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This study presents a two-step fault diagnosis scheme combined with statistical classification and random forests-based classification for rolling element bearings. Considering the inequality of features sensitivity in different diagnosis steps, the proposed method utilizes permutation entropy and variational mode decomposition to depict vibration signals under single scale and multiscale. In the first step, the permutation entropy features on the single scale of original signals are extracted and the statistical classification model based on Chebyshev’s inequality is constructed to detect the faults with a preliminary acquaintance of the bearing condition. In the second step, vibration signals with fault conditions are firstly decomposed into a collection of intrinsic mode functions by using variational mode decomposition and then multiscale permutation entropy features derived from each mono-component are extracted to identify the specific fault types. In order to improve the classification ability of the characteristic data, the out-of-bag estimation of random forests is firstly employed to reelect and refine the original multiscale permutation entropy features. Then the refined features are considered as the input data to train the random forests-based classification model. Finally, the condition data of bearings with different fault conditions are employed to evaluate the performance of the proposed method. The results indicate that the proposed method can effectively identify the working conditions and fault types of rolling element bearings.

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Machine learning approaches are generally adopted in many fields including data mining, image processing, intelligent fault diagnosis etc. As a classic unsupervised learning technology, fuzzy C-means cluster analysis plays a vital role in machine learning based intelligent fault diagnosis. With the rapid development of science and technology, the monitoring signal data is numerous and keeps growing fast. Only typical fault samples can be obtained and labeled. Thus, how to apply semi-supervised learning technology in fault diagnosis is significant for guaranteeing the equipment safety. According to this, a novel fault diagnosis method based on semi-supervised fuzzy C-means(SFCM) cluster analysis is proposed. Experimental results on Iris data set and the steel plates faults data set show that this method is superior to traditional fuzzy C-means clustering analysis.

Fault identification under variable operating conditions is a task of great importance and challenge for equipment health management. However, when dealing with this kind of issue, traditional fault diagnosis methods based on the assumption of the distribution coherence of the training and testing set are no longer applicable. In this paper, a novel state identification method integrated by time-frequency decomposition, multi-information entropies, and joint distribution adaptation is proposed for rolling element bearings. At first, fast ensemble empirical mode decomposition was employed to decompose the vibration signals into a collection of intrinsic mode functions, aiming at obtaining the multiscale description of the original signals. Then, hybrid entropy features that can characterize the dynamic and complexity of time series in the local space, global space, and frequency domain were extracted from each intrinsic mode function. As for the training and testing set under different load conditions, all data was mapped into a reproducing space by joint distribution adaptation to reduce the distribution discrepancies between datasets, where the pseudolabels of the testing set and the final diagnostic results were obtained by the k-nearest neighbor algorithm. Finally, five cases with the training and testing set under variable load conditions were used to demonstrate the performance of the proposed method, and comparisons with some other diagnosis models combined with the same features and other dimensionality reduction methods were also discussed. The analysis results show that the proposed method can effectively recognize the multifaults of rolling element bearings under variable load conditions with higher accuracies and has sound practicability.

We numerically analyze a polarization maintaining (PM) supercontinuum generation (SCG) in all-normal dispersion liquid (CS2)-core photonic crystal fiber (LC-PCF). The proposed LC-PCF affords a high birefringence (10 -3 to 10 -2 ) from 1.0 μm to 2.2 μm wavelength with fundamental mode behavior. The linear polarization and high coherence spectral width for X and Y polarized axes covers 1.32 μm～2.28 and 1.28 μm～2.24 μm with pump wavelength of 1.55 μm at pump power of 2 kW, respectively. Furthermore, we found that the ability of maintaining linear polarization state of SC source for X-axes is better than that of Y-axes as the pulse duration varies from 0.05 ps to 0.6 ps at the same pump wavelength. In addition, the proposed LC-PCF-based SC source is a good candidate for applications such as biomedical imaging, fluorescence lifetime imaging fields, and frequency comb sources.