the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Aug 2023
Uncertainty quantification of structural blade parameters for the aeroelastic damping of wind turbines: a code-to-code comparison
Abstract. Uncertainty quantification (UQ) is a well-established category of methods to estimate the effect of parameter variations on a quantity of interest, based on a solid mathematical fundament. In the wind energy field most UQ studies were focused on the sensitivity of turbine loads. This article presents a framework, wrapped around a modern Python UQ library, to analyze the impact of uncertain turbine properties on aeroelastic stability. The UQ methodology applies a polynomial chaos expansion surrogate model to increase the numerical efficiency. A comparison is made between different wind turbine simulation tools on the engineering model level (alaska/Wind, Bladed, HAWC2/HAWCStab2 and Simpack). Two case studies are used to demonstrate the effectiveness of the method to analyze the sensitivity of the aeroelastic damping of an unstable turbine mode to variations of structural blade cross section parameters. The code-to-code comparison shows a good agreement between the simulation tools for the reference model, but also significant differences in the sensitivities.
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CC1: 'Comment on wes-2023-80', Leonardo Bergami, 31 Aug 2023
Thank you for the very interesting work.
I am not a reviewer, would just like to share a couple of thoughts/comments from reading through the pre-print, in case they could be useful:
- It is not clear from the text how the turbine controller is setup in linear and non-linear simulations. Typically, by default the linear stability analysis tools assume an open-loop configuration, ie. they model a system where the steady equilibrium state is assumed to be maintained without any intervention from a controller (either in torque/speed or pitch). A closed-loop linear analysis requires a linearized version of the controller to be included in the analysis (aero-servo-elastic analysis in HawcStab2 terminology).
The open loop configuration (no interaction with a controller) could be tricky to reproduce in non-linear aeroelastic simulations where a specific steady operational point should be kept.
The manuscript could benefit from better explaining whether a open-loop or a closed-loop configuration is reproduced in both the linearized and non-linear simulations, and if a closed-loop configuration is used also in the linearized tools, how the controller linearization is performed.
A mismatch in between open and closed loop, or in the linearization of the controller behavior could possibly (partly?) explain some of the mismatch observed between linear tools and DMD estimations especially around rated wind speed (where the controller response is typically less linear).
- In the uncertainty quantification case studies (section 3) the operating parameters of pitch and rpm are kept constant. Although practical this could lead to a variation in the steady state and in cases steady state that would not happen in real operation. Variations of eg. torsional stiffness and/or shear center would modify the angle of attack distribution along the blade, and thus change the power output when not compensated for by changes in pitch (whereas in more realistic operation nominal power output would be kept above rated). In other words, keeping a steady state condition more “similar” to the baseline one in terms of eg. power output, loading of the blades and aoa distribution would require instead a variation also of the pitch angle. Without changing the pitch, large variations of torsion or shear would actually bring the blade to be loaded in a completely different way from baseline, and thus make it hard to distinguish whether the observed changes in damping come from the completely changed loading distribution, or from changes in aeroelastic behavior per se.
- Page 8. L.165. Isn’t it the other way around? HS2 and BladedLin have better agreement on 2nd modes than 1st?
- Small “appearance” comment, please consider whether color sequences a bit more friendly towards color blindness could be used in the plots.
Thank you for sharing this good work.
Best regards
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2023-80-CC1 -
AC1: 'Reply on CC1', Hendrik Verdonck, 01 Sep 2023
Dear Leonardo Bergami,
Thank you for the very interesting and valuable comments. In the following I will try to answer your questions and address how we will adapt the paper accordingly.
- We do indeed use an open-loop configuration for the linearized models. We tried to replicate this in the non-linear time domain simulations. In HAWC2 and Simpack it is possible to do time domain simulations with an open-loop configuration, i.e. it is possible to fix the rotor speed and pitch angle to a constant value, without controller intervention. In Bladed (v4.9) and alaska/Wind it was not directly possible to run time simulations with a fixed rotor speed. We therefore used a controller which aims to maintain the rotational speed as constant as possible. The rotational speed is almost constant, but the variation is minimal (especially because the inflow is uniform and constant). We will add a discussion along these lines in section 2.2 of the paper.
- Yes, you are correct that we shift the operating point when we change e.g. the torsional stiffness. It has not been our intention to realize a constant torque or constant power model. Our results would indeed likely differ, if this was done. Rather, our intention was to increase the reproducibility and simplify the comparison between the different tools, such that differences in the stability analysis and differences in the sensitivity of the uncertain parameters on the stability are most likely the result of differences in the structural dynamic and aerodynamic modelling in the tools. Note that the uncertain parameter variations in the uncertainty quantification studies are also relatively small. We will include this explanation of the consequences resulting from our simplification to maintain constant operating settings. This clarification will be added to the first paragraph of section 3 and to the disclaimer on line 365/366 of the conclusion.
- You are correct. The 2nd edge modes are in better agreement than the 1st. This was an editing error and will be corrected.
- We will update the color sequences in the figures to improve the clarity for readers with color blindness.
Thanks again for your helpful comments. I hope we could address them all satisfactorily.
Best regards,
Hendrik Verdonck and co-authors
Citation: https://doi.org/10.5194/wes-2023-80-AC1
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RC1: 'Comment on wes-2023-80', Ozan Gozcu, 15 Sep 2023
Good and interesting work. Please see my comments in the attached pdf.
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AC2: 'Reply on RC1', Hendrik Verdonck, 29 Sep 2023
Dear Ozan Gozcu,
Thank you for your insightful review. Your comments were highly interesting and have led to some internal discussions. For this reason, we had to take some time to complete our response. In the attached document we address your questions and explain how we will amend the paper accordingly.
We will revise the paper once all official reviewers have expressed their opinions.
Best regards,
Hendrik Verdonck and co-authors
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AC2: 'Reply on RC1', Hendrik Verdonck, 29 Sep 2023
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RC2: 'Comment on wes-2023-80', Anonymous Referee #2, 02 Oct 2023
The authors present a methodology to assess the uncertainty related to the blade properties on the aeroelastic stability of a wind turbine. The authors propose to construct a surrogate model of the wind turbine with the PCE approximation to reduce the computational cost and compute the Sobol indices. Different solvers are compared for the computation of the aeroelastic damping of the wind turbine and the effect of the uncertain parameters are compared. The work is interesting as it addresses an important topic for wind turbine design. It covers a large band of methodologies and tools, sometimes making understanding the general workflow difficult.
Here are some general comments to improve the quality and understanding of the paper:
- if applying surrogate modelling to wind turbines is a recent topic, many works have already been done to propagate uncertainties on other mechanical systems with instabilities (squeal, fluttter etc). The authors should include references to some of these works and emphasize how wind turbine models differ from other industrial applications.
- page 7, line 148: there is a <todo>.
- Table 2 gives the different parameters for the DMD methods. It is mentioned that the snapshot must be placed at the beginning of the instability. How do you set this up? How long is the selected time signal? I guess, if the signal is too long, the hypothesis of linearity loses its validity. Maybe an illustration of the different time signals of one dof could help in the understanding?
- why consider only uncertainty on the mechanical properties and not include uncertainty on the wind speed? In some simulations, are there sometimes several unstable modes? If yes, how do you deal with it? If not, how would you generalise your methodology? Similarly, if you extend the variation range of your parameters, you may have a case where your instability is not always present, how would you deal with this case?
- how do you compute the Sobol indices? Are they directly deduced from the PCE coefficients, or do you use some sampling technics?
- for the PCE, what is the size of the expansion? Did you use some truncation technics to reduce the size of the basis?
- could you give some details on the simulation time associated with the different solvers? This would help to emphasize the interest in using surrogate models.
- For the second test case, there are strong differences between the Sobol indices depending on the solver. Could this be explained by differences in the solvers, the initial modelling and/or the uncertain parameter considered? What good practice would you give to engineers in this context?
- Only Sobol indices are compared. However, are the damping distributions impacted in similar ways? What about the resonance frequencies and mode shapes?
Citation: https://doi.org/10.5194/wes-2023-80-RC2 -
AC3: 'Reply on RC2', Hendrik Verdonck, 17 Oct 2023
Dear Referee,
Thank you very much for your insightful comments. We discussed them extensively amongst the co-authors. In the attached document you can find our answers to your questions and when applicable an indication how we will improve the manuscript.
Best regards,
Hendrik Verdonck and co-authors
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AC3: 'Reply on RC2', Hendrik Verdonck, 17 Oct 2023
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