Two-parameter Weibull Probability Distribution Research Articles

자가용 전기설비의 변압기 검사 통계 기반 교체 주기 분석

This study was conducted a reliability analysis of the replacement cycle based on the inspection data of receiving power transformers in domestic private electrical facilities. The dataset was constructed with a sample of 529,024 transformer data from about 2.4 hundred-thousands high voltage electrical consumers. Five examples were selected for cumulative failure probability and failure rate based life indicators. Considering the over or under estimation of reliability analysis, the appropriate data sampling level was selected by examining the correlation with life indicators according to the failure data rate. Two-parameter weibull probability distribution was selected by based on the data distribution pattern and distribution suitability review results based on Anderson-Darling statistics. Finally, the replacement cycle was presented as a cumulative failure probability-based B10, B20, and mean failure to time and failure rate-based life indicator.

Wind quality designation concept and application

Generally, wind energy production is based on the average wind speed without any classification. This article proposes a classification system on the basis of wind speed durations greater than a given threshold value. For this purpose, the wind quality designation (WQD) concept is defined based on the wind potential duration, amount, and intensity on a threshold level. Its classifications are depicted on five risk percentage classes as “excellent,” “very good,” “good,” “fair,” and “weak. Apart from the classification, the change of WQD with wind speed threshold provides qualitative and quantitative wind speed energy production assessment. The specific objective of the article is to present theoretical WQD explanations on the basis of the most frequently employed two-parameter Weibull probability distribution function (PDF). The application is provided for Adiyaman City, Kahta meteorology station wind speed records from the Southeastern province of Turkey. It is noticed that there is no “Weak” category at this station and the most effective quality class is “Excellent” from 14 m/s to almost 27 m/s wind speeds. The average wind speed corresponds to about 62% WQD. Finally, the wind speed potential durations PDF abides by the logarithmic-normal PDF, whereas amount and intensity accord with the Weibull PDFs.

An improved approach to estimate sand-driving winds

Wind resource assessment has important economic and ecological implications. Many developing countries in arid and semiarid areas are caught in a dilemma between the development of wind energy and the threat of sandy desertification. Sand-driving winds are momentous for both generating wind energy and aeolian research. The estimation for the probability of sand-driving winds has been rarely studied. The ability of the two-parameter Weibull distribution to estimate high wind velocities is questioned and parameters appear to have no practical significance. Drift potential (DP) is a way of evaluating potential sand transport volume by sand-driving winds, but the relationship between DP and the wind energy of sand-driving winds has been rarely studied. In this paper, a function was constructed from the expressions of DP and the two-parameter Weibull probability distribution to improve the estimation of sand-driving winds. This is simple and applicable to arid and semiarid areas worldwide. The mean wind velocity and the mean wind power density at a height of 10 m around the Badain Jaran Sand Sea in China, are in the range between 2.64 and 4.79 m·s−1, and 27.61–165.61 W·m−2, respectively. The mean wind power density of sand-driving winds accounted for half or more of the total mean wind power density. The relationship among DP, the wind power density of sand-driving winds and the probability of sand-driving winds, was proved theoretically. Gentle winds and strong winds are distinguished by the drift wind velocity at which potential sand transport activities (potential lost wind power density) reach their maximum. The scale parameter dominates the mean and median wind velocity, and represents the effect of convection. The shape parameter characterizes the atmospheric stability. These results provide a basis for the wind energy development, improve the understanding of aeolian activities, and have implications for sand control engineering.

An improved model to estimate annual sand transport rate by sand-driving winds

Some of the surface on Earth, Mars, Venus, and Titan is covered by ripples, dunes, and other features formed by sand-driving winds. Many developing countries in arid and semiarid areas are caught in a dilemma between the threat of sandy desertification and the development of wind energy. The estimation for the probability of sand-driving winds has been rarely studied. The ability of two-parameter Weibull probability distribution to estimate sand-driving winds is questioned. Sand transport rate is used only for the evaluation of short-term aeolian activities. Drift potential (DP) is an accessible way of evaluating potential sand transport volume by sand-driving winds. However, the relationship among annual sand transport volume, DP and wind energy has been rarely studied. Sand-driving winds can be divided into gentle winds and strong winds, but it is hard to distinguish them and to quantify their effects on aeolian geomorphology. A function was constructed from expressions of sand transport rate and the two-parameter Weibull probability distribution to improve the estimation of sand-driving winds. On this basis, annual sand transport volume was accurately evaluated by sand-driving winds. This is applicable to arid and semiarid areas worldwide. The relationship among annual sand transport volume, DP and wind energy was analyzed from the perspective of dimensional analysis. Gentle winds and strong winds are distinguished by transport wind velocity at which aeolian activities on a sandy underlying surface reach the erosion–deposition balance, and which corresponds to annual maximum sand transport rate. On a sandy underlying surface strong winds control deposition, while gentle winds dominate wind erosion. The transport wind velocity is nearly constant, weakly related to the probability distribution of sand-driving winds. These results provide a basis for an improved understanding of aeolian activities as an important planetary surface process, sand control engineering, and wind energy development.

Silicone 3D Printing: Process Optimization, Product Biocompatibility, and Reliability of Silicone Meniscus Implants

A novel custom-made 3D silicone printer and two-part Ecoflex silicone resins were used to 3D-print standard-shaped silicone coupon and irregular-shaped meniscus structures via a heat-cured extrusion-based method. This article is segmented into three parts: (1) study on the effect of 3D printing parameters on dimensional accuracy and mechanical properties of 3D-printed silicone, (2) reliability and failure analysis of 3D-printed silicone according to ASTM D575 standards under monotonic and cyclic compressive loading, and (3) cytotoxicity of 3D-printed silicone by extraction method according to ISO 10993-12 for different extraction time and extract volume/surface area ratios. Based on analysis using regression method and analysis of variance, we found that the dimensional accuracy of lengths and widths is sensitive to both nozzle diameters and bed temperatures (BTs), while the height is only sensitive to BTs. Failure results were analyzed using the two-parameter Weibull probability distribution model and Weibull regression analysis and revealed that the Weibull modulus had a value greater than 1 in all groups, indicating an increasing failure rate with time for Ecoflex 30 and 50 meniscus implants. Results from quantitative cell proliferative assay exhibit statistically insignificant differences for all samples, pointing to the low cytotoxicity and excellent biocompatibility of printed silicone.

Optimisation and validation of full and half foam filled double circular tube under multiple load cases

In this study, numerical results are conducted to determine the deformation mode of foam filled double circular tubes, namely; half foam filled double circular tube (FD), and full foam filled double circular tube (DD) under oblique loading. To validate the simulation and experimental results, two-parameter Weibull probability distribution was used. The proposed function of the multi-objective optimisation design (MOD) process was based on the Finite Element Analysis results. The metamodels in were constructed to predict the crashworthiness criteria of specific energy absorption and peak crushing force under oblique impact loading. Also examined in the study were the MOD problems of the two structure types under multiple impact angles using the NSGA II algorithm. The findings from the study determined that the optimal full foam filled double circular tube had better crashworthiness under pure axial loading. While the optimal half foam filled, double circular tube had more space to enhance the crashworthiness under an oblique impact.

SKD11 절단금형치구용 소재의 마모손상에 관한 연구

This study is on wear damage of the material for a molding machine that be used at finally cutting of metal beam made in roll forming process of vehicle bump beam process line. SKD11 steel was used with the material for cutting mold jig. In the cutting mold jig, Ti diffusion heat treatment after vacuum heat treatment was carried out for upgrade of surface hardness and anti-wear. Also, the heat treatments by various methods were performed to compare the wear damage degree against above the existing heat treatment. Wear loss and friction coefficient were obtained from wear test. And, micro Vickers hardness values were compared with damaged parts or not of cutting mold jig. Micro Vickers hardness value appeared higher at the undamaged part by Ti diffusion heat treatment. The micro Vickers hardness well followed a two-parameter Weibull probability distribution.

Two and three-parameter Weibull distribution in available wind power analysis

Based on the current EU environmental policy, wind power industry has been growing fast in recent years. Knowledge of wind characteristics helps to define site requirements, choose a proper turbine design and estimate profits from the wind energy production.The paper describes and compares the techniques of available wind energy evaluation using Weibull distributions: two-parameter Weibull probability distribution, and three-parameter Weibull distribution. The two-parameter Weibull distribution is recognized as an appropriate model and the most widely used in the wind industry sector. In some cases, in which the probability of null wind is significant, the Weibull distribution cannot reveal good conformity for the low wind speed. In theory, it seems that the three-parameter Weibull distribution, which takes into account the frequency of null winds, may better represent wind ranges for the low wind speed.In the paper, the available wind energy is calculated for three different turbine locations. The results show that for the higher probability of the null wind the three-parameter Weibull distribution gives better results comparing to the two-parameter Weibull distribution and can be proposed as an alternative to wind energy estimation technique. Additional analyses confirm the observation.

Long-Term Wind Characteristics at Selected Locations in Mauritius for Power Generation

Interests in wind energy have gained impetus in many developed and developing countries worldwide during the last three decades. This is due to awareness of the population about the depletion of fossil fuels as well as Government campaigns and initiatives to encourage the use of renewable sources of energy. This work focuses on the wind energy potential at two selected locations (Plaisance and Vacoas) in Mauritius. The emphasis is to assess whether small-wind turbines have a potential in these regions for generation of power for domestic applications. Such wind turbines can range in size from 400 W to 10 kW depending on the amount of electricity to be generated. The assessment is based on the correlation of the local wind speed data to a two-parameter Weibull probability distribution in order to effectively estimate the average wind power density of the sites. Nearly 40 years of mean wind speed data is utilized. Of the two sites investigated it is found that Plaisance yielded the highest wind velocity (as compared to Vacoas). The study also estimates the energy output of six commercial small-wind turbines of capacity ranging from 1 kW to 3 kW at these two sites, placed at multiple heights.

Flexural Strength Analysis of Dense and Porous Sintered Clay Using Weibull Probability Distribution

This research analyzed the results of flexural strength of dense and porous mullite ceramic prepared from kaolin clay by using two-parameter Weibull probability distribution with different estimates. Chemical and physical characterizations of the clay were conducted using XRF, XRD and FESEM. The samples were tested using three point bending tests. The different estimates used in analyzing the results include mean rank, median rank, modified Kaplan Meier and Kaplan Meier. Among the estimates, Kaplan Meier was found to give the best fit with the highest correlation coefficient (R2) value. The porous ceramic had the higher value of Weibull modulus in comparison to the dense ceramic, while the characteristic strength (scale parameter) of the dense ceramic was higher than that of the porous ceramic. The micrograph of the porous ceramic showed a relatively balanced distribution of rounded pores, which is associated with the higher Weibull modulus in the porous ceramic.

Mapping wind power density for Zimbabwe: a suitable Weibull-parameter calculation method

The two-parameter Weibull probability distribution function is versatile for modelling wind speed frequency distribution and for estimating the energy delivery potential of wind energy systems if its shape and scale parameters, k and c, are correctly determined from wind records. In this study, different methods for determining Weibull k and c from wind speed measurements are reviewed and applied at four sample meteorological stations in Zimbabwe. The appropriateness of each method in modelling the wind data is appraised by its accuracy in predicting the power density using relative deviation and normalised root mean square error. From the methods considered, the graphical method proved to imitate the wind data most closely followed by the standard deviation method. The Rayleigh distribution (k=2 is also generated and compared with the wind speed data. The Weibull parameters were calculated by the graphical method for fourteen stations at which hourly wind speed data was available. These values were then used, with the assistance of appropriate boundary layer models, in the mapping of a wind power density map at 50m hub height for Zimbabwe.

Reliability model selection and validation using Weibull probability plot—A case study

In planning and operation of an electric power transmission system, accurate estimation of the reliability of its different components is a fundamental and challenging concern. Two-parameter Weibull probability distribution has been used frequently for this purpose. However, this model cannot capture all behaviours of the many different components in a transmission system. Over the years several alternative models have been proposed that are either derived from, or in some way related to, the two-parameter Weibull distribution. However, these alternatives have received little attention in reliability analysis of power transmission systems. It seems the lack of a simple and applicable guideline for model selection and validation is one of the main impediments. Many of these derived distributions (Weibull distribution family) have characteristic shape in the Weibull probability plot (WPP). Hence, WPP can be used as a tool for model selection and validation through the Weibull distribution family. This paper provides a WPP-based guideline and flowchart for selection of the most appropriate Weibull method. The application of the guideline is demonstrated by a case study using historical data of power transformer.

Weibull Cumulative Distribution Function for Modeling the Isothermal Kinetics of the Titanium-oxo-alkoxy Cluster Growth

The isothermal kinetics of the titanium-oxo-alkoxy cluster (TOAC) growth obtained in the controlled hydrolysis–condensation reaction of Ti(OPri)4 with H2O in n-propanol solution was investigated. Kinetic curves of the TOAC growth were measured at five different temperatures: 298, 303, 308, 313, and 318 K. It was established that the kinetic curves of the TOAC growth could be mathematically modeled by the cumulative two-parameter Weibull probability distribution function of the growth time (t) in a wide range of the degree of growth (0.05 ≤ DG ≤ 0.95). It was found that the dependencies of the shape parameter (β) and scale parameter (η) on temperature (T) can be described by polynomial functions. The activation energy of TOAC growth (Ea,DG), as well as the pre-exponential factor (ln ADG) for different degrees of growth, were calculated using Friedman’s isoconversional method. On the basis of knowing Ea,DG(DG) dependence, the procedure for calculating isothermal dependence of Ea vs growth time was described. The isothermal probability distribution density functions of Ea for the TOAC growth process were calculated. It was established that the conversion kinetic curves of the TOAC growth process could be fully described by a model of the infinite number of parallel first-order growth reactions with time-varying value of the pre-exponential factor and activation energies which are distributed in accordance with a specific function of Ea.

Application of Weibull distribution function for modelling the isothermal kinetics of the titanium-oxo-alkoxy clusters growth

The isothermal kinetics of the titanium-oxo-alkoxy clusters (TOAC) growth obtained in the controlled hydrolysis–condensation reaction of Ti(OPri)4 with H2O in n-propanol solution was investigated. Kinetic curves of the TOAC growth were measured at five different temperatures: 298K, 303K, 308K, 313K and 318K. It was established that the kinetic curves of the TOAC growth could be mathematically modelled by the cumulative two-parameter Weibull probability distribution function of the growth time (t). The forms of functional dependencies on temperature for the shape (β) and the scale (η) parameters were determined. It was shown that the isothermal TOAC growth is a complex kinetic reaction and the activation energy of growth (Ea,α) for different degrees of growth (α), was calculated. Based on knowing Ea,α(α) dependence, the procedure for calculating isothermal dependence of activation energy (Ea) on growth time, was described. The isothermal probability distribution density functions of Ea for TOAC growth process, were calculated. It was established that the isothermal kinetics of the TOAC growth can be modelled by an infinite number of parallel first-order growth reactions with time-varying value of the pre-exponential factor (lnA) and activation energies which are distributed in accordance with a specific function of Ea.

Theoretical derivation of wind power probability distribution function and applications

The instantaneous wind power contained in the air current is directly proportional with the cube of the wind speed. In practice, there is a record of wind speeds in the form of a time series. It is, therefore, necessary to develop a formulation that takes into consideration the statistical parameters of such a time series. The purpose of this paper is to derive the general wind power formulation in terms of the statistical parameters by using the perturbation theory, which leads to a general formulation of the wind power expectation and other statistical parameter expressions such as the standard deviation and the coefficient of variation. The formulation is very general and can be applied specifically for any wind speed probability distribution function. Its application to two-parameter Weibull probability distribution of wind speeds is presented in full detail. It is concluded that provided wind speed is distributed according to a Weibull distribution, the wind power could be derived based on wind speed data. It is possible to determine wind power at any desired risk level, however, in practical studies most often 5% or 10% risk levels are preferred and the necessary simple procedure is presented for this purpose in this paper.

Statistical Characterization of Fiber-Reinforced Polymer Composite Material Properties for Structural Design

A consistent basis for statistically reducing fiber-reinforced polymer (FRP) composite material property test data for load and resistance factor design (LRFD) of composite structures is developed in this paper. A two-parameter Weibull probability distribution is recommended for modeling both strength and stiffness properties. Consistent with practice for other materials used in structural engineering applications, the 5-percentile value of strength of coupons and components, as well as modulus values, appropriately adjusted for the small size of typical data samples, is recommended for the nominal value of strength for LRFD applications. Statistical uncertainty due to small sample size in the data reduction process is accounted for through the use of a data confidence factor, which is the tolerance limit defined as the 80th percent lower confidence level of the 5-percentile value of the population. With the nominal values so determined, appropriate resistance factors for LRFD-based design codes can be de...

A Simple Method for Evaluating Flaw Distributions Responsible for Size Effects in the Strength of Small-Scale Silicon Specimens

A simple means of deconvoluting the size distributions of fracture-controlling flaws from Weibull strength plots for small-scale specimens is proposed. The method makes use a power-law distribution function, empirical in form but self-consistent with a conventional two-parameter Weibull probability distribution. Literature data for single-crystal silicon beam specimens covering a range of widths from mm to nm are analyzed according to this procedure. The analysis indicates a reduction in scatter in addition to increase in strength with diminishing specimen size, and quantifies a systematic tightening in flaw distribution associated with refinement in fabrication method.

Analysis of wind data and wind energy potential along the northern coast of Senegal

Senegal is one of the developing countries and its dependence upon imported fossil fuels can only be offset by the sustained exploitation of its indigenous resources. Wind energy is renewable and environment friendly, which can be harnessed for various end-uses. A precise knowledge of wind energy regime is a pre-requisite for the efficient planning and implementation of any wind energy project. However, due to the absence of a reliable and accurate Senegalese Wind Atlas, further studies on the assessment of wind energy in Senegal are necessary. The main purpose of this paper is to present and to perform an investigation on the wind energy potential of the northern coast of Senegal along the Atlantic Ocean. Therefore, in this study, wind data collected over a period of two years at five different locations in this region of Senegal were evaluated in order to figure out the wind energy potential along the northern coast of Senegal. The data from selected stations were analyzed using the two-parameter Weibull probability distribution function. With an annual mean wind speed of 3.8 m/s, an annual energy of 158 kWh/m2 could be extracted. It is found that the potential uses of wind energy in these locations are for water pumping in rural areas. The study presented here is also an attempt to promote wind energy in Senegal and to bridge the gap in order to create prospective Wind Atlas of Senegal.

Bimodal versus Weibull Wind Speed Distributions: An Analysis of Wind Energy Potential in La Venta, Mexico

The International Standard IEC 61400-12 and other international recommendations suggest the use of the two-parameter Weibull probability distribution function (PDF) to estimate the Annual Energy Production (AEP) of a wind turbine. Most of the commercial software uses the unimodal Weibull PDF as the default option to carry out estimations of AEP, which in turn, are used to optimise wind farm layouts. Furthermore, AEP is essential data to assess the economic feasibility of a wind power project. However, in some regions of the world, the use of these widely adopted and recommended methods lead to incorrect results. This is the case for the region of La Ventosa in Mexico, where the frequency of the wind speed shows a bimodal distribution. In this work, mathematical formulations by using a Weibull PDF and a bimodal distribution are established to compare the AEP, the capacity factor and the levelised production cost for a specific wind turbine. By combining one year of wind speed data with the hypothetic power performance of the Vestas V27-225 kW wind turbine, it was found that using the Weibull PDF underestimates AEP (and thus the Capacity Factor) by about 12%.