate: An application of stereology and mathematical morphology

The present study deals with the pore feature analysis of porous concrete mixes based on image analysis technique. The porous concrete mixes are prepared with over-burnt brick aggregate having different sizes and different aggregate gradations. The scarcity of natural aggregates in Tripura, India has forced the researchers to use locally available waste bricks as a coarse aggregate in construction purposes. However, the application of bricks in porous concrete is very rare and the porous distribution of porous mixes made of brick aggregates are not well-known. Hence, in this paper, initiatives are made to characterize the porous features of pervious concrete mixes using bricks as coarse aggregates. Stereological analysis and mathematical morphology such as two-point correlation and granulometric distribution analysis are employed in this paper. Statistical analysis is also conducted to identify the distribution of the pores and is observed that the 3-parameter Weibull distribution is the best way to fit the pore diameters of the pervious concrete mixes. Finally, the relative mean pore size is identified and the permeability of the pervious mix is obtained based on this image analysis. From the overall analysis, it is found that the image analysis can be an efficient way to identify the pore features of the porous concrete mixes.

Mathematical representation of Wind Turbine Power reliability

Nowadays wind resource assessment utilize new advanced technologies and appropriate analytical methods which are applied to estimate how much wind as a fossil free fuel will be available from a wind farm over the period of its performance. The utmost important piece of information is determining the expected generation of energy from the power plant and ultimately how much cost effective it will be. In our study we have proposed a new method, the improved mixture Weibull distribution produced from the combination of two and three parameter Weibull distribution with six parameters which include shape, scale, location parameter and the weight component or the mixing parameter. The basic properties of the improved mixture Weibull distribution and the estimation of parameters using maximum likelihood method are discussed. The estimated parameters are used to derive a mathematical model to compute the capacity factor and wind power density.