This paper attempts to investigate the stochastic resonance (SR) phenomenon in a delay-controlled dissipative bistable potential with time-delayed feedback under the action of harmonic excitation and additive noise by using small delay approximation theory and signal-to-noise ratio (SNR) theory. The time delay and feedback strength are able to adjust the potential shapes precisely by fusing potential parameters. Moreover, the steady-state probability distribution (SPD) and output SNR are derived to demonstrate that time-delayed feedback is able to control and improve the SR for enhancing the useful signal embedded in a noisy signal, where moderate time delay and feedback strength can maximize the output SNR. Therefore, a controlled SR method via time-delayed feedback is proposed to enhance useful signals embedded in mechanical signals for mechanical fault diagnosis, where the widely used frequency-shifted and rescaling transform is used to preprocess large-parameter vibration signals of double row cylindrical bearings. The experimental results indicate that the controlled SR method via time-delayed feedback can enhance the useful signal embedded in the vibration signal from double row cylindrical bearings where its amplitude is amplified up to tenfold than that in the envelope spectrum of raw signal.

本文试图利用小延迟近似理论和信噪比（SNR）研究在谐波激励和加性噪声作用下具有时滞反馈的时滞受控耗散双稳态电势中的随机共振（SR）现象。理论。时间延迟和反馈强度能够通过融合电势参数来精确调整电势形状。此外，推导了稳态概率分布（SPD）和输出SNR，以证明时滞反馈能够控制和改善SR，以增强嵌入在噪声信号中的有用信号，其中适度的时间延迟和反馈强度可以最大化输出SNR。因此，提出了一种通过时滞反馈控制的SR方法，以增强嵌入在机械信号中的有用信号，以进行机械故障诊断，其中广泛使用的频移和定标变换用于预处理双列圆柱轴承的大参数振动信号。实验结果表明，通过时滞反馈控制的SR方法可以增强嵌入在双列圆柱轴承振动信号中的有用信号，该信号的振幅被放大到原始信号包络谱的十倍。