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Minimum entropy deconvolution (MED) is not effective in extracting fault features in strong noise environments, which can easily lead to misdiagnosis. Moreover, the noise reduction effect of MED is affected by the size of the filter. In the face of different vibration signals, the size of the filter is not adaptive. In order to improve the efficiency of MED fault feature extraction, this paper proposes a firefly optimization algorithm (FA) to improve the MED fault diagnosis method. Firstly, the original vibration signal is stratified by white noise-assisted singular spectral decomposition (SSD), and the stratified signal components are divided into residual signal components and noisy signal components by a detrended fluctuation analysis (DFA) algorithm. Then, the noisy components are preprocessed by an autoregressive (AR) model. Secondly, the envelope spectral entropy is proposed as the fitness function of the FA algorithm, and the filter size of MED is optimized by the FA algorithm. Finally, the preprocessed signal is denoised and the pulse enhanced with the proposed adaptive MED. The new method is validated by simulation experiments and practical engineering cases. The application results show that this method improves the shortcomings of MED and can extract fault features more effectively than the traditional MED method. [ABSTRACT FROM AUTHOR]