Research On Weak Signal Detection Method Based On Tri-stable Unsaturated Stochastic Resonance Model

Signal detection is an important part of detection technology,and when the energy of its useful component is too low compared with the noise energy,it is called weak signal.Aiming at the problem that weak signal is difficult to detect,a signal feature extraction method based on stochastic resonance(SR)is studied,it is found that the output saturation phenomenon exists in the standard tri-stable stochastic resonance(STSR),and an unsaturated piecewise tri-stable stochastic resonance(UPTSR)model which can overcome the output saturation phenomenon is proposed.And on the basis of this model,it is further improved and extended to obtain better output characteristics and wider application range.Firstly,the Langevin equation is obtained according to the motion of Brownian particle,and then the stochastic resonance system is introduced.The Fokker-Planck equation is derived in detail by the Markov process,and the Kramers escape rate of the system is derived on this basis.The output power spectrum and Signal to Noise Ratio(SNR)of the system are obtained using the adiabatic approximation theory.The fourth order Runge-Kutta equation is used to solve the stochastic resonance model numerically.The STSR potential function is substituted into Langevin equation and the feature extraction capability of stochastic resonance system is verified by simulation signals.The output saturation characteristic of STSR is studied,and then the UPTSR model is proposed to solve this problem,and it is verified that the proposed UPTSR model can successfully overcome the problem of output saturation.The UPTSR model is verified to have better output characteristics by using the output signal-to-noise ratio,and still has a higher output signal-to-noise ratio when only one parameter in the stochastic resonance system is adjusted,which verifies the universality of the results.Finally,STSR method and UPTSR method were used to extract the feature of fault signals from simulation signals and experimental signals respectively,further verifying that UPTSR has better output characteristics than STSR.On the basis of UPTSR,the time-delay feedback unsaturated piecewise tri-stable stochastic resonance(TFUPTSR)model induced by white Gaussian noise is studied.The delay Fokker-Planck equation is obtained,the probability density function and the mean first passage time of TFUPTSR are derived,and the influence of various parameters on TFUPTSR is analyzed.Meanwhile,the influence of time delay term on SR system is discussed deeply by comparing the shape variation of TFUPTSR potential function with parameters.Then,by comparing the output signal-to-noise ratio of UPTSR and TFUPTSR,found that the output characteristic of TFUPTSR is better.Finally,the same experimental signals are processed by UPTSR method and TFUPTSR method respectively to further demonstrate the effectiveness and superiority of TFUPTSR model.On the basis of UPTSR,the UPTSR model in underdamped state is studied,and the second order stochastic resonance equation is solved by Runge-Kutta method.The generalized potential function of the underdamped UPTSR is derived,and the probability density function of the underdamped UPTSR is obtained according to its Fokker-Planck equation.The correctness of the derivation is proved by the images of two physical quantities.By comparing the output signal-to-noise ratio of the UPTSR model under the two conditions,and the processing capacity of the UPTSR model under the two conditions for simulated signals and experimental signals,it is further verified that the underdamped UPTSR model has better performance.In order to further expand the application range of UPTSR,two kinds of color noise(Lévy noise and dichotomous noise)numerical simulation generation methods are studied,and the UPTSR model driven by these two kinds of noise is also studied.Especially,the mean of signal to noise ratio gain(SNR-GM)is studied,the influence of system parameters of UPTSR model on SNR-GM is analyzed,and the effect of the intrinsic numerical parameters of the two kinds of noise on the variation of SNR-GM curve.Finally,the UPTSR system driven by Lévy noise and dichotomous noise is used to process the simulation signal and the experimental signal to verify that under the effect of Lévy noise and dichotomous noise,UPTSR system still has the function of extracting and amplifying characteristic signals.