Adaptive Variational Mode Decomposition for Bearing Fault Detection

Rolling element bearings are commonly used in rotary mechanical and electrical equipment. According to investigation, more than half of rotating machinery defects are related to bearing faults. However, reliable bearing fault detection still remains a challenging task, especially in industrial applications. The objective of this work is to propose an adaptive variational mode decomposition (AVMD) technique for non-stationary signal analysis and bearing fault detection. The AVMD includes several steps in processing: 1) Signal characteristics are analyzed to determine the signal center frequency and the related parameters. 2) The ensemble-kurtosis index is suggested to decompose the target signal and select the most representative intrinsic mode functions (IMFs). 3) The envelope spectrum analysis is performed using the selected IMFs to identify the characteristic features for bearing fault detection. The effectiveness of the proposed AVMD technique is examined by experimental tests under different bearing conditions, with the comparison of other related bearing fault techniques.

Weak signal detection method based on novel composite multistable stochastic resonance

The weak signal detection method based on stochastic resonance is usually used to extract and identify the weak characteristic signal submerged in strong noise by using the noise energy transfer mechanism.We propose a novel composite multistable stochastic-resonance(NCMSR)model combining the Gaussian potential model and an improved bistable model.Compared with the traditional multistable stochastic resonance method,all the parameters in the novel model have no symmetry,the output signal-to-noise ratio can be optimized and the output amplitude can be improved by adjusting the system parameters.The model retains the advantages of continuity and constraint of the Gaussian potential model and the advantages of the improved bistable model without output saturation,the NCMSR model has a higher utilization of noise.Taking the output signal-to-noise ratio as the index,weak periodic signal is detected based on the NCMSR model in Gaussian noise andαnoise environment respectively,and the detection effect is good.The application of NCMSR to the actual detection of bearing fault signals can realize the fault detection of bearing inner race and outer race.The outstanding advantages of this method in weak signal detection are verified,which provides a theoretical basis for industrial practical applications.

Analysis of weak signal detection based on tri-stable system under Levy noise

Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.

Research and application of stochastic resonance in quad-stable potential system

To solve the problem of low weak signal enhancement performance in the quad-stable system,a new quad-stable potential stochastic resonance(QSR)is proposed.Firstly,under the condition of adiabatic approximation theory,the stationary probability distribution(SPD),the mean first passage time(MFPT),the work(W),and the power spectrum amplification factor(SAF)are derived,and the impacts of system parameters on them are also extensively analyzed.Secondly,numerical simulations are performed to compare QSR with the classical Tri-stable stochastic resonance(CTSR)by using the genetic algorithm(GA)and the fourth-order Runge–Kutta algorithm.It shows that the signal-to-noise ratio(SNR)and mean signal-to-noise increase(MSNRI)of QSR are higher than CTSR,which indicates that QSR has superior noise immunity than CTSR.Finally,the two systems are applied in the detection of real bearing faults.The experimental results show that QSR is superior to CTSR,which provides a better theoretical significance and reference value for practical engineering application.

Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises

Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system(CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system(PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time(MFPT), and output signal-to-noise ratio(SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency,and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.