the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Sep 2026
Brief communication: Enhanced wind turbine fatigue load estimation using digital shadows with data-driven bias correction
Abstract. Building on a previously published digital-shadow framework for wind turbine load estimation, this study augments a linearized aeroelastic model with learning-based bias correction (BC). A neural network (NN) learns operating-condition-dependent corrections while preserving the physics-based model structure. The framework is validated using field measurements under simple, complex, and mixed inflow conditions. For blade bending moments at the 25% span location, damage equivalent load (DEL) errors of 14-24% without correction are reduced to below 5%. The largest improvements occur under complex inflow. A hybrid strategy combines baseline and NN-based corrections, improving robustness across varying operating and inflow conditions.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
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.- Preprint
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CC1: 'Comment on wes-2026-156', J. Gordon Leishman, 26 Sep 2026
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AC3: 'Reply on CC1', Hadi Hoghooghi, 22 Oct 2026
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We agree that the available field measurements originate from a single turbine, site, and measurement campaign and therefore do not constitute external validation across turbine platforms, sites, seasons, or measurement systems. The purpose of the present study is to demonstrate the feasibility and performance of the proposed learning-based bias-correction framework for the investigated turbine and datasets, rather than to claim universal transferability of the trained correction.
To avoid overstating the generality of the results, we have revised the manuscript to clarify the scope of the validation. In particular, the mixed and transitional inflow datasets are described as within-turbine holdout periods that were entirely excluded from training, rather than as independent external validation datasets. These datasets assess performance on held-out operating and inflow conditions while remaining within the same turbine and site dataset. Validation across other turbines, sites, seasons, and measurement campaigns is required before broader transferability can be established, and this is now explicitly stated as an important limitation and direction for future work.
We also agree that the blade-root and 25% span bending moments are structurally related. The blade bending moment at 25% span is not assimilated by the digital shadow and is not used as a training target; therefore, it provides an unassimilated output quantity for evaluating the estimated structural response. However, it should not be interpreted as independent evidence that the complete aerodynamic load distribution has been reconstructed. We have revised the manuscript to make this distinction explicit. The tower-base bending moment provides an additional validation quantity associated with a different structural component and is also not used as an NN training target.
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AC3: 'Reply on CC1', Hadi Hoghooghi, 22 Oct 2026
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CC2: 'Comment on wes-2026-156', J. Gordon Leishman, 26 Sep 2026
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I also note that Carlo L. Bottasso is the corresponding author of this manuscript and, more importantly, the Editor-in-Chief of Wind Energy Science. The manuscript discloses only that at least one author is a member of the journal's editorial board. Given the corresponding author's position as Editor-in-Chief, this represents a significant potential conflict of interest in the paper's editorial handling. In my view, an independent editor should handle the manuscript, reviewer selection, review evaluation, and any publication decision, with no involvement from the corresponding author in any editorial capacity. For transparency, the public review record should also clarify the identity and independence of the handling editor.
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-2026-156-CC2 -
RC1: 'Comment on wes-2026-156', Anonymous Referee #1, 07 Oct 2026
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Please see attachment.
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AC1: 'Reply on RC1', Hadi Hoghooghi, 22 Oct 2026
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Reply to the reviewers’ comments for the paper “Brief communication: Enhanced wind turbine fatigue load estimation using digital shadows with data-driven bias correction.”
The authors would like to thank the reviewers for their time and for the useful feedback. All the inputs they provided have helped improve the paper.
A list of point-by-point replies to the reviewers’ comments is provided below. The reviewer’s comments are in black, and our replies are in blue.
A revised version of the manuscript is attached to the present reply, with additions highlighted in blue and deletions marked in red.
Reviewer 1
General comments
The paper has been shortened from the original version, which has impaired replicability. The work is still valid, so only minor revisions are advised. However, the authors should be aware that it will be quite hard for a reader to implement the proposed method based on the concise description presented here.
We thank the reviewer for this constructive comment. We acknowledge that shortening the manuscript resulted in some methodological details being described too concisely. We have therefore revised the manuscript to provide additional information needed to understand and reproduce the proposed approach, including clarification of the bias-correction methodology, the training/testing procedure, and the implementation of the different correction strategies. We have also reorganized related methodological information to provide a more coherent description. We believe these additions substantially improve the reproducibility of the work while preserving the focused scope of the Brief Communication.
Specific comments
- L58: Please clarify what “flapwise” and “edgewise” refer to (displacements, loads, velocities, combinations of those, etc.).
We thank the reviewer for pointing out this ambiguity. Here, “flapwise” and “edgewise” refer to the flapwise and edgewise components of the static correction force f0 in Eq. (1b), respectively, rather than to displacements or velocities. We have revised the text accordingly.
- L75: Please clarify how the training vs. testing split is implemented (e.g., random split or time-based split) and the implication for data leak due to the strong autocorrelation of atmospheric and wind turbine time series data.
We thank the reviewer for this important comment. The training and testing sets were separated temporally rather than obtained by randomly splitting individual samples. In particular, no data from the selected test days were included in the training set. This prevents strongly autocorrelated neighboring samples from being shared between the training and test sets, reducing the risk of data leakage. We have clarified this procedure in the revised manuscript.
- L66 and L90: please unify the description of the BC strategies that are now provided in two separate sections.
We thank the reviewer for this suggestion. We have consolidated the description of the different BC strategies in Section 2.1, including the shear-based and harmonic-based NN formulations and the hybrid strategy. The description in the Results section has been streamlined to focus on the training and validation setup, thereby avoiding repetition of methodological details.
- L99: It is unclear why it says that “only the mixed-inflow case is illustrated” while the table right after discusses the other inflow cases. Please remove or clarify.
We thank the reviewer for pointing out this ambiguity. The statement was intended to indicate that, due to the figure limitation of the brief communication format, only the mixed-inflow cases are shown as time-series figures. The simple- and complex-inflow cases are nevertheless evaluated and reported quantitatively in Table 1. We have revised the text to clarify this distinction.
- L106: Please provide a table for the tower base load too, it is hard to understand which BC correction works better from just one sentence.
We thank the reviewer for this suggestion. We performed the requested comparison of MTB for all BC strategies. The additional analysis shows that the differences among the corrected strategies are small at the reporting precision used throughout the manuscript and therefore do not provide a meaningful basis for identifying one strategy as superior for the tower-base load. In particular, under complex inflow, the rounded RMSE and DEL errors are essentially identical across the correction strategies.
This limited sensitivity is consistent with the tower-base load formulation: the steady-state contribution remains unchanged, while the BC primarily affects the perturbation response through the corrected blade states. Consequently, the baseline BC already provides robust estimates of MTB, with only minor changes resulting from the learning-based corrections.
We have clarified this behavior in the revised manuscript and now report the corresponding MTB performance for the simple, complex, and mixed-inflow cases. Because the strategy-to-strategy differences in MTB are small at the reporting precision used in the manuscript, an additional table would provide little quantitative distinction among the corrected approaches. We therefore explicitly report the corresponding MTB results in the text for the simple, complex, and mixed-inflow cases, while retaining Table 1 for the blade-load quantity, where the correction strategies show clearer differences.
- 1 and 2: The description of the line colors can be removed, but please explain what the green box is.
We thank the reviewer for pointing this out. The descriptions of the line colors have been removed from the captions of Figures 1 and 2, and the captions have been revised to clarify that the green dashed boxes highlight periods characterized by variations in wind speed and shear.
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AC1: 'Reply on RC1', Hadi Hoghooghi, 22 Oct 2026
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RC2: 'Comment on wes-2026-156', Anonymous Referee #2, 13 Oct 2026
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Although the proposed learning-based bias correction is potentially useful, I do not consider the dataset and training-validation framework sufficient to establish that it reliably improves fatigue-load estimation across varying inflow conditions.
The training data comprise 43 h of simple inflow and 20 h of complex inflow from a single turbine at one site, collected during two campaigns in the same month. The corresponding test sets contain only 6 h and 3 h. High-frequency sampling does not necessarily provide a large number of independent training examples because of temporal correlation. The manuscript does not adequately establish whether these data cover sufficient independent operating conditions for training or how temporal separation between training and testing was ensured. The additional 7.5 h of mixed and transitional inflow provide useful within-turbine holdout validation, but offer limited evidence of performance beyond the experimental setting used for training.
The hybrid results also require clarification. Under complex inflow, Table 1 reports a DEL error of 13% for the hybrid strategy, identical to the baseline correction, whereas the harmonic-based NN achieves 4%. Thus, the hybrid provides no improvement over the baseline in this case despite the better performance of the harmonic-based NN. The manuscript should explain why the switching strategy does not capture this improvement. Although this result alone does not disprove robustness, it leaves the claimed benefit insufficiently demonstrated.
A single-turbine study can provide a valuable proof of concept. However, the present manuscript does not sufficiently establish the adequacy of its training data or the independence and reliability of its validation. Addressing these concerns requires stronger experimental evidence and a clearly documented, temporally separated evaluation, rather than presentation changes alone.
Citation: https://doi.org/10.5194/wes-2026-156-RC2 -
AC2: 'Reply on RC2', Hadi Hoghooghi, 22 Oct 2026
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Reply to the reviewers’ comments for the paper “Brief communication: Enhanced wind turbine fatigue load estimation using digital shadows with data-driven bias correction.”
The authors would like to thank the reviewers for their time and for the useful feedback. All the inputs they provided have helped improve the paper.
A list of point-by-point replies to the reviewers’ comments is provided below. The reviewer’s comments are in black, and our replies are in blue.
A revised version of the manuscript is attached to the present reply, with additions highlighted in blue and deletions marked in red.
Reviewer 2
General comments
Although the proposed learning-based bias correction is potentially useful, I do not consider the dataset and training-validation framework sufficient to establish that it reliably improves fatigue-load estimation across varying inflow conditions
The training data comprise 43 h of simple inflow and 20 h of complex inflow from a single turbine at one site, collected during two campaigns in the same month. The corresponding test sets contain only 6 h and 3 h. High-frequency sampling does not necessarily provide a large number of independent training examples because of temporal correlation. The manuscript does not adequately establish whether these data cover sufficient independent operating conditions for training or how temporal separation between training and testing was ensured. The additional 7.5 h of mixed and transitional inflow provide useful within-turbine holdout validation, but offer limited evidence of performance beyond the experimental setting used for training.
A single-turbine study can provide a valuable proof of concept. However, the present manuscript does not sufficiently establish the adequacy of its training data or the independence and reliability of its validation. Addressing these concerns requires stronger experimental evidence and a clearly documented, temporally separated evaluation, rather than presentation changes alone.
We thank the reviewer for this important comment. We agree that the original manuscript did not sufficiently document the temporal separation of the training and test datasets and that the number of high-frequency samples alone is not an appropriate measure of the amount of independent information available for training and validation. We have therefore performed an additional dataset audit specifically addressing temporal separation, temporal correlation, the effective number of operating-condition blocks, and coverage of the training and validation conditions. We have also revised the manuscript to frame the present study explicitly as a single-turbine proof of concept, rather than as evidence of transferability across turbines or sites.
First, we verified the training/test split directly from the absolute Date timestamps in each measurement file. The Simple dataset consists of seven training records totaling 43 h and a separate 6 h test record, while the Complex dataset consists of four training records totaling 20 h and a separate 3 h test record. Two additional mixed/transitional records totaling 7.5 h were excluded from training and retained as holdout data.
Importantly, no temporal overlap occurs between any training and test measurement records. For the Simple condition, the minimum separation between the test interval and any training interval is 73 h; for the Complex condition, it is 21 h. Thus, the test data were not constructed by randomly sampling from or selecting neighboring high-frequency samples from the training records. For clarity, the Simple test period lies between earlier and later training records, and we therefore describe the procedure as temporally non-overlapping held-out measurement-record validation rather than chronological forecasting.
Second, we agree with the reviewer that the 10 Hz measurements cannot be interpreted as independent training examples. Our additional autocorrelation analysis confirms substantial temporal dependence in the raw signals. We therefore no longer use the high-frequency sample count as evidence for the effective amount of training information. Instead, we quantified the data using non-overlapping 10-, 30-, and 60-min operating-condition blocks, with blocks constructed separately within each measurement file. At the 10-min scale, the Simple dataset contains 251 training and 35 test blocks, while the Complex dataset contains 116 training and 17 test blocks. The within-turbine mixed/transitional holdout contains an additional 43 ten-minute blocks. At 30 min, the corresponding training/test counts are 79/11 for Simple and 36/5 for Complex; at 60 min they are 36/5 and 16/2, respectively.
We additionally quantified the residual serial dependence between consecutive block means. For the primary 10-min representation, the 251 Simple training blocks correspond to approximately 41–96 effective blocks, depending on the operating variable analyzed, while the 116 Complex training blocks correspond to approximately 37–60 effective blocks. The sensitivity analysis using 30- and 60-min blocks showed generally lower residual dependence at longer averaging intervals; for example, the effective fractions for the Complex training variables at 30 min are approximately 0.79–0.94. We report these values as approximate dependence diagnostics rather than interpreting individual high-frequency observations as independent realizations.
Third, we evaluated whether the held-out operating conditions are simply repetitions of the training conditions. For the Simple test set, 5.7% of the 10-min blocks lie outside the defined multivariate training-support threshold. For the Complex test set, this fraction is 17.6% at the 10-min scale. Thus, the validation records are temporally separated and include operating-condition combinations that are not fully represented in their respective training datasets.
Finally, the two mixed/transitional periods were kept entirely outside the training procedure. They comprise 43, 13, and 6 complete blocks at 10-, 30-, and 60-min scales, respectively. At the block level, all of these mixed/transitional conditions fall within the multivariate support obtained from the combined training datasets; at the sample level, 4.5% lie outside the defined support threshold. We agree with the reviewer that this remains within-turbine validation and therefore does not establish transferability to other turbines, sites, or campaigns. We have revised the text to explicitly state this limitation.
We believe these additional analyses substantially strengthen the study's experimental basis by demonstrating that the reported results are based on temporally non-overlapping measurement records, explicitly account for temporal dependence, and are evaluated on held-out operating conditions with quantified training-domain coverage. At the same time, we have moderated the manuscript's claims accordingly: the results are presented as a field-based proof of concept for the investigated turbine and operating domain, while validation on additional turbines, sites, seasons, and measurement campaigns remains necessary to establish broader transferability.
The hybrid results also require clarification. Under complex inflow, Table 1 reports a DEL error of 13% for the hybrid strategy, identical to the baseline correction, whereas the harmonic-based NN achieves 4%. Thus, the hybrid provides no improvement over the baseline in this case despite the better performance of the harmonic-based NN. The manuscript should explain why the switching strategy does not capture this improvement. Although this result alone does not disprove robustness, it leaves the claimed benefit insufficiently demonstrated.
We agree that the previous discussion did not sufficiently explain why the hybrid strategy still exhibits a 13% DEL error despite the 4% error achieved by the harmonic-based NN. The hybrid does not select the correction method based on the resulting DEL error; instead, it applies a predefined switching criterion. For this complex-inflow case, that criterion retains the baseline correction and consequently does not exploit the improvement provided by the harmonic-based NN. We have clarified this behavior in the revised manuscript and now explicitly identify it as a limitation of the current switching strategy. Further refinement of the switching criterion is therefore required to better identify conditions under which NN-based correction provides a clear benefit.
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AC2: 'Reply on RC2', Hadi Hoghooghi, 22 Oct 2026
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I reviewed the previous version of this work. The present manuscript is considerably shorter and more focused, and several aspects of the presentation have been clarified. However, I do not find that the principal scientific concern raised previously has been materially resolved. The underlying experimental evidence remains essentially the same, and in my view the manuscript has largely been repackaged and shortened rather than substantially strengthened.
My main concern is the very limited dataset used to establish the performance and generality of the proposed approach. The evaluation is based on measurements from a single 3.5 MW eno126 turbine at one site, with data obtained during two measurement campaigns in October 2020. After filtering, approximately 49 h of simple-inflow data and 23 h of complex-inflow data remain, of which only 6 h and 3 h, respectively, are reserved for testing. An additional 7.5 h of mixed and transitional inflow data are used to examine generalization.
These data may be sufficient to show that the proposed method performs satisfactorily for this particular turbine, site, instrumentation, and measurement period. They are not, in my opinion, sufficient to establish the broader generality of a data-driven bias-correction methodology. The so-called unseen datasets are still obtained from the same turbine, at the same site, using the same instrumentation, and during the same overall measurement campaign. This constitutes holdout validation within a single experimental dataset rather than genuinely independent external validation.
This issue is particularly important for a learning-based correction method. The learned relationship may depend on turbine-specific structural properties, controller behavior, sensor characteristics, atmospheric conditions, and site characteristics. The authors present no evidence that the correction transfers to another turbine, another measurement campaign, another season, or another site. The authors identify wake flow, yawed conditions, offshore conditions, additional turbine platforms, and strongly transient operation as subjects for future work. These are precisely the kinds of conditions needed to establish the method's broader applicability.
A secondary concern is the degree of independence of the load validation. The manuscript states that the digital shadow assimilates blade-root bending moments and provides the training signal for the correction, whereas the blade bending moment at the 25% span location is subsequently used as a validation quantity. A bending moment is an integrated structural response to aerodynamic, inertial, gravitational, and dynamic loading. It is not a unique measure of the underlying aerodynamic load distribution. Furthermore, root and inboard blade bending moments are structurally related quantities. Agreement with the bending moment at another spanwise station is therefore useful as a check on structural-load estimation, but it does not constitute a strongly independent demonstration that the underlying aerodynamic loading has been reconstructed correctly.
The revised manuscript does provide a clearer comparison between the uncorrected digital shadow, the baseline bias correction, the neural-network approaches, and the hybrid method. This is useful. However, these comparisons do not address the more fundamental limitation that all results arise from a relatively restricted experimental dataset. I remain unconvinced that the evidence presented supports the generality the manuscript implies. The work demonstrates the method's performance for the particular turbine and datasets considered, but it has not established broader applicability. In my view, shortening and reorganizing the previous manuscript has not resolved this central limitation.