Sparse Elitist Group Lasso Denoising in Frequency Domain for Bearing Fault Diagnosis

The fault-induced impulse responses of localized bearing fault are usually interfered by the background noise and other harmonic components. They are strongly coupled together and are hard to be separated. It is crucial to develop a fast and reliable method to extract the impulse-based feature for online bearing fault diagnosis in the industry application. In this article, we propose a new sparse elitist group lasso denoising (SEGLD) algorithm in frequency domain to detect the incipient impulse-based fault feature, which is free of utilizing the prior knowledge. We first reveal the sparse characteristics of the bearing fault signals in frequency domain. Then, a tailored denoising model is proposed. To obtain a satisfactory analytical stationary solution, the Douglas-Rachford splitting solver is employed for the denoising model. Moreover, we explore the relationship between the best regularization parameters, the periodic information and the normalization estimated noise of the rolling bearing fault signal. A rule of adaptively selecting the best regularization parameters is demonstrated. Finally, the robustness and effectiveness of the proposed SEGLD algorithm are profoundly verified by the numerical simulation and two evaluation experiments under the conditions of early fault stage and low speed scenario. Also, it is demonstrated that the proposed approach outperforms the state-of-the-art method for extracting the weak fault feature.