Abstract: In industrial production, bearings are widely used in rotating machinery. Bearing fault diagnosis plays an important role in preventing disasters and protecting lives and properties. Because weak bearing fault characteristics are often submerged in a noise background, the difficulty of extracting the bearing fault feature information is increased. Therefore, this paper proposed a method which combined the general scale transformation theory with the adaptive stochastic resonance in a periodical potential system. This method was used to detect the fault characteristics of the bearing rolling element in the noise background. In the proposed method, general scale transformation was first used to satisfy the condition of small parameters in the stochastic resonance. Then the random particle swarm optimization algorithm was applied to choose the optimal system parameters to affect the adaptive stochastic resonance. Meanwhile, an improved signal-to-noise ratio (ISNR) was set as the evaluation index in the adaptive stochastic resonance. After being processed and optimized by the adaptive stochastic resonance based on the general scale transformation method, the experimental weak signal with a rolling element bearing failure under the noise background could be effectively extracted. In addition, the effect of processing fault signals by the adaptive stochastic resonance in the periodical potential system was compared with the adaptive stochastic resonance method in a bistable system based on the general scale transformation. The results show that the adaptive stochastic resonance in the periodical potential system increases the signal-to-noise ratio better than the adaptive stochastic resonance in the bistable system. Moreover, the adaptive stochastic resonance in the periodical potential system involves fewer iterations, and the computation time is shorter than that of the adaptive stochastic resonance in the bistable system. This indicates that the proposed method of diagnosing bearing element fault based on the general scale transformation and the adaptive stochastic resonance in a periodical potential system is superior. Especially in engineering systems, a large amount of data and extensive computation time is required for fault diagnosis. Because of the early fault warning system achieved by the proposed method, fault diagnosis is more efficient and unnecessary losses are reduced. Therefore, the proposed method can serve as a reference in improving the efficiency of mechanical equipment fault diagnosis in engineering systems.