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

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... onally 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. dynamics of wind turbine blades, which capture all of the kinetic energy transported by the surrounding flow of wind, and improve the reliability of power generation from wind plants. 5 Better understanding of the wind turbine blades is essential, since the blades carry most of the structural loads that become imparted on the entire wind turbine. Better models would make more accurate predictions of performance, which would mitigate the operation and maintenance expenses associated with wind energy. These expenses currently start as low as $5/MWh but climb to costs as high as $20/MWh over a 20 year evolution of service. 6 Modeling and simulation (M&S) offers a quicker, safer and more economical alternative to the conventional cycle of designing, prototyping and testing to study wind turbine blade behavior. 7 The versatility of modeling can be used to predict the response to many complex load cases, 8 but only idealized loads can usually be implemented in full-scale experiments. 9 In addition, parametric studies of damage to wind turbine blades can be investigated in an economical way through M&S, whereas the feasibility of such experimental campaigns would be limited because of the cost and safety implications. Because of demands for faster turn-around times and the, sometimes, limited access to computing resources, there is a growing need to develop simplified 'engineering' models that can keep parametric and calibration studies to a manageable size. 10 It is also expensive, both in terms of memory management and time to solution, to couple a computational fluid dynamics (CFD) code to flexible dynamics models of the blades and, potentially, models of structural damage, to develop credible simulations of entire wind plants. 11 One approach to reduce this computational burden is to simplify the flexible dynamics of the wind turbine blade to speed up the calculations without, to the extent possible, sacrificing the prediction accuracy. The study presented in this paper, together with a companion publication, demonstrates the application of verification and validation (V&V) technology to achieve these goals. 12 Our objective is to develop a structural model that, while simplified as much as possible, still captures the dynamics of interest. The V&V activities deployed in the companion paper (Mollineaux et al. 12 ) and in this paper support essential steps of the model development process to guarantee that the simplifications introduced are justified for the intended purpose. V&V also serves the purpose of quantifying the experimental variability and numerical uncertainty (discussed in Mollineaux et al. 12 ) and the model parameter uncertainty (discussed in this paper). As explained in Mollineaux et al. 12 , the structure investigated is the 9 m, all-composite CX-100 blade designed at the Sandia National Laboratories. The finite element (FE) software is ANSYS version 12.1. The simplified model is developed on the basis of an as-accurate-as-possible description of the geometry obtained from design specifications. However, implementation of the materials relies on a strong assumption: the cross-sectional areas for the blade are modeled as smeared and isotropic material properties instead of modeling the multiple composite layers embedded in the epoxy matrix. The overarching goal of this effort is to demonstrate the extent to which V&V can be integrated to the model development of a simplified yet validated FE model, which delivers an acceptable level of predictive capability. Validated models that satisfy given time-to-solution requirements for the application of interest provide a competitive advantage. Developing a predictive capability motivates the need to quantify the uncertainty introduced by assumptions imposed during the development of an FE model. Understanding the approximate behavior of a model renders it imperative to take into consideration all sources of uncertainty, as discussed in Section 2. Section 3 provides a cursory overview of the FE model of the CX-100 blade. (See Mollineaux et al. 12 for an in-depth discussion.) Section 4 discusses three V&V activities: the propagation of uncertainty from input parameters of the FE model to output predictions, sensitivity analysis and effect screening, and model calibration. These investigations are applied to low-order resonant frequencies of the blade according to a two-step approach. The response of the free-free model, followed by the fixed-free model, is evaluated, in an effort to decouple our understanding of material properties from that of model parameters that represent the boundary condition compliance. Section 5 presents an independent validation assessment on the basis of the ability of the calibrated model to correlate predicted and measured mode shape deflections. The implications and limitations of this study are discussed in Section 6. REVIEW OF PERTINENT LITERATURE Assumptions and simplifications, which are emphasized to only be able to provide an approximation of reality, are regularly imposed in numerical models. For example, beam property extraction methods, which require low computational cost and can be used for fast-running calculations, have been developed. 13 However, one study attempting to model a wind turbine system found that neglecting the effect of damping produced predictions with low goodness of fit to the experimental data. 14 This study, along with similar observations from other disciplines, suggests that not accounting for the uncertainty introduced by the simplifications and modeling assumptions can have a degrading effect on the quality of model predictions. Another consideration is the relationship between goodness of fit to test data and the predictive capability of a model. It can be shown that fidelity to data, robustness to assumptions and predictive capability are antagonistic attributes of any family of models. 15 This can be described using the case of over-fitting, which happens when a model produces accurate predictions for configurations to which it was calibrated. But this may come at the cost of reducing its predictive capability, that is, the accuracy of its predictions when attempting to simulate other, non-tested configurations. Understanding these 742 Wind Energ. 2013; 16:741-758