Bayesian method for estimating Weibull parameters for wind resource assessment in the Equatorial region: a comparison between two-parameter and three-parameter Weibull distributions

The two-parameter Weibull distribution has garnered much attention in the assessment of windenergy potential. The estimation of the shape and scale parameters of the distribution has broughtforth a successful tool for the wind energy industry. However, it may be inappropriate to use thetwo-parameter Weibull distribution to assess energy at every location, especially at sites wherelow wind speeds are frequent, such as the Equatorial region. In this work, a robust technique inwind resource assessment using a Bayesian approach for estimating Weibull parameters is firstproposed. Secondly, the wind resource assessment techniques using a two-parameter Weibulldistribution and a three-parameter Weibull distribution which is a generalized form of twoparameterWeibull distribution are compared. Simulation studies confirm that the Bayesianapproach seems a more robust technique for accurate estimation of Weibull parameters. Theresearch is conducted using data from seven sites in Equatorial region from 1o N of Equator to 19oSouth of Equator. Results reveal that a three-parameter Weibull distribution with non-zero shiftparameter is a better fit for wind data having a higher percentage of low wind speeds (0-1 m/s) andlow skewness. However, wind data with a smaller percentage of low wind speeds and highskewness showed better results with a two-parameter distribution that is a special case of threeparameterWeibull distribution with zero shift parameter. The results also demonstrate that theproposed Bayesian approach and application of a three-parameter Weibull distribution areextremely useful in accurate estimate of wind power and annual energy production.

Nondestructive Photoelastic and Machine Learning Characterization of Surface Cracks and Prediction of Weibull Parameters for Photovoltaic Silicon Wafers

A nondestructive photoelastic method is presented for characterizing surface microcracks in monocrystalline silicon wafers, calculating the strength of the wafers, and predicting Weibull parameters under various loading conditions. Defects are first classified from through thickness infrared photoelastic images using a support vector machine learning algorithm. Characteristic wafer strength is shown to vary with the angle of applied uniaxial tensile load, showing greater strength when loaded perpendicular to the direction of wire motion than when loaded along the direction of wire motion. Observed variations in characteristic strength and Weibull shape modulus with applied tensile loading direction stem from the distribution of crack orientations and the bulk stress field acting on the microcracks. Using this method it is possible to improve manufacturing processes for silicon wafers by rapidly, accurately, and nondestructively characterizing large batches in an automated way.

Reliability of Electric Submersible Pumps ESP & Determination of Weibull Parameters for Failure Characterization, Ecuador Case Study

The current research focuses on data modeling of ESP (Electric Submersible Pumps) reliability by obtaining, through mathematical calculations, the parameters that define the Weibull shape (β), scale (ɳ) and location (ϒ) parameters. The scale parameter ɳ is the characteristic life at which 63.2% of the population has failed. These parameters can be helpful in characterizing failure behavior and the ESP system run life. This research stemed from the need to better understand failure behavior to improve maintenance program design and enhance equipment reliability.160 wells from four fields (7-21, 56, 57) of the Ecuadorian Oriente basin were analyzed. Well selection considered only the mechanic failures and excluded other type of failures leaving aside the ESP failures caused by operative issues (reservoir, completions, workover, redesign, zone change). Three mathematical tools were applied to determine the Weibull parameters more accurately. Another type of analysis could have limited this research since the normal distribution shows limitations with asymmetric data, and the exponential distribution assumes a fixed failure rate, but the ESP failure behavior is asymmetric and the failure rate is variable through time due to factors such as wear and also infant failures (e.g. installation errors). For these reasons, Weibull distribution is the best option because it fits asymmetric data better and it has a variable failure rate. Determining the value of the Weibull parameters can assist in answering questions such as: what percentage of failures is expected to occur in time? How many failures can be expected before the warranty period? When should regular maintenance be scheduled? Ultimately, Weibull parameters are the basis of any future reliability analysis. The Weibull parameters obtained in this study can be applied for future ESP reliability analyzes that are being operated in any field in the Oriente Basin of Ecuador. From the research, two relevant findings were foundThere are a significant number of failures in the initial stage of operation of the pumps,, which could be associated with the installation of the equipment, and the failure risk is drastically reduced in the equipment that reaches life time similar to the characteristic life (ɳ)and pumps that operate without failure to a time similar to characteristic life (ɳ) continue to follow this trend throughout their operating life. Initial stage failures are presumed to be associated with unanticipated conditions: solid binding, design errors, defective equipment, or assembly of equipment with reused and new parts. The performance of the ESP affects the productivity of the wells and therefore will influence decision-making to develop a field. The reliability of the ESP systems can favor the productivity of a field when the equipment works within its efficiency range without showing recurrent failures. This significantly improves field production costs and profitability.

Comparison of numerical methods in estimating Weibull parameters to install a sustainable wind farm in mount Bamboutos, Cameroon

Purpose The purpose of this paper is to evaluate the wind energy potential of Mount Bamboutos in Cameroon by comparing nine numerical methods in determining Weibull parameters for the installation of a sustainable wind farm. Design/methodology/approach By using statistical analysis, the analysis of shape and scale parameters, the estimation of the available wind power density and wind direction frequency distributions, the objective of this paper is to compare nine numerical methods in estimating Weibull parameters for the installation of a sustainable wind farm in Mount Bamboutos, Cameroon. Findings The results suggested that the minimum and maximum values of the standard deviation occurred in the months of May and November 2016, respectively. The graphical method appeared to be the most effective method with the maximum value of variance and minimum values of chi-square and RMSE. The scale factor parameter values indicated that Mount Bamboutos hills were a potential site for electricity generation. The analysis of wind power density showed that it reached the maximum and minimum values in February and September, respectively. The wind direction frequency distributions showed that the prevailing wind directions were North-East. Originality/value The wind energy potential of Mount Bamboutos in Cameroon was performed by using nine numerical methods. Therefore, it could be effective to have a prediction model for the wind speed profile. The analysis of wind power density showed that it reached the maximum and minimum values in February and September, respectively. The wind direction frequency distributions showed that the prevailing wind directions were North-East.