Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Abstract

Early fault diagnosis of rolling bearings is of great significance in the application of mechanical equipment, which makes the extraction of weak fault signals particularly critical by stochastic resonance (SR). Compared with bistable SR, tristable SR has stronger advantages in weak signal extraction, but the classical tristable system (CTSR) was limited by output saturation, which resulted in insufficient signal amplification ability. To solve the above problems, combined with asymmetric system whose output can be improved to a higher degree, a novel piecewise unsaturated asymmetric tristable stochastic resonance (NPUATSR) system is proposed. Through numerical simulation, it is concluded that NPUATSR output amplitude varies proportionally with the amplitude of the input, which overcomes the output saturation of CTSR. Secondly, the stationary probability density and mean first passage time of particles are derived by using adiabatic approximation theory, and the variation law caused by parameters is analyzed in combination with potential function, the internal mechanism of the system is further studied. Through the output signal-to-noise ratio (SNR), it is found that the performance advantage of NPUTASR system is the most obvious, and different parameters affect the output SNR. Finally, the adaptive genetic algorithm is used to optimize the parameters, and the proposed system is applied to early fault diagnosis on different types of bearings. After comparison with different systems, the results show that NPUATSR can effectively detect the fault frequency, and has the most outstanding advantages in spectrum amplification and anti-noise performance, which proves that NPUATSR system has significant value in practical engineering application.

Adaptive progressive learning stochastic resonance for weak signal detection

“…By changing the order of the SR system equation, two-dimensional Duffing oscillator SR [33] and fractional SR [34] appear. By changing the model of the potential function, there are multi-stable potential [22], piecewise unsaturated potential [11], asymmetric potential [24] and so on. The parameter optimization method proposed in this paper is not only applicable to the classical bistable SR system, Rt + 1 = 0; 6.1.6 Update Q-table constantly with equation ( 16).…”

“…Meanwhile, each S L (L = 1,2, …, M) represents a set of states in a coordinate grid. The relationship between adjacent coordinate grids can be expressed as equation (11),…”

“…Yang et al [10] introduced the concept of coherent resonance (CR), an ordered dynamic behavior similar to SR, and by distinguishing CR and SR, a bearing fault can be diagnosed successfully. Zhang et al [11] proposed a piecewise unsaturated asymmetric tristable SR system on early bearing fault diagnosis. López et al [12] explored the SR system based on the FitzHug-Nagumo potential to extract the rolling bearing fault signal, and used particle swarm optimization (PSO) to search for the optimum SR parameters.…”

Fault diagnosis of rolling bearing based on the three-dimensional coupled periodic potential-induced stochastic resonance

“…In the context of Industry 4.0, as mechanical equipment structures become increasingly complex, the subtle incipient fault characteristics that manifest during operation prove faint and frequently overshadowed by significant noise, posing a substantial challenge in the diagnosis of bearing incipient faults [1]. To ensure the prolonged and precise operation of mechanical equipment, numerous methods for diagnosing incipient faults have been developed.…”

Linearly-coupled sigmoid bistable stochastic resonance for weak signal detection

“…The linear response theory is then developed by Gammaitoni et al [13], and the theory of residence time distribution is later introduced by Zhou and Moss [14]. By then, the three major theories which lay the classical theoretical framework of SR systems are formally proposed, and they are successfully applied in the fields of mechanical fault diagnosis [15][16][17][18], electromagnetism and communication [19][20][21], image processing [22][23][24] and medical signal analyses [25][26][27][28], etc.…”