Research On Weak Fault Diagnosis Method Of Bearing Based On Time-Delayed Under-Damped Stochastic Resonance

Due to the influence of many irresistible factors,rotating machinery sometimes has various types of failures,thereby reducing the predetermined functions of the mechanical equipment.If the mechanical failures are not checked in time,huge economic losses will be caused due to the inability of the production process to operate normally or mechanical equipment damage,and even lead to catastrophic accidents and serious social impacts.Therefore,it is a very urgent problem to carry out condition monitoring and fault diagnosis by means of weak fault signals from bearings and other components to eliminate accidents.However,weak signals are often submerged in a strong noise background,which will interfere with signal extraction and processing.Traditional signal processing methods use different noise reduction techniques to suppress or filter out the negative effects of noise,but they also weaken the energy of useful signals.Stochastic resonance uses the synergy between the nonlinear system,noise and periodic signals to convert part of the noise energy into useful signal energy,thereby overcoming the shortcomings of traditional methods,achieving the purpose of enhancing useful signals and becoming a new way of weak signal detection under strong noise background.After describing the fault diagnosis methods and the current research status of stochastic resonance,this article then starts from the basic theory of classical bistable stochastic resonance,focusing on the weak signal detection methods of time-delay constrained bistable type,second-order underdamped continuous type and time-delayed underdamped tristable type,and the proposed methods are respectively applied to the fault diagnosis of rolling bearings.The main research work of this paper is as follows:(1)The application of time-delay constrained potential bistable stochastic resonance in bearing fault detection is studied.For the structural problems of classical stochastic resonance,and the effect of adding historical information to the system on stochastic resonance is not considered,a fault signal detection method of time-delay constrained potential stochastic resonance is proposed.Firstly,a time-delay constrained potential stochastic resonance model is established,the structure and functional characteristics of its potential function are described,the mathematical expression of the output signal-to-noise ratio is theoretically derived,and the influence of system parameters,time extension and feedback strength on the relationship between signal-to-noise ratio and noise intensity is investigated.Secondly,the best matching of the stochastic resonance system is achieved by using the parameter optimization algorithm.Finally,the proposed method is applied to the experiments of bearing fault signals,which has better results than the classical stochastic resonance method.(2)The application of underdamped continuous potential stochastic resonance in bearing fault detection is studied.In the classical stochastic resonance,the effect of inertia term is considered,and the damping factor is introduced to transform the first-order equation into the second-order equation to realize the secondary filtering effect of the signal.Firstly,a second-order underdamped continuous potential stochastic resonance model is established,and the influence of system parameters on the movement of particles between potential wells is studied.Then,the relationship between each parameter and the signal-to-noise ratio is further analyzed,and the ant colony algorithm is used to optimize the parameters of the potential function to obtain the optimal output signal.Finally,simulation and bearing experiments show that the proposed method has better characteristic frequency amplitude and anti-noise ability,and is superior to the classic stochastic resonance method in terms of weak fault feature extraction.(3)The application of time-delayed underdamped tristable stochastic resonance in bearing fault detection is studied.Combining the time-delayed model and the underdamped model,a time-delayed underdamped tristable stochastic resonance system is proposed.Firstly,the characteristics of the potential model are analyzed and the influence of each parameter on the potential model is studied.Then,the delay parameter,feedback parameter and damping parameter are introduced,combined with the Fokker-Planck equation to obtain the probability density function and signal-to-noise ratio of particle motion.Finally,simulation and bearing verification are carried out and compared with the processing results of time-delayed stochastic resonance system and underdamped stochastic resonance system to verify that the proposed method has higher signal-to-noise ratio and reliability.In summary,this paper investigates the time-delayed underdamped stochastic resonance method for bearing weak fault diagnosis and its application.The effectiveness of the proposed method is better verified in the bearing weak fault experiments when compared with the classical stochastic resonance and other methods in this paper.