Identification Uncertainties of Bending Modes of an Onshore Wind Turbine for Vibration-Based Monitoring

This study considers the identification uncertainties of closely spaced bending modes of an operating onshore concrete-steel hybrid wind turbine tower. The knowledge gained contributes to making mode shapes applicable to wind turbine tower monitoring rather than just mode tracking. One reason is that closely spaced modes make it difficult to determine reliable mode shapes for them. For example, the well-known covariance-driven stochastic subspace identification (SSI-COV) yields complex mode shapes with multiple mean phases in the complex plane, which does not allow error-free transformation to the real space. In contrast, the Bayesian Operational Modal Analysis (BAYOMA) allows the determination of real mode shapes. The application of BAYOMA presents a further challenge when quantifying the associated uncertainties, as the typical assumption of a linear, time-invariant system is violated. Therefore, validity is not self-evident and a comprehensive investigation and comparison of results is required. It has already been shown in a previous study that the significant part of the uncertainty in the mode shapes corresponds to their orientation in the mode subspace (MSS). Despite all the challenges mentioned, there is still a great need to develop reliable monitoring parameters (MPs) for Structural Health Monitoring (SHM). This study contributes to this by analysing metrics for comparing mode shapes. In addition to the well-known Modal Assurance Criteria (MAC), the Second-Order MAC (S2MAC) is also used to eliminate the alignment uncertainty by comparing the mode shape with a MSS. In addition, the mode shape identification uncertainties of BAYOMA are also considered. Including uncertainties is also essential for the typically used natural frequencies and damping ratios, which can be more appropriately used if the identification uncertainty is known.