Underdetermined Blind Source Separation for Multi-fault Diagnosis of Planetary Gearbox

Abstract

Due to the advantage of strong load capacity and large transmission ratio, planetary gearboxes are widely used in heavy-duty machinery. The complex structure and tough working environment make the gears and bearings in planetary gearbox prone to failure, especially the occurrence of multi-faults. If these faults cannot be diagnosed in time, the shutdown of the entire equipment and even major accidents may happen. The analysis of vibration signal collected from acceleration transducer is regarded as an effective method for fault diagnosis of planetary gearbox to prevent accidents and save cost. In practical application, the collected measurements are always a mixture of signals from many unknown sources, which is considered challenging as an underdetermined blind source separation (UBSS) problem for fault location and recognition. A novel method is proposed in this study to tackle this challenge by three stages: vibration signal sparsity, mixing matrix estimation and source signal recovery. In the first stage, the vibration signals are transformed into the time-frequency (TF) domain by Wigner-Ville distribution (WVD) and then the K-singular value decomposition (K-SVD) is used to further improve the sparsity of time-frequency distribution (TFD) of vibration signals. In the second stage, according to the clustering distribution characteristics of TFDs, a clustering algorithm, namely the Variational Bayesian Gaussian Mixture Model (VBGMM), is used to estimate the number of sources and the values of mixing matrix at the same time. In the last stage, the source signal can be recovered from the source TFD estimate by a TF synthesis algorithm. In order to verify the practicability and effectiveness of the proposed method, a scale-down test rig for planetary gearbox of quay crane is built to simulate the occurrence of fault under variable work conditions. And several acceleration transducers are fixed on the gearbox to collect multi-channel vibration signals. The experimental results, compared with some existing methods, show that the source signals separated by using the proposed method have a clearer frequency spectrum characterization, which remarkably reduces the difficulty of fault feature extraction and improves the accuracy of multi-fault diagnosis.