自适应多尺度噪声调节二阶随机共振增强方法

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摘要经典双稳态随机共振系统通过各种参数的调节可实现噪声、周期信号及非线性双稳态系统的最佳匹配从而实现随机共振，促使系统输出的微弱周期分量得到了一定的噪声能量而达到增强的效果，从而有效检测出微弱的周期分量，但噪声能量利用有限，系统响应中仍存在一定的噪声能量。二阶随机共振增强的系统模型，借助“双重积分”实现噪声的重复利用，将噪声进行二次利用，有效促进高频噪声能量进一步转移到低频区域，有效提高输出响应的信噪比。考虑到多尺度带限噪声对随机共振的影响，并基于随机共振特殊低通滤波器的数学本质，本文提出了以协同信噪比为目标函数，基于Paul小波的自适应多尺度噪声调节（Mutiscale noise tuning，MST）二阶随机共振增强方法，充分利用了小波的多分辨时频分析能力，将输入信号和噪声划分到不同频带，实现了不同频带信号和噪声强度大小的控制，以进一步改善随机共振检测效果。数值仿真、实验数据及工程实际应用均验证了该方法的有效性。

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	李国英1
	王诗彬2
	杨志勃2
	李继猛3
	陈雪峰2

关键词 ：随机共振, 噪声调节, 故障诊断, 非线性系统

Abstract：The best matching between noise, periodic signal and nonlinear bistable system can be realized through tuning various parameters to achieve stochastic resonance in the classical bistable stochastic resonance system. That makes a weak periodic component in the system output got a certain amount of noise energy and achieved enhanced effect. Thus the weak periodic components can be effectively detected. However, the capability of using noise to enhance signal is limited. There are still some useful noise in the system response. Hence, aiming at the repeated utilization of the noise by virtue of double integration, a system model with second-order stochastic resonance enhanced method is proposed to reuse the noise twice and effectively promote high-frequency noise energy transferring to the low-frequency area in order to improve the signal-to-noise ratio of output response effectively. The second order stochastic resonance enhancement method based on the adaptive multiscale noise tuning of using Paul wavelet with the collaborative SNR as the objective function is proposed in the thesis taking the effect of the multiscale noise on stochastics resonance into account, and based on the mathematical nature of the special low-pass filter of stochastic resonance. This method makes full use of the ability of multi-resolution time-frequency analysis of wavelet, which can divide the input signals and noise into different frequency bands for realizing the control of intensity of signal and noise in different frequency bands, has been fully applied in the method. The property of the second order stochastic resonance, which can achieve the enhancement utilization of the noise energy in the signals, has been fully used. The proposed method has been validated by simulation tests and actual application in engineering.

Key words： Stochastic resonance Noise tuning Fault diagnosis Nonlinear systems

收稿日期: 2020-12-29 出版日期: 2022-06-28

引用本文:

李国英1，王诗彬2，杨志勃2，李继猛3，陈雪峰2. 自适应多尺度噪声调节二阶随机共振增强方法[J]. 振动与冲击, 2022, 41(12): 8-15.
LI Guoying1，WANG Shibin2，YANG Zhibo2，LI Jimeng3，CHEN Xuefeng2. An adaptive multiscale noise tuning second order stochastic resonance enhanced method. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(12): 8-15.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I12/8

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