Noise-boosted weak signal detection in fractional nonlinear systems enhanced by increasing potential-well width and its application to mechanical fault diagnosis

Noise is seen as the annoying something for weak signal detection, but noise is beneficial to enhance weak signals of interest embedded in noise in nonlinear systems. Moreover, the fractional-order derivative can reinforce noise-boosted weak signal detection. However, the role of varying potential-well depth and width individually on noise-boosted weak signal detection in overdamped and underdamped fractional-order nonlinear systems has not been investigated yet. For this purpose, this paper designs a special bistable potential with varying potential-well depth and width individually to study their influences on weak signal detection numerically. Then, based on simulated conclusions a noise-boosted weak fault diagnosis method enhanced by increasing potential-well width is proposed to enhance weak fault characteristics of machinery, where the amplitude amplification factor is seen as an indicator to quantify the performance of weak signal detection. Finally, some simulations and a bearing fault experiment with an outer race defect were performed to demonstrate the proposed method. Simulated conclusions are identical to experimental ones and indicate that increasing potential-well width would improve noise-boosted weak signal detection but increasing potential-well depth would weaken it regardless of underdamped or overdamped fractional-order nonlinear systems. Nonetheless, increasing the potential-well width endlessly would make the amplitude at the outer race fault characteristic frequency unchanged. That is because the signal with the constant energy would not accelerate the particles to jump across the wide potential wells adequately, where it is not an optimal SR. The compared results with a classical denoising method demonstrate the superiority of the proposed method further.