Mechanism Analysis Of The Large Signal Scale-transformation Stochastic Resonance And Its Engineering Application Study

Taking a nonlinear bistable system, on the basis of describing the properties of the bistable system, noise and response of the system to noise, respectively, the stochastic resonance (SR) phenomenon created by cooperation of the three parts of the bistable system, noise and an input signal is thoroughly investigated in detail under the condition of small parameters. The SR mechanism is analyzed from the structure of frequency spectrum, and it is considered that the bistable system changes the uniform distributed power spectrum of white noise, which makes most of the noise energy accumulate to low frequency area to form Lorentz distributed response spectrum. Only the frequency of the input signal locates in the low frequency region, can the signal be selected by a proper noise level to produce SR phenomenon. Once the signal frequency departs from the low frequency band concentrated by most noise energy, the SR phenomenon may be weakened quickly or even disappear. Although the enhancement of noise intensity is able to widen the low frequency district, this wideness is very limited and quite difficult to choose the input signal to reach SR. Therefore, the SR is comparatively more sensitive to the frequency of the input signal. Increasing the signal amplitude or decreasing the parameter value of the bistable system, i.e., reducing the potential barrier is benefit to make SR. To solve such a problem met in engineering application frequently as detecting weak signal submerged in strong noise by means of the SR technique, in terms of the theory of small parameter SR, a novel method of Scale-transformation Stochastic Resonance (STSR) is proposed. The core of the method is that, by selecting the compressed (or twice sampling) frequency, the transformation of the large frequency to the small one can postpone the large frequency signal to satisfy the condition of the small parameter SR. Then with large parameters, the SR-like phenomenon may be brought, this is, a detected SR spectral spike at the signal frequency can be created. The quantitive study of the large parameter SR confirms how to choose the compressed frequency for different noise strength and provides the low frequency band for producing the detected SR spectral peak, i.e., the ratio of signal frequency and practical sampling frequency should be equal to or larger than 50, since only the number can move the signal frequency into the low frequency area to build the large parameter SR. For bistable systems connected in series, under the analysis of color noise property, the time waveform of the cascaded system and its frequency spectrum are researched comparatively. The result proves that a single bistable system has better spectral characters than a cascaded bistable system does. However, a cascaded bistable system possesses stronger ability in weak signal extraction in time domain because of its effectiveness of eliminating high frequency burrs and revealing waveform's outline prominently. According to the STSR technique, a set of self-adaptive frequency-sweeping SR system has been developed for practical engineering application. The system can realize all over search for sampling frequency and system parameter and fulfill large parameter SR. The developed system has been applied to such engineering cases as monitoring and diagnosis of electromotor faults, vibration analysis of metal cutting, magnetic leakage detection of oil pipe faults, and so on. The application has presented the practicability and effectiveness of the technique, and hence it has a spreading value and a promising future.