CRDM (Control Rod Drive Mechanism) is the key equipment of nuclear reactors. Accurate fault diagnosis can improve the reliability of CRDM equipment and effectively and quickly eliminate related faults, thus ensuring the safety of reactors. However, due to its complex operating environment, the fault characteristics of CRDM are easily masked by complex and changeable noises, resulting in difficulty in fault identification. To solve this problem, this paper proposes a fault diagnosis method for KELM based on ensemble empirical Mode decomposition (EEMD), wavelet threshold denoising and whale optimization (WOA). Firstly, an EEMD-Wavelet threshold signal denoising method is proposed according to correlation criterion and kurtosis criterion. Then, the time domain feature, frequency domain feature, EEMD modal component energy and sample entropy feature of noise reduction signal were extracted to construct a multi-scale feature set that can accurately reflect the fault state. Finally, a classification method based on WOA-KELM is proposed to diagnose the fault feature set accurately. The proposed method is validated with CRDM vibration signal data set, and compared with common fault diagnosis methods, the results show that the fault diagnosis method based on EEMD-Wavelet threshold denoising and WOA-KELM has higher fault classification accuracy.