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A novel fault diagnosis method for rolling bearings based on multi-scale redefined dimensionless indicators and an unsupervised feature selection method using density peak clustering with geodesic distances is proposed in this paper. First, a new feature extraction method is proposed based on redefined dimensionless indicators and multi-scale analysis called multi-scale redefined dimensionless indicators. Then, density peak clustering with geodesic distances is utilized to automatically find the important multi-scale redefined dimensionless indicators. To the best of our knowledge, this is the first study to use density peak clustering with geodesic distances to explore unsupervised feature selection in the fault diagnosis field. Finally, the selected multi-scale redefined dimensionless indicators are fed into a quadratic discriminant analysis classifier to simultaneously identify 12 different conditions of rolling bearings. Experimental results demonstrated that the proposed method can successfully differentiate 12 localized fault types, fault severities, and fault orientations of rolling bearings.

Machinery fault diagnosis methods based on dimensionless indicators have long been studied. However, traditional dimensionless indicators usually suffer a low diagnostic accuracy for mechanical components. Toward this end, an effective fault diagnosis method based on redefined dimensionless indicators (RDIs) and minimum redundancy maximum relevance (mRMR) is proposed to identify the health conditions of mechanical components. In the proposed method, the vibration signals are first processed by the variational mode decomposition, and multiple RDIs are constructed based on the decomposed signals. Subsequently, the mRMR approach is introduced to select the RDIs and several important RDIs can be obtained. Finally, the obtained RDIs are fed into a grid search support vector machine to perform fault pattern identification. To verify the superiority of the proposed method, two experimental examples for different fault types of mechanical components including rolling bearing and gearbox are conducted. The experimental results demonstrated that the RDIs as new fault features can effectively solve the deficiency of the traditional dimensionless indicator, and has stronger distinguishing ability for machinery faults. Additionally, our proposed method successfully differentiated 12 fault conditions of rolling bearings and nine fault conditions of gears with average accuracies of 97.47% and 97.12% with 11 and 5 RDIs, respectively.

In underdetermined blind source separation (UBSS) of vibration signals, the estimation of the mixing matrix is often affected by noise and by the type of the used clustering algorithm. A novel UBSS method for the analysis of vibration signals, aiming to address the problem of the inaccurate estimation of the mixing matrix owing to noise and choice of the clustering method, is proposed here. The proposed algorithm is based on the modified k-means clustering algorithm and the Laplace potential function. First, the largest distance between data points is used to initialize the cluster centroid locations, and then the mean distance between clustering centroids average distance range of data points is used for updating the locations of cluster centroids. Next, the Laplace potential function that uses a global similarity criterion is applied to fine-tune the cluster centroid locations. Normalized mean squared error and deviation angle measures were used to assess the accuracy of the estimation of the mixing matrix. Bearing vibration data from Case Western Reserve University and our experimental platform were used to analyze the performance of the developed algorithm. Results of this analysis suggest that this proposed method can estimate the mixing matrix more effectively, compared with existing methods.