Estimation of extreme response and failure probability of wind turbines under normal operation using probability density evolution method

Abstract

Estimation of extreme response and failure probability of structures subjected to ultimate design loads is essential for structural design of wind turbines according to the new standard IEC61400-1. This task is focused on in the present paper in virtue of probability density evolution method (PDEM), which underlies the schemes of random vibration analysis and structural reliability assessment. The short-term rare failure probability of 5-mega-watt wind turbines, for illustrative purposes, in case of given mean wind speeds and turbulence levels is investigated through the scheme of extreme value distribution instead of any other approximate schemes of fitted distribution currently used in statistical extrapolation techniques. Besides, the comparative studies against the classical fitted distributions and the standard Monte Carlo techniques are carried out. Numerical results indicate that PDEM exhibits well-pleasing accuracy and high efficiency for dynamic reliability analysis of complex engineering structures. Typically, the estimation values of design quantities, such as ultimate deformation and ultimate stress, are relevant to the low structural failure probability in the order 10. So the IEC61400-1 standard recommends the statistical extrapolation techniques to determine nominal design load during the operation of wind turbines. The previous researches have shown that the predicted design values depend strongly upon the relevance of the approaches to extract extreme value from raw times-series process such as the Method of Global Maxima or Peak-Over-Threshold (POT) method and the type of extreme value distribution. Many choices of distributions have been suggested to fit data, such as 3-parameter Weibull, Gumbel, Lognormal, etc. Nevertheless, due to the inherent uncertainties in the fitting type, these methods cannot achieve accurate estimates of the low failure probability of this highly nonlinear system influenced by pitch controller, i.e. it is not clear that which type of extreme value distribution should be used in different situations. Alternative to curve fitting and extrapolation of extreme values, simulation techniques are introduced to the estimation of the low-probability events, such as Enhance Monte Carlo method and Markov Chain Monte Carlo. Advanced simulation techniques provide very good and consistent estimates for the general structural dynamic problem (fixed speed wind turbines). While for the variable-speed pitch-controlled wind turbines because of the inherent nonlinearity, they might be more or less encountered with computational efficiency and computational costs. Recently the probability density evolution method (PDEM) has demonstrated its values that successfully paves a new way towards the realization of the evolution of the probability density function (PDF) of a stochastic process, and gives a more efficient scheme for the estimation of the dynamic reliability of general linear or nonlinear systems. The objective of this work is to obtain the short-term rare failure probability of 5-mega-watt wind turbine at a certain mean wind speed through the extreme value distribution solved by PDEM, instead of any other approximate schemes of fitted distribution currently used in statistical extrapolation technique. Before that, the wind turbine model and physical stochastic turbulence model are introduced, which are followed by the outline of the method associated with extreme value distribution. In the illustrative example, the estimated response value and failure probability by PDEM are compared with those by regular fitted distributions and Standard Monte Carlo. The effect of turbulence level is also considered. The result indicates that PDEM is consistent, accurate and efficient for relevant dynamic reliability analysis problem.