In the field of fault detection, the nonstationary characteristics caused by external disturbances of wind turbines and other reasons can mask the fault signals, while the inconsistent data distribution between training data and test data due to equipment loss and other reasons can lead to model mismatch problems, both of which can lead to the degradation of fault detection performance. In order to solve the above problems, a novel adaptive fault detection framework is proposed in this work. First, the stationary features of nonstationary variables are extracted based on short-time Fourier analysis, after which the features are combined with the stationary variables. Second, isolation-based anomaly detection using nearest-neighbor ensembles is introduced as monitoring metrics for designing the statistic for the slow feature analysis method. Then, the differences between online normal data and training data are calculated, the model update factor and update strategy are designed, and an adaptive fault detection framework based on short-time Fourier transform-slow feature analysis (STFT-SFA) is proposed. Finally, the effectiveness of the proposed fault detection framework is verified using the Tennessee-Eastman process and actual wind turbine data. The results show that the proposed STFT-SFA method has a 94.0% correct monitoring rate (CMR) for Tennessee Eastman process failures, and the proposed adaptive STFT-SFA method has a 95.6% CMR for wind turbine failures, which are better than other comparative fault detection methods.