Compressive sensing reconstruction for rolling bearing vibration signal based on improved iterative soft thresholding algorithm

In order to solve the problem of high data transmission pressure and storage cost caused by collecting massive data in rolling bearing health monitoring, a new method of acquisition and reconstruction based on compressive sensing is introduced in this paper, which can recover the original signal accurately with a small amount of data. However, the traditional iterative soft thresholding algorithm (ISTA) has some shortcomings in the recon-struction process of vibration signal, such as fixed gradient step size, slow convergence speed, and poor reconstruction accuracy. To overcome this problem, an improved ISTA (IISTA) is put forward. Firstly, an ac-celeration operator considering step size is proposed to estimate the gradient, which can accelerate convergence speed. Then for breaking the limitation of fixed internal gradient step size, a bidirectional search principle is introduced to backtrack its iteration step size. Finally, the constraint of quadratic approximation model on the reconstruction objective function is used to adaptively determine optimal iteration step size. The effectiveness of the approach is verified by the reconstruction of bearing vibration signals in different health states. The results show that the proposed method outperforms the conventional ISTA in terms of reconstruction accuracy and efficiency.