Low-Frequency Fatigue monitoring using nacelle-mounted accelerometers

Chaar, Mustapha; Weijtjens, Wout; Devriendt, Christof

doi:10.5194/wes-2026-133

Preprints

https://doi.org/10.5194/wes-2026-133

Preprints

30 Jul 2026

| 30 Jul 2026

Status: this preprint is currently under review for the journal WES.

Low-Frequency Fatigue monitoring using nacelle-mounted accelerometers

Mustapha Chaar, Wout Weijtjens, and Christof Devriendt

Abstract. Thrust loading on wind turbines causes quasi-static loading that ultimately introduces fatigue loading on the turbine. Monitoring these quasi-static loads is relevant for assessing the residual lifetime of the asset. However, installing strain gauges on all assets is practically and economically infeasible; only a subset of turbines, referred to as fleet leaders, are instrumented to this level. Interestingly, these quasi-static loads also result in a temporary inclination or tilt of the tower, which can be picked up by accelerometers or inclinometers installed on the tower or nacelle. This paper proposes using gravity-sensitive tri-axial MEMS accelerometers placed in the nacelle to estimate the inclination and load characteristics of a fleet of turbines. To do this accurately, the MEMS sensor needs to be calibrated to offset installation errors and compensate for the turbines’ permanent inclination. For this purpose, long-term data from the MEMS accelerometer are processed, and the constituting offsets are estimated. After calibration, the quasi-static angles induced by loading can be estimated from the accelerometer. The derived load characteristics can then be used to extrapolate bending moments from fully instrumented fleet-leader turbines to the remainder of the wind farm. The bending moment is then used to assess damage-equivalent moments, and it was found that the accelerometer produces damage estimates similar to those obtained from strain gauges. Thus, the approach enables scalable and cost-effective farmwide load monitoring.

Received: 24 Jul 2026 – Discussion started: 30 Jul 2026

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Mustapha Chaar, Wout Weijtjens, and Christof Devriendt

Status: final response (author comments only)

RC1:
'Comment on wes-2026-133', Anonymous Referee #1, 24 Aug 2026
The paper
“Low-Frequency Fatigue monitoring using nacelle-mounted accelerometers”
presents a practically relevant monitoring strategy in which nacelle-mounted tri-axial MEMS accelerometers are calibrated for sensor mounting offsets and permanent tower tilt and subsequently used to infer fore-aft bending moments and low-frequency fatigue loads.
The fleet-leader concept, the use of operational offshore measurements, and the attempt to obtain a low-maintenance farmwide fatigue-monitoring solution give the work clear engineering relevance.
However, This Reviewer considers that several aspects of the physical assumptions, calibration procedure, data processing, and fatigue validation require substantial clarification and additional evidence before the conclusions can be considered sufficiently robust and reproducible.
In summary, This Reviewer recommends reconsideration after major revision. The following points should be addressed:
This Reviewer considers the extension from 10 min mean acceleration to the time-resolved 0-0.08 Hz signal to be the most important physical assumption requiring validation. A nacelle accelerometer measures both the gravity projection caused by tilt and translational/rotational inertial acceleration. Equation (6) is derived using mean acceleration, whereas Sect. 5 applies a 0.08 Hz low-pass filter and interprets the retained signal as a load-induced tilt proxy. The authors should demonstrate, using spectra, coherence/transfer functions, or an equivalent analysis, that inertial acceleration is negligible or properly accounted for over the retained band, and should state the frequency range over which the quasi-static relation is valid.

This Reviewer recommends a stronger justification for the definition of low-frequency fatigue dynamics and for the 0.08 Hz cutoff adopted in Sect. 5.1. The statement that this band lies below the lowest cyclic loads, including wave loading, is not sufficiently demonstrated. The authors should show site-specific spectra of measured bending moment/strain and nacelle acceleration, identify the relevant 1P and wave-energy bands, and provide a sensitivity analysis showing how the rainflow spectrum and DEM change for reasonable alternative cutoff frequencies.

The “zero-load” calibration assumption at 3.6- 3.9 m/s is insufficiently substantiated. The method assumes that horizontal wind loading counteracts the rotor-nacelle assembly eccentricity so that only sensor offset and permanent tower tilt remain. The authors should provide the fitting equations or objective function, the number of samples and yaw coverage per turbine, uncertainty or confidence bounds for the estimated tilt/heading/offset parameters, and sensitivity to the selected wind-speed interval and turbine state. Because Chaar et al. (2026) is central to this step but is cited without complete publication details, the present manuscript should remain sufficiently self-contained to reproduce the calibration.

The sensors were installed manually without a dedicated mounting bracket, yet Sect. 2.2 assumes that the relative yaw misalignment between the sensor and nacelle is exactly 0 degrees and states that it cannot be resolved afterwards. Such an azimuthal misalignment would mix the fore-aft and side-side components and could bias the inferred pitch and bending moment. The authors should report the installation/alignment tolerance, quantify the sensitivity of the results to plausible yaw misalignment, and incorporate this third sensor rotation in the calibration if it cannot be shown to be negligible.

Please provide a more explicit assessment of transferability across turbines with different substructure designs, water depths, and boundary conditions. The mapping from nacelle pitch to tower-transition-piece bending moment is expected to depend on structural stiffness and geometry. The authors should report the fitted slopes/intercepts, or an equivalent measure, for the available fleet leaders and examine whether prediction error correlates with structural differences. The manuscript should clearly state the conditions under which a model calibrated on one or two fleet leaders can be transferred to an uninstrumented turbine and whether any turbine-specific calibration remains necessary.

The fatigue-processing description insufficient for full reproducibility. The manuscript should define the DEM equation, reference number of cycles or equivalent frequency, reference duration, rainflow-counting settings, treatment of half cycles and residues, Wöhler exponents, any mean-stress correction, and the precise normalization applied. The values of the outer radius and second moment of area used in Eq. (8), or the basis for their normalization, should also be stated. In addition, Sect. 5.2 refers to stress range in MPa whereas Figure 9 is labelled “Normalized stress range”; dimensional and normalized quantities should be distinguished consistently.

There seems to be an important numerical inconsistency between Table 2 and the conclusion. Table 2 reports MAPE values of 8.61-9.89 %, whereas the conclusion states that the total DEM is predicted with a margin of error below 3 %. These statements cannot both describe the same error measure. The authors should reconcile them and define precisely what “margin of error” represents. If MAPE and RMSE were computed over multiple subintervals rather than from the single aggregate DEM values shown in Table 2, the sample basis and equations should be reported; otherwise the use of “mean” and RMSE is unclear.

The fatigue validation in Sect. 5 is limited to approximately one week and one fleet-leader turbine, whereas the broader motivation concerns long-term and farmwide fatigue monitoring. If additional data are available, a longer and/or multi-turbine fatigue validation would considerably strengthen the work. At minimum, the authors should report the number and duration of curtailment events, the distribution of operating states and wind speeds, and the missing-data fraction in the validation week. If broader validation is not available, the abstract and conclusions should explicitly frame the evidence as a short-term proof of feasibility rather than a fully validated farmwide fatigue-monitoring solution.

This Reviewer recommends adding the sensor and acquisition details needed to assess low-frequency/DC performance. The manuscript should identify the accelerometer model or relevant specifications, sampling frequency, measurement range, noise density, bias stability and temperature sensitivity, together with strain-gauge sampling, time synchronisation, resampling, and preprocessing. The implementation of the Butterworth filter should be specified, including whether it is causal or zero-phase and how edge transients are handled. These details are particularly important because low-frequency tilt estimates are sensitive to bias, drift, and timing.

Structural health monitoring, condition monitoring, and fault detection have paramount importance in the growing wind industry. The proposed methodology can be most likely applied to wind turbine generators or other mechanical components. In this context, https://doi.org/10.3390/s22041627 recently reported on the current state of the art in this field. This can be added to the introduction of the paper to provide further context to this research.

A final technical and language proofreading is strongly recommended. Examples include the reference to Figure 8 instead of Figure 9 for the rainflow histograms, “medium value” in the Figure 6 caption where “median value” appears intended, inconsistent “DEM/Dem” capitalization, “not to different” in the Figure 1 caption, the “0. 98” entry in Table 1, and the description of R² as correlation rather than coefficient of determination. The notation around Eqs. (2)-(6) should also be checked; in particular, the statement that only yaw needs to be known should be reconciled with Eq. (6), which still uses the previously estimated tower-tilt parameters.
Citation: https://doi.org/10.5194/wes-2026-133-RC1
RC2: 'Comment on wes-2026-133', Anonymous Referee #2, 28 Aug 2026

Study titled “Low-Frequency Fatigue monitoring using nacelle-mounted accelerometers” presents a concept for low-maintenance farm wide fatigue-monitoring.

Due to its importance and relevance, this work should provide more clarification and verification on several points. In the text, the authors state in more than one place that there is some approximation and a lot of error included, but still, they still assess their model(s) as a success with “below 3%” error. I’m not sure I agree with that. Also, some of the equations need netter and more detailed explanation (like Equation 6 and 8. Finally, Conclusion section should address all shortcomings included in this work and mention all assumptions and rooms for error before addressing “error remaining below 3%”. I think the manuscript needs proofreading and fixing tiny typos as well.

Some specific lines to clarify:

Line 119: is it Figure 2 or Figure 3? Please check.

Figure 5: blue color should be less intense since it masks information (the mean)

Line 240: it would be nice to include a graphical representation of locations of all 5 turbines (and their position on Figure 5a)

Line 255: “which could be attributed to similar boundary conditions” this needs more explanation (what is considered as a part of “boundary conditions”? This is why more info about location of 5 disused turbines would be useful).

Line 278: “ we adopt a fourth-order Butterworth low-pass filter at 0.08 Hz.” This part needs some reference and more explanation

Line 355: “with the margin of error remaining below 3%” I’m not sure I found anywhere in the text that errors are below 3%. Where is this coming from?

Citation: https://doi.org/10.5194/wes-2026-133-RC2
RC3: 'Comment on wes-2026-133', Anonymous Referee #3, 22 Sep 2026

The manuscript presents an approach for estimating low-frequency fatigue loads in wind turbines using nacelle-mounted acceleration measurements. It combines correction for sensor mounting offsets and permanent tower tilt with a calibrated relationship between estimated nacelle tilt and fore-aft bending moments for subsequent fatigue assessment. The use of operational measurements and a fleet-leader strategy gives the study practical relevance, particularly for monitoring turbines without extensive load instrumentation.
However, substantial revision is needed to clarity the methodology, improve the presentation of results, and align the conclusions with the support evidence. The current description does not sufficiently distinguish physical assumptions from validated relationships or demonstrated performance from potential applicability. This makes it difficult to assess the reproducibility of the approach and the extent to which the results support the conclusions.
The following points should be addressed.
1. Improve the organisation and focus of the introduction
The introduction provides relevant background, but the proregression from the practical monitoring problem to the research gap and proposed contribution could be clearer. This discussion of non-uniform sensor installation is repeated across several paragraphs and should be consolidated to distinguish installation-related calibration issues from the broader challenges of farm-wide fatigue monitoring. The introduction should also clarify which challenges the proposed approach addresses and how its contribution differs from previous work.
2. Provide a complete description of the methodology
The processing chain is not sufficiently clear to allow readers to follow to reproduce the approach. Essential information is dispersed across references to previous work and the discussion sections. Please present the complete workflow in the methodology section, including the conversion of acceleration measurements to estimated tilt, the relationship between tilt and bending moment, and the subsequent fatigue calculations. The underlying physical assumptions should also be stated and justified, particularly the used of mean acceleration and the conditions under which a quasi-static interpretation is valid.
3. Clarify how differences between turbines are addressed
The authors stated that ‘the turbines are from the 7 to 10 MW generation and are installed on XL-monopiles at moderate water depths’, suggesting that their tower structures may differ. Please provide the relevant tower and support-structure characteristics.
Where differences exist, discuss their implications for the calibrated tilt-bending moment relationship and how they are accommodated when transferring the calibration between turbines.
4. Improve the figures, tables, and definitions of reported quantities
Several figures and tables are difficult to interpret because the plotted elements, normalisation procedures, or reported quantities are insufficiently defined.
Figure 1: Please revise the schematic’s legibility and ensure that the relevant components and their relationships are clearly labelled and explained.
Figure 4: Please clarify what the dots represent and why the curve extends beyond the values they indicated.
Figures 7-9: Please define the residual in Figure 7 and identify the reference quantity used for normalisation in Figure 7-9.
Table 1: Please provide units for all appliable quantities.
5. Present the validation results more comprehensively
The discussion considered only one of the 33 turbines, whereas the broader motivation concerns farm-wide monitoring. Comparisons across turbines and time periods are therefore needed to demonstrate the applicability of the approach at the farm level.
The results distinguish between different operational stages, but provide insufficient information on the operating conditions or their influence on the proposed approach. These aspects should be described and discussed.
The fatigue damage index appears to be calculated using a single-slope S-N curve. Using a realistic S-N curve, such as one recommended in DNC-RP-C203, would provide more fare comparison on tower fatigue behaviour than slope-sensitivity analysis alone, especially considering the substantial discrepancies in the high-cycle portion of the results.
6. Clarify the limitations and revise the conclusions accordingly
The manuscript would benefit from a dedicated discussion of the assumptions, uncertainties, and applicability limits of the proposed approach. This should cover the calibration assumptions, the validity range of the quasi-static interpretation, the restriction to the retained low-frequency band, and the transfer of the calibrated relationship between turbines.
Finally, a thorough revision of the manuscript’s organization and scientific writing is needed, with particular attention to consistent terminology, complete definitions, and accurate references to figures and equations.

Citation: https://doi.org/10.5194/wes-2026-133-RC3

Mustapha Chaar, Wout Weijtjens, and Christof Devriendt

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Short summary

With advances in sensor technology, wind farm operators are installing low-cost sensors across the fleet to monitor structural integrity. However, these sensors cannot directly measure fatigue or remaining lifetime. This study shows that they can provide this information by learning from their peers with more instrumentation. The results demonstrate that slow-changing loads linked to high fatigue can be estimated accurately which are key to extending turbine lifetime.


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