A new peer-reviewed study published in Wind Energy Science has quantified how well a virtual sensing method holds up when applied to one of the industry’s largest reference turbines. Lead researcher Mads Greve Pedersen, along with co-authors Jennifer Marie Rinker, Isaac Farreras Alcover, and Jan Høgsberg, working with the Technical University of Denmark and COWI, tested multi-band modal decomposition and expansion (MDE) across the full support structure of the IEA 15 MW offshore reference wind turbine – and found that the method performs reliably across most elevations but breaks down at two specific zones.
What the study examined
Rinker and Farreras Alcover applied multi-band MDE to estimate fatigue damage equivalent loads (DELs) and damage equivalent stresses (DESs) at every node along the full support structure of the IEA 15 MW reference wind turbine – from the embedded monopile tip to the tower top at 144 m above mean sea level.
The analysis drew on a publicly available HAWC2 simulation database compiled by Pedersen et al. This dataset covers the turbine’s full fatigue-limit-state design life and comprises 4,902 simulation files, each containing time series from 898 sensor channels.
Virtual sensing extrapolates structural responses from a small number of accessible sensors to locations that are difficult or impossible to instrument directly (such as sub-sea and sub-soil structural elements). The technique supports asset integrity management and informs life-extension decisions for aging offshore wind assets.
Why errors arise: rotor flexibility and wave loading
The finite-element model used to generate mode shapes for the MDE represents the rotor-nacelle assembly as a lumped mass rather than a flexible body. That simplification causes inaccuracies in the second and third tower bending mode shapes, which in turn distort stress estimates near the tower top.
The problem extends beyond mode shape accuracy. Rotor modes that couple with tower vibrations can’t be represented within a lumped-inertia model at all, so they’re omitted from the MDE entirely — and those missing modes matter most during normal operation and under locked-rotor fault conditions.
Wave loading introduces a separate source of error. The wave-load Ritz vector is time-invariant and computed for a single representative wind speed, meaning it neither accounts for wind-speed-dependent wave height nor captures the dynamic shift between drag-dominated and inertia-dominated loading regimes. That simplification concentrates additional errors in the zone around mean sea level.
Where and how large the errors are
Across most of the support structure, the method performs well. Relative MDE errors for damage equivalent stresses in individual simulations are predominantly within ±5%, which the authors describe as generally accurate performance.
The picture changes sharply near the tower top. In the elevation range from 120 to 144 m above mean sea level, errors grow substantially — the worst-case recorded reaches approximately 188% in the side-side direction for operating conditions, driven by the inaccurately modeled second and third tower bending modes and by rotor modes absent from the model.
A separate, more consistent error pattern appears around mean sea level. The MDE underestimates damage equivalent stresses by up to 6% within roughly ±15 m of the waterline across all design load cases and in both the fore-aft and side-side directions, a pattern the study attributes to the oversimplified wave-load representation.
MDE errors also increase with wind speed. The authors link this to the method’s core assumption of a linear, time-invariant structural response — one that can’t capture the operational variability introduced by changing rotor speed, blade pitch, and wave conditions.
Which operating conditions drive fatigue damage
Normal power production, classified as design load case 1.2, accounts for roughly 90% of the turbine’s design life and dominates fatigue damage across most of the support structure. At the tower top, 3P rotor effects — arising from tower shadow, wind shear, and turbulence — amplify damage specifically in that region.
Two non-operating conditions contribute disproportionately high damage relative to their duration. The parked-idle condition (DLC 6.4) and the locked-rotor fault condition (DLC 7.2) both lack aerodynamic damping, allowing resonant excitation to build unchecked. DLC 7.2 is particularly influential above roughly 75 m, where blade vibrations in the locked configuration generate large moments at the tower top.
Start-up and shut-down events appear less critical in the analysis, but the authors flag an important caveat: real-world curtailment increases the frequency of those transitions beyond the values specified in the IEC standard, so their contribution to lifetime damage may be under-represented in the current dataset.
Recommended improvements and next steps
The most direct path to better accuracy at the tower top is incorporating a flexible rotor model into the finite-element prediction model. Prior work cited in the study shows that blade flexibility significantly affects the natural frequency and shape of the second tower bending modes — exactly the modes responsible for the largest errors observed.
For the zone around mean sea level, the authors propose replacing the single fixed wave-load Ritz vector with a wind-speed-dependent version. That change would allow the model to track how wave characteristics shift across the operating envelope, reducing the consistent underestimation found there.
Two further priorities emerge for future work. The study should be repeated with a reduced sensor set representative of monitoring systems already installed on operating turbines, rather than a configuration purpose-built for virtual sensing. Results also need validation against field measurements from real structures — something synthetic simulation data alone can’t provide.
Problems trace back to modeling
The study establishes that multi-band MDE can estimate fatigue damage equivalent stresses reliably across most of the IEA 15 MW offshore reference turbine’s support structure, with errors staying within ±5% for the majority of elevations and operating conditions.
Two zones are exceptions. Errors near the tower top can exceed 100% under operating conditions, and a consistent underestimation of up to 6% persists within ±15 m of mean sea level for every design load case examined. Both problems trace back to specific modeling choices: the lumped-inertia rotor representation and the time-invariant wave-load Ritz vector.
Normal power production governs most of the turbine’s fatigue life, while parked and locked-rotor conditions produce outsized damage per unit time due to the absence of aerodynamic damping. Addressing rotor flexibility in the structural model and adding wind-speed dependence to the wave-load representation are the two improvements most likely to close the accuracy gap identified here.
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