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With a view to solving the defect that multiscale amplitude-aware permutation entropy (MAAPE) can only quantify the low-frequency features of time series and ignore the high-frequency features which are equally important, a novel nonlinear time series feature extraction method, hierarchical amplitude-aware permutation entropy (HAAPE), is proposed. By constructing high and low-frequency operators, this method can extract the features of different frequency bands of time series simultaneously, so as to avoid the issue of information loss. In view of its advantages, HAAPE is introduced into the field of fault diagnosis to extract fault features from vibration signals of rotating machinery. Combined with the pairwise feature proximity (PWFP) feature selection method and gray wolf algorithm optimization support vector machine (GWO-SVM), a new intelligent fault diagnosis method for rotating machinery is proposed. In our method, firstly, HAPPE is adopted to extract the original high and low-frequency fault features of rotating machinery. After that, PWFP is used to sort the original features, and the important features are filtered to obtain low-dimensional sensitive feature vectors. Finally, the sensitive feature vectors are input into GWO-SVM for training and testing, so as to realize the fault identification of rotating machinery. The performance of the proposed method is verified using two data sets of bearing and gearbox. The results show that the proposed method enjoys obvious advantages over the existing methods, and the identification accuracy reaches 100%.

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As a pivotal part of machine driven system, the health states of rolling bearings usually determine the normal operation of the whole equipment. Consequently, it is very necessary to make accurate and timely judgments on the operating conditions of rolling bearings. In this paper, a synthesized diagnosis technology including fault pre-judgment and identification for rolling bearings is raised. In the first part, a threshold value is defined on the basis of the sensitivity of amplitude-aware permutation entropy (AAPE) to bearing faults. Based on this value, whether the bearing has defects is judged. If the defect exists, a feature extraction scheme combining the modified complete ensemble empirical mode decomposition with adaptive noise (MCEEMDAN) and the modified hierarchical amplitude-aware permutation entropy (MHAAPE) is adopted to fully mine the hidden state features. Firstly, the scheme uses MCEEMDAN, which enjoys good time-frequency decomposition capability, to divide the trouble signal into a group of intrinsic mode functions (IMFs). Secondly, the MHAAPE of each IMF component is computed to form the candidate state features. Then, multi cluster feature selection (MCFS) is employed to compress high-dimensional fault features to form low-dimensional sensitive feature vectors required for subsequent classification. Finally, the sensitive feature vectors are input into the random forest (RF) classifier for training and classification, so as to ascertain the different fault type and severity. In addition, different contrastive methods are tested based on experimental data. The experiment results indicate that compared to contrastive methods, the raised scheme enjoys better performance, which can effectively judge whether the bearing is healthy and accurately identify different fault state of bearings.