Simulating the dynamics of wind turbine blades: part II, model validation and uncertainty quantification

Abstract

Verification and validation (V&V) offers the potential to play an indispensable role in the development of credible models for the simulation of wind turbines. This paper highlights the development of a three‐dimensional finite element model of the CX‐100 wind turbine blade. The scientific hypothesis that we wish to confirm by applying V&V activities is that it is possible to develop a fast‐running model capable of predicting the low‐order vibration dynamics with sufficient accuracy. A computationally efficient model is achieved by segmenting the geometry of the blade into six sections only. It is further assumed that each cross section can be homogenized with isotropic material properties. The main objectives of V&V activities deployed are to, first, assess the extent to which these assumptions are justified and, second, to quantify the resulting prediction uncertainty. Designs of computer experiments are analyzed to understand the effects of parameter uncertainty and identify the significant sensitivities. A calibration of model parameters to natural frequencies predicted by the simplified model is performed in two steps with the use of, first, a free–free configuration of the blade and, second, a fixed–free configuration. This two‐step approach is convenient to decouple the material properties from parameters of the model that describe the boundary condition. Here, calibration is not formulated as an optimization problem. Instead, it is viewed as a problem of inference uncertainty quantification where measurements are used to learn the uncertainty of model parameters. Gaussian process models, statistical tests and Markov chain Monte Carlo sampling are combined to explore the (true but unknown) joint probability distribution of parameters that, when sampled, produces bounds of prediction uncertainty that are consistent with the experimental variability. An independent validation assessment follows the calibration and is applied to mode shape vectors. Despite the identification of isolated issues with the simulation code and model developed, the overarching conclusion is that the modeling strategy is sound and leads to an accurate‐enough, fast‐running simulation of blade dynamics. This publication is Part II of a two‐part effort that highlights the V&V steps required to develop a robust model of a wind turbine blade, where Part I emphasizes code verification and the quantification of numerical uncertainty. Approved for unlimited public release on August 26, 2011, LA‐UR‐11‐4997. Copyright © 2012 John Wiley & Sons, Ltd.

Quantification and reduction of uncertainties in a wind turbine numerical model based on a global sensitivity analysis and a recursive Bayesian inference approach

“…Such methods to reduce uncertainties involved in models used in wind energy are currently investigated 11 . In the literature, Van Buren et al 12 have developed a framework to quantify and reduce such uncertainties based on ANOVA decomposition and Bayesian inference. However, our approach is innovative due to the fact that we are dealing with a high‐fidelity wind turbine numerical model and by the recursive aspect of our inference procedure.…”

Aeroelastic validation and Bayesian updating of a downwind wind turbine

“…Calibration of simpler models (RANS, Jensen wake models) using high‐fidelity large eddy simulation (LES) data has been implemented to reduce the computational expense . The model parameters of a simplified finite element‐based structural model are calibrated using Bayesian inference in order to predict the blade dynamics . Modal decomposition methods have also been applied to high‐fidelity simulation data in order to obtain simplified models for studying wake dynamics .…”

Development of robust and adaptive controller for blade testing machine

“…[7]. The load history could be approximated by wind turbine blade simulations [8,9]. The equivalent fatigue test load is obtained by matching the damage caused by 20-year-design load spectrum [7].…”