In this study, the system with fractional power nonlinearity is introduced into the theory of aperiodic stochastic resonance (ASR). The fractional exponent is a key parameter and its effect on the ASR phenomenon excited by aperiodic binary signal is investigated in this system. Compared to the classical bistable system, the system with fractional power nonlinearity shows better performance. It can adjust not only the noise intensity but also the fractional exponent to enhance weak signal. In the field of signal transmission, pure aperiodic binary signal is usually submerged in the noise and the signal is unknown. Thus, an effective method is proposed based on ASR and moving average. By the method, the unknown aperiodic binary signal can be recovered in the noise background. To improve the efficiency of the signal recovery, the adaptive ASR is realised with the help of adaptive particle swarm optimisation (APSO) algorithm to optimise the parameters. The method may provide some reference to the engineering field.

在这项研究中，将具有分数功率非线性的系统引入非周期性随机共振（ASR）理论。分数指数是关键参数，在该系统中研究了分数指数对非周期性二进制信号激发的ASR现象的影响。与经典的双稳态系统相比，具有分数幂非线性的系统表现出更好的性能。它不仅可以调节噪声强度，而且可以调节分数指数以增强微弱信号。在信号传输领域，纯非周期二进制信号通常被淹没在噪声中，并且该信号是未知的。因此，提出了一种基于ASR和移动平均的有效方法。通过该方法，可以在噪声背景中恢复未知的非周期性二进制信号。为了提高信号恢复的效率，通过自适应粒子群算法（APSO）对参数进行优化，实现了自适应ASR。该方法可以为工程领域提供一些参考。