Research On Weak Signal Detection Method Of Two-Dimensional Stochastic Resonance System

Stochastic resonance is a phenomenon widely existing in nonlinear systems.It is characterized by the orderly output of the nonlinear system is abnormally enhanced under the combined action of random force and periodic driving force.Therefore,the use of stochastic resonance for weak signal detection is a new approach,which is to use noise to enhance the periodic response of the system by inducing the occurrence of stochastic resonance,so as to achieve the purpose of detecting weak target signals in a strong noise environment.The one-dimensional stochastic resonance system only requires one system variable to describe its dynamic behavior.However,a single system variable is not enough to cover all dynamic models in the field of stochastic resonance.An additional system variable is introduced to describe the system in the thesis,so that the one-dimensional potential field is expanded to the two-dimensional potential field.The stochastic resonance theory in the two-dimensional potential field is applied to the weak signal detection,and the detection of low-frequency signals in the strong noise environment is realized.The main research contents and methods of the thesis are as follows:1.A two-dimensional double-well stochastic resonance system is proposed to study the stochastic resonance mechanism and application of a two-dimensional double-well potential system driven periodically in noise.The analytical formula of the system output signal-to-noise ratio(SNR)is derived based on the adiabatic approximation theory.It is found that the system has a significant stochastic resonance phenomenon,and the output SNR can be further improved by increasing the driving force,coupling coefficient,correlation coefficient or reducing the driving frequency.The system is applied to the actual fault diagnosis of industrial bearings.The experimental results show that the system can effectively diagnose the faults of the inner and outer rings of the bearing,and by comparing the peak size and the peak recognition degree,it is proved that the fault detection effect of the system is better than that of the one-dimensional unsaturated bistable system.2.A two-dimensional tristable stochastic resonance system is proposed.The potential field structure of the two-dimensional tristable potential system and its stochastic resonance phenomenon under the combined action of noise and periodic driving force are analyzed.The probability flow method is used to derive the spectral power amplification(SPA)of the system,and the SPA is used as a measurement index.It is found that the SPA is proportional to the driving force amplitude and coupling coefficient,but inversely proportional to the driving frequency.The two-dimensional tristable stochastic resonance system is applied to the field of weak signal detection,and it is found that the twodimensional tristable stochastic resonance system can effectively detect the low-frequency signal and bearing fault signal in the extremely low SNR environment,and the detection performance is better than the one-dimensional asymmetric tristable stochastic resonance system.3.Two kinds of two-dimensional multi-stable potential systems are designed to study their potential field structure,and the probability flow equations of the transition between wells are obtained.According to the Langevin equation,the equivalent potential functions are derived,and then the transition rates between each steady state and the amplitude responses of each potential well are obtained by the probability flow method.Finally,the SPA of the systems for the target frequency are deduced.The theoretical results show that the stochastic resonance phenomenon of the system can be enhanced by appropriately increasing the coupling coefficient,asymmetry coefficient or reducing the driving frequency.The weak signal detection experimental results prove that the quadrangular twodimensional multi-stable potential system can successfully detect weak signals,and the performance of diagnosing bearing inner and outer ring faults is better than the onedimensional tristable stochastic resonance system.