Feature-guided Regularization Parameter Selection in Sparse De-Noising for Fault Diagnosis

Using the sparse and redundant representation model to de-noise vibration signals is an effective method for mechanical fault diagnosis. The selection of the regularization parameter in the sparse de-noising algorithm plays a vital role in reconstructing fault features. The current choices, however, are primarily based on fixed-form parameters derived under the assumption of additive white noise or based on the “trial and error” method. As a result, the extracted de-noised signals often fail to show fault features. To solve this difficulty, a self-adaptive regularization parameter selection strategy is proposed, which directly measures the significance of fault features in sparse de-noised signals. Firstly, the entire solution path is obtained by the computationally efficient least angle regression (LARS) algorithm. Besides, a feature presence probability index (FP) is well designed to measure the significance of fault features in the reconstructed signal envelope demodulation spectrum. Accordingly, with the help of the maximal FP indicator, the optimal regularization parameter and LARS solution is determined. The proposed method is not limited by noise probability distributions; therefore, it shows the superiority of extracting fault features in both the simulation and experimental data analysis.