Damage identification on a large-scale wind turbine rotor blade using sample-based deterministic model updating

Wolniak, Marlene; Ragnitz, Jasper; Jonscher, Clemens; Hofmeister, Benedikt; Jauken, Helge; Hübler, Clemens; Rolfes, Raimund

doi:10.5194/wes-2025-219

Preprints

https://doi.org/10.5194/wes-2025-219

Preprints

06 Nov 2025

| 06 Nov 2025

Status: a revised version of this preprint was accepted for the journal WES and is expected to appear here in due course.

Damage identification on a large-scale wind turbine rotor blade using sample-based deterministic model updating

Marlene Wolniak, Jasper Ragnitz, Clemens Jonscher, Benedikt Hofmeister, Helge Jauken, Clemens Hübler, and Raimund Rolfes

Abstract. Wind turbine rotor blades are among the most critical components of wind turbines, with their structural integrity directly affecting reliability, lifetime, and maintenance costs. Reliable damage identification is therefore essential for structural health monitoring (SHM) strategies in wind energy applications. In this context, the updating of numerical models represents an established method for vibration-based non-destructive damage identification, including damage detection, localization and quantification. Naturally, the model-updating process is affected by different sources of uncertainty. On the one hand, the numerical model always represents an idealization that introduces unavoidable discrepancies between its basic assumptions and reality. On the other hand, the measurement data and identified modal parameters, typically serving as damage-sensitive features, are subject to uncertainty. Despite extensive research on uncertainty quantification and propagation in model updating, comparative studies of model-updating procedures applied to large-scale structures, particularly wind turbine rotor blades, remain scarce. Moreover, the level of model fidelity and the impact of different design variable configurations associated with the selected numerical model are seldom examined in the context of model updating, typically formulated as an optimization procedure.

This study addresses this gap by systematically evaluating how model fidelity and design variable parameterization influence the model-updating results while considering uncertainty associated with the measurement data and identification process. The investigations are conducted using measurement data from a 31 m rotor blade subjected to edgewise fatigue loading. A comparison of the results shows that all design variable configurations yield consistent results, confirming the robustness of the presented model-updating procedures. Model fidelity, however, strongly influences the outcomes, with higher accuracy and detail leading to distinctly improved damage identification.

Received: 24 Oct 2025 – Discussion started: 06 Nov 2025

Competing interests: Raimund Rolfes is a member of the editorial board of the wind energy science journal.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Marlene Wolniak, Jasper Ragnitz, Clemens Jonscher, Benedikt Hofmeister, Helge Jauken, Clemens Hübler, and Raimund Rolfes

Status: closed

RC1:
'Comment on wes-2025-219', Anonymous Referee #1, 02 Dec 2025
In their manuscript submitted for publication in Wind Energy Science, the authors present a study of fatigue damage identification for a wind turbine rotor blade. The blade is a specimen of 31 m long which was tested in the lab and subjected to cyclic edgewise loading in order to generate (realistic) fatigue damage. During the test, the blade was instrumented with accelerometers to monitor changes in modal parameters resulting from the fatigue damage. Three states of the blade are considered in the damage identification which occurs through the updating of a finite element model of the blade. A beam as well as a shell model of the blade are used, where damage is represented as a reduction in stiffness in a zone of the blade, considering different damage parameterizations. As on objective function, a fit of the difference in modal properties between two (of the three) states is considered rather than tuning the model to each distinct state and subsequently checking the difference in parameters. Statistical uncertainty in the estimated modal characteristics is considered by repeating the updating for 53 sets of individually identified modal characteristics for different time records. A multi-objective optimization approach is used in the model updating of each set, considering a trade-off between the fit in the difference in natural frequencies between two states and the fit in the difference in eigenmode. It is concluded that the shell model provides the most accurate and reliable characterization of the evolution in damage from one state to another.
The work presented in the manuscript is valuable, in particular for which concerns the experimental data of the blade which are made publicly available on a repository of the institute of the first author. The damage identification presented in the manuscript is also of potential interest but I would like the authors to consider the following comments before it is given further consideration for publication:
A multi-objective optimization approach in model updating was previously presented by the group of Costas Papadimitriou at the University of Thessaly, see e.g. K. Christodoulou et al., CMAME, 2008. In their work, a Pareto front considering optimal solutions corresponding to trade-offs between fits in natural frequencies on the one hand and mode shapes on the other hand was presented as well. It also provides some interesting insight into the influence of model error on the trade-off. Please include this work in the state of the art and use it to situate the present work.

The authors state that the key idea behind the SDMU approach “is to exclude the uncertainty from the design-variable dependent part of the objective function… Instead the uncertainty is incorporated by generating multiple discrete input samples”. Please be more specific as to what type of uncertainty is considered here as “the uncertainty” in the present formulation suggests that uncertainty in general is considered. If I understand correctly, however, it is mainly the statistical uncertainty on the identified modal characteristics which is considered here and transferred to the model parameters (but this relates also to the next comment).

It is not entirely clear how the CDF’s of the model parameters are generated. It is clear that these CDF’s cover the variability residing in the combination of the 53 sets for each two damage states, but it is not clear if these also include the variability in the Pareto optimal solutions of the multi-objective optimization framework for a specific set.

In my personal opinion, reporting results in terms of CDF’s is less intuitive than histograms? This seems confirmed by the fact that the authors focus more on the slope of the CDF’s rather than on the actual CDF’s in the discussion, for example when it is stated “this probability reaches approximately 50%”.

The authors consider two finite element models of the structure, a beam model and a shell model, and this with different parameterizations of damage. First, I am wondering to what extent the simplification of the load shears to point masses in the beam model has an impact on the results. Wouldn’t it be a more fair comparison between the beam and the shell model if the beam model also accounted for the rotational inertia of the load shears so that this part of the model is closer to the shell model. Second, one wonders how large the difference is between the results of both models. Can’t the authors include a comparison of natural frequencies and mode shapes (e.g. MAC matrix for sensor positions) for the two models, using nominal parameter values in undamaged conditions.

One wonders at the end also what model would be preferred? In a Bayesian approach, one could apply a model selection approach which considers a trade-off between the complexity of the model and the fit of the data. Is a similar reasoning possible here?

In the damage identification, the authors use the natural frequencies and mode shapes of 5 modes. It would be useful to have an idea of the extent to which these data allow for an accurate identification of the data. For example, at the end the authors indicate some differences between the identified stiffness reduction and physical fatigue crack. I am wondering here, should the authors change the parameters of the stiffness reduction to bring it closer to the physical crack, what would be the difference in natural frequency shift and mode shape? If those shifts are insignificant, the identification errors are simply a consequence of the limited information contained in the modal data. Along the same line, it would also be useful to add a figure with the 6 identified mode shapes in subsection 3.1.

The authors parameterize the damage as a stiffness reduction, with a spatial distribution according to a (truncated) Gaussian distribution. This is fine, but at some points it seems that this spatial distribution is mixed up with a PDF of the damage which it is not. I would recommend not to use the term PDF when it is really a spatial distribution (for example when explaining equation (6)). Likewise, I find the following statement in subsection 4.1.2. misleading “As the one-dimensional damage distribution is formulated based on a Gaussian distribution function, mu_L+/sigma_L represents the range including 68% of the data”. I think the statement is incorrect as mu_L and sigma_L do not capture the variability in the crack location resulting from the statistical uncertainty in the data but describe the spatial extent of the stiffness reduction. Along a similar line, statements such as “The location … is identified at mu_L …, which overestimates the actual damage location” (also in subsection 4.1.2) are misleading. One can overestimate the intensity of damage or the extent of the damage zone but not the damage location.

Can the authors give an indication of the accuracy of the meta-model relative to the range of the natural frequencies and mode shapes considered? For the meta-model to provide meaningful results for different sets of input data, the error should be small compared to the (small) range of modal data considered. A direct comparison of the error on individual natural frequencies and mode shapes would be more clear than the global error reported in figure 8.

It’s a detail, but in section 4, the authors state “As demonstrated in Section 3.1, the measurement conditions were stationary, i.e. no significant variations in temperature, humidity, …”. I did not find any discussion of these parameters in subsection 3.1, however.

It seems that the method adopted for the authors assumes that the stiffness reduction occurs in a single zone, so I was wondering what would happen if the procedure was applied for a case where it occurs in two distinct zones?

How did the authors consider the spatial variation of the stiffness in the mesh? Did they evaluate the stiffness distribution at the midpoint? How does sigma_L compare to the element size?
Citation: https://doi.org/10.5194/wes-2025-219-RC1
RC2:
'Comment on wes-2025-219', Anonymous Referee #2, 12 Dec 2025
The paper
“Damage identification on a large-scale wind turbine rotor blade using sample-based deterministic model updating”
presents a very interesting, very important vibration‐based damage identification study performed on a 31 m wind turbine blade under controlled fatigue loading.
The authors apply a sample-based deterministic model-updating (SDMU) framework to both a beam and a high-fidelity shell model, using one-dimensional and two-dimensional Gaussian parameterisations of stiffness reduction to infer damage localization and severity. The work leverages a valuable full-scale dataset, and the systematic comparison of model fidelities and parameterizations offers useful insight for SHM practitioners.
In summary, the study is timely, relevant, and contains several strong elements, particularly the experimental dataset and the structured model-updating comparison. However, before reconsideration for full acceptance, the following issues should be addressed:
The Gaussian-shaped 1D and 2D damage distribution functions impose restrictive geometries on possible damage fields. There is no evidence that actual rotor-blade damage follows Gaussian distributions, nor is sensitivity to this assumption tested. This limitation seems to be indeed acknowledged, but deserves earlier and deeper discussion, ideally with a brief demonstration of its effect.

The approach cross-combines 53 × 53 BayOMA-derived modal data, implicitly assuming the independence and equal plausibility of all reference–analysis pairings. This statistical interpretation is not fully explained and may artificially inflate the uncertainty space. A clearer conceptual rationale, comparison with using full Bayesian posterior samples, or discussion of alternative sampling strategies would strengthen credibility.

Localization performance can be checked against the crack position, but the inferred stiffness reduction magnitudes (D₁D, D₂D) seem not to be directly validated.

Some modes included in the updating (e.g., flapwise modes) seem to exhibit minimal damage sensitivity. Using low-sensitivity modes in multi-objective optimisation may dilute the updating signal. A brief sensitivity analysis or justification for including all five modes would be appropriate.

Computational performance should be reported fully. Only modal analysis times seems to be explicitly reported; Readers may need the full cost of a complete SDMU run, especially for the shell model, to judge applicability in practice.

The state-of-the-art review is reliable but relatively limited. Please consider expanding it to include works such as https://doi.org/10.3390/s22041627.

The limitations section should explicitly mention the lack of environmental variability in the dataset.

It is not totally clear, in the text, if the Authors applied an already-available third-party version of BAYOMA, or if they implemented their own variant based on Siu-Kui Au’s textbook Operational Modal Analysis Modeling, Bayesian Inference, Uncertainty Laws. This aspect should be clarified.

Related to the above, for reproducibility, either a link to the used version (if available online) or a detailed pipeline (otherwise) should be provided.

Please carefully revise the text for typos and mistakes. For instance, “Knebusch et al. (2020)” should be (“Knebusch et al., 2020)”
Citation: https://doi.org/10.5194/wes-2025-219-RC2
AC1: 'Comment on wes-2025-219', Marlene Wolniak, 04 Feb 2026

The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2025-219/wes-2025-219-AC1-supplement.pdf

Citation: https://doi.org/10.5194/wes-2025-219-AC1

Status: closed

RC1:
'Comment on wes-2025-219', Anonymous Referee #1, 02 Dec 2025
In their manuscript submitted for publication in Wind Energy Science, the authors present a study of fatigue damage identification for a wind turbine rotor blade. The blade is a specimen of 31 m long which was tested in the lab and subjected to cyclic edgewise loading in order to generate (realistic) fatigue damage. During the test, the blade was instrumented with accelerometers to monitor changes in modal parameters resulting from the fatigue damage. Three states of the blade are considered in the damage identification which occurs through the updating of a finite element model of the blade. A beam as well as a shell model of the blade are used, where damage is represented as a reduction in stiffness in a zone of the blade, considering different damage parameterizations. As on objective function, a fit of the difference in modal properties between two (of the three) states is considered rather than tuning the model to each distinct state and subsequently checking the difference in parameters. Statistical uncertainty in the estimated modal characteristics is considered by repeating the updating for 53 sets of individually identified modal characteristics for different time records. A multi-objective optimization approach is used in the model updating of each set, considering a trade-off between the fit in the difference in natural frequencies between two states and the fit in the difference in eigenmode. It is concluded that the shell model provides the most accurate and reliable characterization of the evolution in damage from one state to another.
The work presented in the manuscript is valuable, in particular for which concerns the experimental data of the blade which are made publicly available on a repository of the institute of the first author. The damage identification presented in the manuscript is also of potential interest but I would like the authors to consider the following comments before it is given further consideration for publication:
A multi-objective optimization approach in model updating was previously presented by the group of Costas Papadimitriou at the University of Thessaly, see e.g. K. Christodoulou et al., CMAME, 2008. In their work, a Pareto front considering optimal solutions corresponding to trade-offs between fits in natural frequencies on the one hand and mode shapes on the other hand was presented as well. It also provides some interesting insight into the influence of model error on the trade-off. Please include this work in the state of the art and use it to situate the present work.

The authors state that the key idea behind the SDMU approach “is to exclude the uncertainty from the design-variable dependent part of the objective function… Instead the uncertainty is incorporated by generating multiple discrete input samples”. Please be more specific as to what type of uncertainty is considered here as “the uncertainty” in the present formulation suggests that uncertainty in general is considered. If I understand correctly, however, it is mainly the statistical uncertainty on the identified modal characteristics which is considered here and transferred to the model parameters (but this relates also to the next comment).

It is not entirely clear how the CDF’s of the model parameters are generated. It is clear that these CDF’s cover the variability residing in the combination of the 53 sets for each two damage states, but it is not clear if these also include the variability in the Pareto optimal solutions of the multi-objective optimization framework for a specific set.

In my personal opinion, reporting results in terms of CDF’s is less intuitive than histograms? This seems confirmed by the fact that the authors focus more on the slope of the CDF’s rather than on the actual CDF’s in the discussion, for example when it is stated “this probability reaches approximately 50%”.

The authors consider two finite element models of the structure, a beam model and a shell model, and this with different parameterizations of damage. First, I am wondering to what extent the simplification of the load shears to point masses in the beam model has an impact on the results. Wouldn’t it be a more fair comparison between the beam and the shell model if the beam model also accounted for the rotational inertia of the load shears so that this part of the model is closer to the shell model. Second, one wonders how large the difference is between the results of both models. Can’t the authors include a comparison of natural frequencies and mode shapes (e.g. MAC matrix for sensor positions) for the two models, using nominal parameter values in undamaged conditions.

One wonders at the end also what model would be preferred? In a Bayesian approach, one could apply a model selection approach which considers a trade-off between the complexity of the model and the fit of the data. Is a similar reasoning possible here?

In the damage identification, the authors use the natural frequencies and mode shapes of 5 modes. It would be useful to have an idea of the extent to which these data allow for an accurate identification of the data. For example, at the end the authors indicate some differences between the identified stiffness reduction and physical fatigue crack. I am wondering here, should the authors change the parameters of the stiffness reduction to bring it closer to the physical crack, what would be the difference in natural frequency shift and mode shape? If those shifts are insignificant, the identification errors are simply a consequence of the limited information contained in the modal data. Along the same line, it would also be useful to add a figure with the 6 identified mode shapes in subsection 3.1.

The authors parameterize the damage as a stiffness reduction, with a spatial distribution according to a (truncated) Gaussian distribution. This is fine, but at some points it seems that this spatial distribution is mixed up with a PDF of the damage which it is not. I would recommend not to use the term PDF when it is really a spatial distribution (for example when explaining equation (6)). Likewise, I find the following statement in subsection 4.1.2. misleading “As the one-dimensional damage distribution is formulated based on a Gaussian distribution function, mu_L+/sigma_L represents the range including 68% of the data”. I think the statement is incorrect as mu_L and sigma_L do not capture the variability in the crack location resulting from the statistical uncertainty in the data but describe the spatial extent of the stiffness reduction. Along a similar line, statements such as “The location … is identified at mu_L …, which overestimates the actual damage location” (also in subsection 4.1.2) are misleading. One can overestimate the intensity of damage or the extent of the damage zone but not the damage location.

Can the authors give an indication of the accuracy of the meta-model relative to the range of the natural frequencies and mode shapes considered? For the meta-model to provide meaningful results for different sets of input data, the error should be small compared to the (small) range of modal data considered. A direct comparison of the error on individual natural frequencies and mode shapes would be more clear than the global error reported in figure 8.

It’s a detail, but in section 4, the authors state “As demonstrated in Section 3.1, the measurement conditions were stationary, i.e. no significant variations in temperature, humidity, …”. I did not find any discussion of these parameters in subsection 3.1, however.

It seems that the method adopted for the authors assumes that the stiffness reduction occurs in a single zone, so I was wondering what would happen if the procedure was applied for a case where it occurs in two distinct zones?

How did the authors consider the spatial variation of the stiffness in the mesh? Did they evaluate the stiffness distribution at the midpoint? How does sigma_L compare to the element size?
Citation: https://doi.org/10.5194/wes-2025-219-RC1
RC2:
'Comment on wes-2025-219', Anonymous Referee #2, 12 Dec 2025
The paper
“Damage identification on a large-scale wind turbine rotor blade using sample-based deterministic model updating”
presents a very interesting, very important vibration‐based damage identification study performed on a 31 m wind turbine blade under controlled fatigue loading.
The authors apply a sample-based deterministic model-updating (SDMU) framework to both a beam and a high-fidelity shell model, using one-dimensional and two-dimensional Gaussian parameterisations of stiffness reduction to infer damage localization and severity. The work leverages a valuable full-scale dataset, and the systematic comparison of model fidelities and parameterizations offers useful insight for SHM practitioners.
In summary, the study is timely, relevant, and contains several strong elements, particularly the experimental dataset and the structured model-updating comparison. However, before reconsideration for full acceptance, the following issues should be addressed:
The Gaussian-shaped 1D and 2D damage distribution functions impose restrictive geometries on possible damage fields. There is no evidence that actual rotor-blade damage follows Gaussian distributions, nor is sensitivity to this assumption tested. This limitation seems to be indeed acknowledged, but deserves earlier and deeper discussion, ideally with a brief demonstration of its effect.

The approach cross-combines 53 × 53 BayOMA-derived modal data, implicitly assuming the independence and equal plausibility of all reference–analysis pairings. This statistical interpretation is not fully explained and may artificially inflate the uncertainty space. A clearer conceptual rationale, comparison with using full Bayesian posterior samples, or discussion of alternative sampling strategies would strengthen credibility.

Localization performance can be checked against the crack position, but the inferred stiffness reduction magnitudes (D₁D, D₂D) seem not to be directly validated.

Some modes included in the updating (e.g., flapwise modes) seem to exhibit minimal damage sensitivity. Using low-sensitivity modes in multi-objective optimisation may dilute the updating signal. A brief sensitivity analysis or justification for including all five modes would be appropriate.

Computational performance should be reported fully. Only modal analysis times seems to be explicitly reported; Readers may need the full cost of a complete SDMU run, especially for the shell model, to judge applicability in practice.

The state-of-the-art review is reliable but relatively limited. Please consider expanding it to include works such as https://doi.org/10.3390/s22041627.

The limitations section should explicitly mention the lack of environmental variability in the dataset.

It is not totally clear, in the text, if the Authors applied an already-available third-party version of BAYOMA, or if they implemented their own variant based on Siu-Kui Au’s textbook Operational Modal Analysis Modeling, Bayesian Inference, Uncertainty Laws. This aspect should be clarified.

Related to the above, for reproducibility, either a link to the used version (if available online) or a detailed pipeline (otherwise) should be provided.

Please carefully revise the text for typos and mistakes. For instance, “Knebusch et al. (2020)” should be (“Knebusch et al., 2020)”
Citation: https://doi.org/10.5194/wes-2025-219-RC2
AC1: 'Comment on wes-2025-219', Marlene Wolniak, 04 Feb 2026

The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2025-219/wes-2025-219-AC1-supplement.pdf

Citation: https://doi.org/10.5194/wes-2025-219-AC1

Marlene Wolniak, Jasper Ragnitz, Clemens Jonscher, Benedikt Hofmeister, Helge Jauken, Clemens Hübler, and Raimund Rolfes

Viewed

Total article views: 645 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	BibTeX	EndNote
435	177	33	645	29	30

HTML: 435
PDF: 177
XML: 33
Total: 645
BibTeX: 29
EndNote: 30

Views and downloads (calculated since 06 Nov 2025)

Month	HTML	PDF	XML	Total
Nov 2025	108	24	12	144
Dec 2025	116	53	11	180
Jan 2026	133	45	6	184
Feb 2026	55	30	1	86
Mar 2026	23	25	3	51

Cumulative views and downloads (calculated since 06 Nov 2025)

Month	HTML	PDF	XML	Total
Nov 2025	108	24	12	144
Dec 2025	116	53	11	180
Jan 2026	133	45	6	184
Feb 2026	55	30	1	86
Mar 2026	23	25	3	51

Viewed (geographical distribution)

Total article views: 621 (including HTML, PDF, and XML) Thereof 621 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 19 Mar 2026

Short summary

This study investigates how FE models of different fidelity affect the damage identification in a 31 m wind turbine rotor blade tested under edgewise fatigue loading. Different design variable configurations are compared, whereby the FE model updating is based on modal parameters identified from measured vibration data.


Total:	0
HTML:	0
PDF:	0
XML:	0