In order to timely and effectively diagnose the incipient weak faults of a wind turbine gearbox, a fault diagnosis method for a wind turbine gearbox is proposed, which deals with the nonlinear, nonstationary, low amplitude and low SNR vibration signals. Firstly, the original vibration signal is decomposed into multiple intrinsic mode functions by using the optimal variational mode decomposition. Meanwhile, an “information entropy-kurtosis-envelop spectrum kurtosis” multidimensional feature evaluation model is constructed, which is combined with the entropy weight method to screen key intrinsic mode functions to reconstruct the signal. Then an improved wavelet threshold method is designed to perform secondary noise reduction, and the obvious fault shock characteristics are obtained. The broad learning system is used for fault classification, and the $L_{21