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Floating Offshore Wind Turbines (FOWTs) operate in the harsh marine environment with limited accessibility and maintainability. Not only failures are more likely to occur than in land-based turbines, but also corrective maintenance is more expensive. In the present study, a mixed model and signal-based Fault Diagnosis (FD) architecture is developed to detect and isolate critical faults in FOWTs. More specifically, a model-based scheme is developed to detect and isolate the faults associated with the turbine system. It is based on a fault detection and approximation estimator and fault isolation estimators, with time-varying adaptive thresholds to guarantee against false-alarms. In addition, a signal-based scheme is established, within the proposed architecture, for detecting and isolating two representative mooring lines faults. For the purpose of verification, a 10MW FOWT benchmark is developed and its operating conditions, which contains predefined faults, are simulated by extending the high-fidelity simulator. Based on it, the effectiveness of the proposed architecture is illustrated. In addition, the advantages and limitations are discussed by comparing its fault detection to the results delivered by other approaches. Results show that the proposed architecture has the best performance in detecting and isolating the critical faults in FOWTs under diverse operating conditions.