A new time-domain analysis method that uses second generation wavelet transform (SGWT) for weak fault feature extraction is proposed. To extract incipient fault feature, a biorthogonal wavelet with the characteristics of impact is constructed by using SGWT. Processing detail signal of SGWT with a sliding window devised on the basis of rotating operation cycle, and extracting modulus maximum from each window, fault features in time-domain are highlighted. To make further analysis on the reason of the fault, wavelet package transform based on SGWT is used to process vibration data again. Calculating the energy of each frequency-band, the energy distribution features of the signal are attained. Then taking account of the fault features and the energy distribution, the reason of the fault is worked out. An early impact-rub fault caused by axis misalignment and rotor imbalance is successfully detected by using this method in an oil refinery.