基于双输入信号驱动的耦合分段对称三稳随机共振的轴承故障检测

Bearing fault detection based on coupled piecewise symmetric tri-stable stochastic resonance driven by dual-input signals

为解决传统双输入信号驱动的二维三稳随机共振系统(two-dimensional tri-stable stochastic resonance system driven by dual-input signals, DTDTSR)所存在的输出饱和和信号放大差等问题,独创性地提出了一种全新的系统:双输入信号驱动的耦合分段对称三稳态随机共振系统(coupled piecewise symmetric tri-stable stochastic resonance system driven by dual-input signals, DCPSTSR)。首先深入研究系统输出饱和性的问题,为系统性能的优化提供了关键理论基础。其次,在绝热近似理论的框架下,推导了系统的输出谱放大函数(spectral amplification, SA)。详尽分析了系统参数对其的影响,为更深层次的理解提供了理论支持。进一步,通过数值模拟对DCPSTSR、耦合分段对称三稳态随机共振系统(coupled piecewise symmetric tri-stable stochastic resonance system, CPSTSR)和DTDTSR系统进行了全面比较,结果明确指出DCPSTSR系统在输出谱放大函数方面显著优越于其他系统。最后,通过遗传算法对系统参数进行了精密优化,并将其成功应用于轴承故障检测。实验结果验证了DCPSTSR系统在性能上的卓越表现,为未来理论研究和工程应用提供了有力的理论支持和可行性验证。这一设计以及其在轴承故障检测方面的成功应用,为共振系统领域的进一步研究和实际应用提供了新的方向和范例,具有重要的科学和工程价值。

In order to solve the problems of output saturation and signal amplification difference of the traditional two-dimensional tristable stochastic resonance system driven by dual-input signals(DTDTSR),a novel system,coupled piecewise symmetric tri-stable stochastic resonance system(coupled piecewise symmetric tri-stable stochastic resonance system)driven by dual-input signals,is ingeniously proposed.A novel system is proposed:coupled piecewise symmetric tri-stable stochastic resonance system driven by dualinput signals(DCPSTSR).Firstly,the problem of output saturation of the system is studied in depth,which provides a key theoretical foundation for the optimization of the system performance.Secondly,the output spectral amplification(SA)function of the system is derived within the framework of the adiabatic approximation theory.The influence of system parameters on it is analyzed in detail,which provides theoretical support for deeper understanding.Further,a comprehensive comparison of the DCPSTSR,coupled piecewise symmetric tri-stable stochastic resonance system(CPSTSR)and DTDTSR systems is carried out through numerical simulations,and the results clearly indicate that the DCPSTSR system is significantly superior to the other systems in terms of output spectral amplification function.Finally,the system parameters are precisely optimized by genetic algorithm and successfully applied to bearing fault detection.The experimental results verify the excellent performance of the DCPSTSR system and provide strong theoretical support and feasibility verification for future theoretical research and engineering applications.This design and its successful application in bearing fault detection provide a new direction and example for further research and practical application in the field of resonance systems,which has important scientific and engineering value.