Research On Weak Signal Detection Model Based On Stochastic Resonance And Its Application

In weak signal detection,noise interference has always been the object that people try to eliminate.However,in some nonlinear systems,an appropriate amount of noise can help enhance the system response.We call this phenomenon of using noise energy to enhance weak characteristic signals as stochastic resonance(SR).Different from the traditional method of extracting fault signals through noise reduction,SR realizes the extraction of weak fault characteristics by transferring noise energy to weak fault characteristic signals.Therefore,the research of weak signal detection based on stochastic resonance mechanism is of great significance.Aiming at the shortcomings of the existing SR method,this paper proposes corresponding solutions.Finally,the proposed method is applied to the weak fault signal diagnosis of mechanical equipment.The main research content and contributions are as follows:(1)A weak fault feature extraction method based on Ensemble Empirical Mode Decomposition(EEMD)and Woods-Saxon stochastic resonance is proposed.First,we use EEMD to extract sensitive IMFs.Secondly,Woods-Saxon stochastic resonance is performed on sensitive IMFs to realize weak fault feature extraction.Simulation and bearing experiment results show that the extraction effect of EEMD combined with Woods-Saxon stochastic resonance is better than that of only using Woods-Saxon stochastic resonance.(2)Aiming at the saturation characteristics of SR,that is,as the input signal continues to increase,while the output signal tends to be stable,the proposed piecewise nonlinear bistable stochastic resonance(PNBSR)model has achieved certain results.However,the potential barrier in the middle of the piecewise potential function of the PNBSR method still uses the traditional SR potential function completely.There is no fundamental solution to the fourth-order limitation.An improved piecewise mixed stochastic resonance potential model is proposed.This model is compared with the PNBSR model,and it is applied to the experimental verification of early bearing failure.(3)An asymmetric underdamped second-order stochastic resonance(AUSSR)weak fault feature extraction method is proposed.By adjusting the damping factor and the asymmetry,weak signals,noise,and potential wells are matched to each other to achieve the best stochastic resonance state.Furthermore,we combine the constrained potential function with the underdamped second-order system,and propose a constrained potential underdamped second-order stochastic resonance(CPUSSR)system.Under adiabatic approximation conditions,the output signal-to-noise ratio of the system is derived.Finally,the above two methods are compared with the traditional underdamped second-order stochastic resonance method.(4)The classic bistable stochastic resonance(CBSR)model is a short-memory system,and historical information cannot be added to the negative feedback process of stochastic resonance through an appropriate way.A weak signal detection method based on time-delay feedback mixed potential stochastic resonance(TFMSR)is proposed to enhance weak fault characteristic signal.It not only overcomes the saturation characteristics of CBSR,but also solves the short memory problem of the system(5)Aiming at the problem that the intermediate potential well part of the traditional three-stable method cannot be adjusted independently,a new compound tri-stable stochastic resonance(CTSR)model is proposed by combining the Gaussian Potential model and the mixed bi-stable model.Compared with the traditional tri-stable stochastic resonance(TTSR)method,all parameters of CTSR model have no coupling characteristics.The CTSR model retains the advantages of constraint and continuity of the Gaussian Potential model,and has a higher utilization rate of noise.In summary,based on the stochastic resonance model,this paper studies the influence of nonlinear systems on weak signal detection from several aspects such as combining with traditional method,saturation characteristics,model order,time delay feedback and potential well influence.The practicability and superiority of the proposed methods are verified by simulation and experiment.