A New Dynamical Method for Bearing Fault Diagnosis Based on Optimal Regulation of Resonant Behaviors in a Fluctuating-Mass-Induced Linear Oscillator

Abstract

Stochastic resonance (SR), a typical randomness-assisted signal processing method, has been extensively studied in bearing fault diagnosis to enhance the feature of periodic signal. In this study, we cast off the basic constraint of nonlinearity, extend it to a new type of generalized SR (GSR) in linear Langevin system, and propose the fluctuating-mass induced linear oscillator (FMLO). Then, by generalized scale transformation (GST), it is improved to be more suitable for exacting high-frequency fault features. Moreover, by analyzing the system stationary response, we find that the synergy of the linear system, internal random regulation and external excitement can conduct a rich variety of non-monotonic behaviors, such as bona-fide SR, conventional SR, GSR, and stochastic inhibition (SI). Based on the numerical implementation, it is found that these behaviors play an important role in adaptively optimizing system parameters to maximally improve the performance and identification ability of weak high-frequency signal in strong background noise. Finally, the experimental data are further performed to verify the effectiveness and superiority in comparison with traditional dynamical methods. The results show that the proposed GST-FMLO system performs the best in the bearing fault diagnoses of inner race, outer race and rolling element. Particularly, by amplifying the characteristic harmonics, the low harmonics become extremely weak compared to the characteristic. Additionally, the efficiency is increased by more than 5 times, which is significantly better than the nonlinear dynamical methods, and has the great potential for online fault diagnosis.

Bearing fault diagnosis based on the active energy conversion of generalized stochastic resonance in fluctuating-frequency linear oscillator

“…which can be comprehended as a function of regulatable parameters γ, ω, σ, λ, and R. It is worth emphasizing that σ and λ are the internal parameters to control SDN intensity and correlation rate, which play an active role in transforming internal noise energy to signal. It is quite different from the passive regulation of conventional SR method [27,35,36], where the noise originates from the external input, and the system only cooperates it and passively transforms its energy to signal by SR mechanism.…”

“…All the methods mentioned above follow the framework of the classical SR theory with nonlinearity, periodicity and random force as the basic elements, but this view has been overturned by many studies on generalized SR (GSR) phenomena in recent years, and it is extended it to linear Langevin system by introducing multiplicative noises [27][28][29][30][31][32][33][34]. Thus, Chen et al [35] explored the bearing fault diagnosis method based on a fluctuating-mass linear oscillator, where the internal randomness acting upon the second-order term was introduced to regulate the dynamical behaviors. By analyzing the system stationary response, it was found that the synergy of linear system, internal random regulation and external excitement could generate GSR behaviors, which played an important role in adaptively optimizing the system parameters to improve diagnosis performance of weak fault signal under the strong-noise background.…”

The adaptive bearing fault diagnosis based on generalized stochastic resonance in a scale-transformed fractional oscillator driven by unilateral attenuated impulse signal

“…In order to ensure that the transformed system has an equivalent dynamical behavior to equation (1), we make the input signal recover to the original strength [28,29]. It is equivalently extended to…”

“…with the Grünwald-Letnikov definition of fractional-order derivation; (c) GSR-based scale-transformed linear oscillator (GSR-SLO) [28],…”

“…In recent studies, SR-like phenomena were also observed in linear systems with multiplicative noises [26,27], then the initial understanding of SR was extended to generalized SR (GSR), which resulted in the non-monotonic dependence of output signal or some function of it (such as moments, autocorrelation functions, power spectrum, and signal-to-noise ratio (SNR)) on the system parameters. Recently, Chen et al [28] developed a bearing fault diagnosis method based on the fluctuating-mass linear oscillator, where the internal randomness acting upon the second-order term was introduced to regulate the GSR behaviors. It was found that the synergy of linear system, internal random regulation and external excitement could generate GSR behaviors, which played an important role in adaptively optimizing the system parameters to improve diagnosis performance.…”