Performance of Multi-Band MDE-Based Virtual Sensing for Estimating Lifetime Fatigue Damage Equivalent Loads for the IEA 15 MW Reference Wind Turbine

Abstract. Growing Offshore Wind Turbines (OWTs) are increasingly vulnerable to fatigue damage, motivating stress monitoring at critical, often inaccessible locations, for asset integrity management and life-extension. Virtual sensing methodologies, such as multi-band Modal Decomposition and Expansion (MDE), offer a solution by extrapolating measurements from sensors at accessible locations. However, existing MDE studies often model the Rotor-Nacelle-Assembly (RNA) as a lumped mass inertia, thereby ignoring blade flexibility and rotor operation. This leads to errors in estimated strains or stresses, particularly close to the tower top, where blade vibrations significantly influence the structural response. Moreover, neglecting blade flexibility can also lead to inaccurate tower mode shapes, causing errors not limited to the tower top.

The present paper investigates the errors of multi-band MDE estimates resulting from modelling the RNA as a lumped inertia. To this end, a dataset of HAWC2 simulations covering the Fatigue Limit State (FLS) design life of the IEA Wind 15-Megawatt Offshore Reference Wind Turbine with a monopile foundation (IEA 15-MW RWT) is considered. Utilizing this dataset, multi-band MDE is used to estimate section moments along the entire supporting structure of the IEA 15-MW RWT. These estimates are compared against the true response extracted from the dataset in terms of Damage Equivalent Loads (DELs) and Damage Equivalent Stresses (DESs) combined for the individual Design Load Cases (DLCs). Additionally, the error of the MDE estimates is assessed for individual 10-minute time series from the same dataset. Based on the combined DELs and DESs, it is concluded that the MDE used in the present work performs well for long-term estimates, except in the area around the tower top, where blade vibrations and 3P effects significantly impact the quality of the estimates. It is shown that the MDE errors for the individual 10-minute time series are generally in the range of. However, the error is as high as in the tower top, where the impact from the lumped inertia RNA model is large. Finally, the error of the MDE estimates exhibits wind speed dependency. This underlines the inherent limitation in the MDE, which assumes a linear and time-invariant response and thus cannot capture the temporal variability of the dynamic model due to changing operational and environmental conditions. In conclusion, multi-band MDE provides accurate estimates of section moments across most of the IEA 15-MW RWT supporting structure, though without capturing the effects of operational and environmental variability. Furthermore, improvements are necessary to effectively capture the effects of blade flexibility, particularly near the tower top.