Bayesian spline method for assessing extreme loads on wind turbines

This study presents a Bayesian parametric model for the purpose of estimating the extreme load on a wind turbine. The extreme load is the highest stress level imposed on a turbine structure that the turbine would experience during its service lifetime. A wind turbine should be designed to resist such a high load to avoid catastrophic structural failures. To assess the extreme load, turbine structural responses are evaluated by conducting field measurement campaigns or performing aeroelastic simulation studies. In general, data obtained in either case are not sufficient to represent various loading responses under all possible weather conditions. An appropriate extrapolation is necessary to characterize the structural loads in a turbine's service life. This study devises a Bayesian spline method for this extrapolation purpose, using load data collected in a period much shorter than a turbine's service life. The spline method is applied to three sets of turbine's load response data to estimate the corresponding extreme loads at the roots of the turbine blades. Compared to the current industry practice, the spline method appears to provide better extreme load assessment.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS670 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical Analysis and Assessment of Wind Energy Potential in Sarajevo, Bosnia and Herzegovina

In this paper, wind energy potential in Sarajevo area, Bosnia and Herzegovina, was analyzed statistically. The analysis of wind energy potential was performed based on measured wind data in a one-year period from 1 January to 31 December 2019. Measured data were obtained on the basis of a meteorological station installed on the roof of the building of the Faculty of Mechanical Engineering in Sarajevo at 30 m height. Measured wind characteristics were statistically analyzed using the Weibull and Rayleigh distribution functions. The Weibull parameters were obtained using two methods, the energy pattern factor method and the maximum likelihood method, and both methods were used to find the Weibull parameters and the wind power density. The results of this investigation showed that the analyzed place falls under Class 1 of the international system of wind classification as the mean annual wind velocity recorded in the analyzed area was 1.215 m/s and the corresponding annual mean power density was estimated to be 6.7 W/m2 at 30 m height. The results show that the available wind energy potential to generate electricity in Sarajevo is low and wind power cannot be used to meet the energy needs in that region

Vertical wind profile characterization and identification of patterns based on a shape clustering algorithm

Wind power plants are becoming a generally accepted resource in the generation mix of many utilities. At the same time, the size and the power rating of individual wind turbines have increased considerably. Under these circumstances, the sector is increasingly demanding an accurate characterization of vertical wind speed profiles to estimate properly the incoming wind speed at the rotor swept area and, consequently, assess the potential for a wind power plant site. The present paper describes a shape-based clustering characterization and visualization of real vertical wind speed data. The proposed solution allows us to identify the most likely vertical wind speed patterns for a specific location based on real wind speed measurements. Moreover, this clustering approach also provides characterization and classification of such vertical wind profiles. This solution is highly suitable for a large amount of data collected by remote sensing equipment, where wind speed values at different heights within the rotor swept area are available for subsequent analysis. The methodology is based on z-normalization, shape-based distance metric solution and the Ward-hierarchical clustering method. Real vertical wind speed profile data corresponding to a Spanish wind power plant and collected by using a commercialWindcube equipment during several months are used to assess the proposed characterization and clustering process, involving more than 100000 wind speed data values. All analyses have been implemented using open-source R-software. From the results, at least four different vertical wind speed patterns are identified to characterize properly over 90% of the collected wind speed data along the day. Therefore, alternative analytical function criteria should be subsequently proposed for vertical wind speed characterization purposes.The authors are grateful for the financial support from the Spanish Ministry of the Economy and Competitiveness and the European Union —ENE2016-78214-C2-2-R—and the Spanish Education, Culture and Sport Ministry —FPU16/042

Statistical methods for estimating tephra source and dispersal : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Palmerston North, New Zealand

Tephra refers to any pyroclastic fragments ejected from a volcanic vent and its dispersal is one of the major hazards with explosive eruptions. The attenuation of tephra fall thickness is most commonly estimated after contouring field measurements into smooth isopachs. I explicitly describe the variability in thickness by using a semiempirical tephra attenuation relation as a link function. This opens the way to fitting models to actual tephra observations through maximum likelihood estimation (MLE). The method is illustrated using data published from the 1973 Heimaey eruption in Iceland. Complex eruptions commonly produce several phases of tephra fall from multiple vents. When attempting to precisely reconstruct past eruptions from the geological record alone, separate phases are often indistinguishable. Augmented by a mixture framework, the MLE attenuation model was able to identify the sources and directions of tephra deposition for the 1977 Ukinrek Maars eruption in Alaska, US, from only the tephra thickness data. It was then applied to the unobserved 1256 AD Al-Madinah eruption in Saudi Arabia. The estimation of the spatio-temporal hazard from a monogenetic volcanic field is criti- cally dependent on a reconstruction of past events. The Auckland Volcanic Field (AVF) has produced about 50 volcanoes in the last 250,000 years. Although inconsistent, age data for many of these volcanoes exist from various dating methods with various re- liabilities. The age order of some pairs is also known due to the overlaying of lavas (stratigraphy). A discussion is provided on how informative priors are obtained via ex- pert elicitation, on both the individual volcano ages, and the reliabilities of the dating methods. A possible Bayesian model for reconciling the available inconsistent volcano age data to estimate the true eruption ages is also discussed. To improve these eruption age estimates, some of the volcanoes can be correlated with the better dated tephra layers recovered from five maars in the field. The likelihood of any combination of volcano and tephra, incorporating the spatial variability based on the attenuation model and temporal components, is evaluated and is maximised numer- ically using linear programming. This statistical matching provides an improvement in the volcano age-order model and age estimates of the volcanoes in the AVF