Vibration signals acquired from a gearbox usually are complex, and it is difficult to detect the symptoms of an inherent fault in a gearbox. In this paper, an adaptive redundant second generation wavelet (ARSGW) based on second generation wavelet (SGW) is developed. It adopts data-based optimization algorithm to design the initial prediction operator and update operator at each scale. The initial operators are interpolated with zero, and then the redundant prediction operator and update operator are obtained. The splitting step in ARSGW is removed, the approximation signal at each scale is predicted and updated with redundant prediction operator and update operator directly, and the length of approximation signal and detail signal at every scale remains the same, ARSGW eliminates translation variance of SGW. Since the redundant prediction operator and update operator lock on to the dominant structure of the signal, ARSGW can well reveal the characteristics of the signal in time domain. ARSGW is found to be very effective in detection of symptoms from the vibration signal of a large air compressor gearbox with impact rub fault. SGW is also used to analyze the same signal for comparison, no modulation signals and periodic impulses appear at any scale.