Under the background of strong noise, it is difficult to detect and extract weak signals. To solve the above problems, a new combination model of power and exponential function in tri-stable system was proposed based on the classic bistable system model and the Gaussian Potential model. First of all, the tri-stable system model was constructed by combining power function and exponential function, then the stochastic resonance was generated by adjusting related parameters, which was validated by numerical simulations. Secondly, using the average Signal-to-Noise Ratio (SNR) of output as a measure index, the artificial fish swarm intelligence algorithm was used to optimize the corresponding parameters, which makes the tri-stable system combining the power function and the exponential function achieve the maximum output SNR, and the phenomenon stochastic resonance was generated. Finally, it was applied to the diagnosis of bearing faults. At the same condition that the output SNR is -25.8 dB, the output SNR of the bistable system and tri-stable system combining the power function and the exponential function is -13.1 dB and -8.59 dB respectively. Simulation results demonstrate that the performance of the proposed system is better than the bistable system, and it is effective in weak signal detection and extraction.