Floating offshore wind turbine (FOWT) can harvest more wind energy in deep waters. However, due to the complex mechanical structures and harsh working conditions, various sensors, actuators, and components of FOWT can malfunction and fail. To avoid serious accidents and reduce operation and maintenance costs, fault detection plays a critical role in wind energy engineering, particularly for offshore wind energy. Because of the complex characteristics such as dynamics and nonlinearity, an accurate mathematical model can not be easily obtained from first principles for FOWT. In this paper, a new data-driven fault detection method based on kernel canonical variable analysis (KCVA) is proposed for FOWTs. In the proposed method, the collected measurements are first augmented into time-lagged variables to capture the dynamics of FOWT. Then, the time-lagged variables are mapped to a high-dimensional feature space to extract nonlinear features. Specifically, canonical variable analysis (CVA) is carried out to explore the correlations in high-dimensional feature space. For fault detection, two monitoring indexes, including $T^2$ and $SPE$ statistics are established. To verify the performance of the proposed KCVA based fault detection method, experiments on a high-fidelity FOWT benchmark, which was created from the National Renewable Energy Laboratory (NREL) FAST v8.0 simulator were carried out. Results show the capability and efficiency of the proposed KCVA-based fault detection method in comparison with other related methods.

In this paper, a novel randomized Fisher discriminant analysis (RFDA) based bearing fault diagnosis method is proposed. First, several representative time-domain features are extracted from the raw vibration signals. Second, linear Fisher discriminant analysis (FDA) is extended to nonlinear FDA named RFDA by introducing the random feature map to deal with the non-linearity issue. Specifically, the extracted time-domain features data are mapped onto a high-dimensional space using the random feature map function rather than kernel functions. Third, the time-domain features are fed into the built RFDA model to extract the discriminant features for diagnosis. Moreover, a Bayesian inference is employed to identify the class of the collected vibration signals to diagnose the bearing status. The proposed method uses random Fourier features to approximate the kernel matrix in the kernel Fisher discriminant analysis. Through employing randomized Fisher discriminant analysis, the nonlinearity issue is dealt with, and the computational burden is remarkably reduced compared to the kernel Fisher discriminant analysis (KFDA). To illustrate the superior performance of the proposed RFDA-based bearing fault diagnosis method, comparative experiments are conducted on two widely used datasets, the Case Western Reserve University (CWRU) bearing dataset and the Paderborn University (PU) bearing dataset. For the CWRU dataset, the computation time of RFDA is much shorter than KFDA, while the accuracy rate reaches the same level of KFDA. For the PU dataset, the accuracy rate of RFDA is slightly higher than KFDA, and the computation time is only 44.14% of KFDA.