组合型幂指函数三稳态随机共振微弱信号检测

在强噪声背景下，针对微弱信号的检测和提取困难的问题，在经典的双稳态系统模型基础上，结合Gaussian Potential模型提出了一种新的组合型幂指函数的三稳态系统模型。首先，构造组合型幂指函数的三稳态系统模型，通过调节系统参数进行数值仿真，验证新型的三稳态系统模型能够产生随机共振现象；其次，以输出的平均信噪比（SNR）作为测度指标，结合人工鱼群智能算法进行相应参数寻优，使得组合型幂指函数的三稳态系统输出信噪比最大，从而达到随机共振现象。轴承故障诊断实验分析中，在输入信噪比为-25.8 dB条件下，分别通过双稳态系统和组合型幂指函数的三稳态系统得到的输出信噪比分别为-13.1 dB和-8.59 dB，说明组合型幂指函数三稳态系统性能优于双稳态系统性能。

Weak signal detection based on combination of power and exponential function model in tri-stable stochastic resonance

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.