Fast-varying Natural Frequencies and Damping Ratio Identification for Linear Time-Varying System

This work proposes a physics-enhanced machine learning approach for the system identification of Linear Time-Varying (LTV) systems under time-varying operating conditions in terms of fast-varying natural frequencies and damping ratios by combining a long short-term memory network with an Extended Kalman Filter (EKF). The proposed approach uses vibration data (displacement and velocity measurements), domain knowledge of modal damping ratios, and a physics-based model that can yield an approximate natural frequencies time-dependency model. The approach is validated using synthetic data generated from a finite element model of a 2-blade offshore wind turbine under realistic environmental and operating conditions. This system displays fast time-varying frequencies due to operating conditions, whose identification is particularly challenging because of the wind and wave loading. The robustness of the proposed approach is assessed under assumed incorrect system information (e.g. damping ratio). The proposed approach is evaluated across different environmental and operating conditions to show its applicability to different operating regimes. The results show the approach can accurately identify the selected fast-varying natural frequency, 1st Fore-Aft (FA-1) mode, with a maximum root mean square error of 0.0012 Hz. The results demonstrate that the model trained on EKF estimates depends on accurate damping values, whereas the model trained on physics-based data exhibits robustness to incorrect damping assumptions. The approach is extended to damping ratio identification for the selected mode by estimating the root mean square error between models trained on EKF estimates and physics-based data. The results show that the approach can yield a good approximation of the FA-1 mode damping ratio using grid search, offering an improvement over covariance-driven stochastic subspace identification.