Purpose

To solve the problem that it is difficult to detect the weak bearing fault signal from high-intensity noise, a method of bearing fault detection based on the two-dimensional tri-stable system (TDTS) is proposed.

Methods

The analytical expression for the spectral power amplification (SPA) of the TDTS is derived using the probabilistic flow method. The stochastic resonance (SR) mechanism of the TDTS is studied with the SPA as a measure index. The fourth-order Runge–Kutta method and the genetic algorithm are utilized to carry out the numerical simulation. Apply the TDTS to the weak periodic signal detection and the bearing fault detection.

Results

In this work, the potential field structure of the TDTS is discussed. The SPA of the TDTS to the periodic driving force is derived. The influence of the coupling coefficient, the driving frequency, and the driving force amplitude on the SPA is analyzed. The performance of the TDTS and the ODATS to detect weak signals from intense noise are compared.

Conclusions

The theoretical analysis shows that SR phenomena occur in the TDTS. As the noise intensity increases, the SPA presents a unimodal trend, that is, the noise of a specific intensity can enhance the response of the TDTS to the weak external driving force. Moreover, the enhancement effect is proportional to the amplitude of the driving force and the coupling coefficient, and inversely proportional to the driving frequency. The experimental results indicate that the TDTS can effectively detect the weak periodic signal and detect the inner and outer ring faults of the bearings. The detection effects are preferable to that of the one-dimensional asymmetric tri-stable system (ODATS). The effectiveness and advancement of the proposed method are proved.

中文翻译：

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基于二维三稳态随机共振系统的滚动轴承故障检测方法

目的

为了解决难以从高强度噪声中检测出较弱的轴承故障信号的问题，提出了一种基于二维三稳态系统（TDTS）的轴承故障检测方法。

方法

TDTS的频谱功率放大（SPA）的解析表达式是使用概率流方法得出的。以SPA为指标，研究了TDTS的随机共振（SR）机制。利用四阶Runge–Kutta方法和遗传算法进行数值模拟。将TDTS应用于弱周期性信号检测和轴承故障检测。

结果

在这项工作中，讨论了TDTS的潜在场结构。得出TDTS对周期性驱动力的SPA。分析了耦合系数，驱动频率和驱动力幅度对SPA的影响。比较了TDTS和ODATS从强噪声中检测微弱信号的性能。

结论

理论分析表明，在TDTS中会出现SR现象。随着噪声强度的增加，SPA呈现单峰趋势，即特定强度的噪声可以增强TDTS对弱外部驱动力的响应。此外，增强效果与驱动力的振幅和耦合系数成正比，与驱动频率成反比。实验结果表明，TDTS可以有效地检测弱周期性信号，并检测轴承的内，外圈故障。检测效果优于一维非对称三稳态系统（ODATS）。证明了该方法的有效性和先进性。