Reliability-based Calibration of Partial Safety Factors for Wind Turbine Blades

1. Reliability-based Calibration of Partial Safety Factors for Wind Turbine Blades Henrik Stensgaard Toft(1) Kim Branner(2) Peter Berring(2) John Dalsgaard Sørensen(1,2) (1)Aalborg University, Denmark (2)Risø-DTU, Denmark

2. Outline of Presentation Introduction Reliability-based design Modelling of uncertainties Illustrative example: Reliability of wind turbine blade Conclusions & Future work [www.lmwindpower.com]

3. Wind Turbine Blades Wind turbine blades consist normally of a main spar and an aerodynamic shell. Blades are typically made of glass fiber reinforced epoxy, but carbon fibers are also used. Optimal structural design of the blades will lead to load reduction on other major wind turbine component (e.g. tower and foundation). [www.lmwindpower.com]

4. Observed Annual Failure Rates and Downtime [ISET, 2008]

5. Reliability-based Design Limit state equation: Probability of failure: Reliability index: Reliability Estimation based on Finite Element Analysis Evaluation of large and nonlinear FE models is very time consuming. This demands for a simple and fast way to estimate the reliability. Smart simulation methods (e.g. importance sampling). First or Second Order Reliability methods (FORM/SORM). Response-surface method

6. Design and Limit State Equation Design equation according to IEC 61400-1: Limit state equation: Response surface technique: The constants a, bi and ci are determined by evaluating the limit state equation (FE- model) in the points for each stochastic variable Xi. The partial safety factors  can be calibrated in order to obtain a target reliability index t for each failure mode.

7. Modelling of Uncertainties The uncertainties can be divided into the following four groups: Physical uncertainty (aleatory) Measurement uncertainty (epistemic) Statistical uncertainty (epistemic) Model uncertainty (epistemic) The uncertainties are modelled by stochastic variables. [www.lmwindpower.com]

8. Uncertainty – Material Properties Stochastic models for the material properties have been modelled from micro-scale using the properties of the fiber and matrix (model uncertainty included). Scatter between the uncertainties in the literature is observed due to e.g. variations in the manufacturing procedure and basic material.

9. Uncertainty – Load-effect The uncertainty related to the load-effect corresponds to DLC 1.1 in IEC 61400-1 (normal operation – blade out-of-plane bending). The physical uncertainty related to the load-effect is estimated from statistical load extrapolation for the NREL 5MW reference wind turbine.

10. Uncertainty – Failure Prediction Failure of the blade is estimated by First Ply Failure (no redundancy and damage tolerance). Ply failure is estimated by the Tsai-Wu criteria. The uncertainty related to failure predictions is estimated from test results in the World Wide Failure Exercise. Based on UD and MD-laminates. Final failure - degradation of the structure is taken into account. Part B: XR~LN(1.14; 0.30) Part A: XR~LN(1.31; 0.40)

11. Illustrative Example: Reliability Wind Turbine Blade Blade for a 1.5MW pitch controlled wind turbine (shortened after 25.4m). Geometrical nonlinear finite element analysis (mesh size 40x40mm). Load case: Combined edgewise and flapwise loading (normal operation).

12. Illustrative Example: Reliability Wind Turbine Blade Buckling of main spar cap at 3.4m, 9.0m, 11.6 and 13.6m. First ply failure (Tsai-Wu) in UD-lamina due to high strains in transverse direction (9m from blade root). Failure mode seems robust related to changes of the material properties.

13. Illustrative Example: Reliability Wind Turbine Blade The annual reliability is estimated using the response surface technique and Monte Carlo simulation / FORM. Implicit target reliability in IEC 61400-1: =3.1 corresponding to PF=10-3.

14. Illustrative Example: Reliability Wind Turbine Blade The most important stochastic variables are determined from the-vector estimated by FORM: Model uncertainty failure criteria XR (2=0.60). Model uncertainty exposure Xexp (2=0.26). The material properties has in general only a small influence. The estimated reliability varies significantly dependent on the points which is used for estimating the response surface. Especially the points for the load and failure criteria are important.

15. Conclusion Stochastic models for the uncertainty related to the material properties, load-effect and failure prediction for wind turbine blades have been proposed. The reliability have of the blade have been estimated using the response surface technique based on nonlinear finite element analysis. The estimated reliability level is slightly lower than the target reliability in IEC 61400-1. Future Work The uncertainty related to failure prediction should be studied further in order to improve the stochastic models. The reliability is sensitive to the points used for evaluating the response surface. This demands for a more robust way of estimating the response surface. Estimate the influence of system effects (redundancy) and damage tolerance.

16. Reliability-based Calibration of Partial Safety Factors for Wind Turbine Blades Henrik Stensgaard Toft(1) Kim Branner(2) Peter Berring(2) John Dalsgaard Sørensen(1,2) (1)Aalborg University, Denmark (2)Risø-DTU, Denmark