## 1 Introduction
However, the feature extraction method based on multiscale permutation entropy and multiscale fuzzy entropy ignore the influence of the amplitude of element on entropy in time series, which will make the extracted features have greater randomness and affect the fault identification accuracy. [PERSON] and [PERSON] proposed the Amplitude-aware permutation entropy (AAPE) to improve the sensitivity of PE to the amplitude and frequency of time series [27]. Different from the permutation entropy algorithm, AAPE algorithm takes into account the mean of signal amplitude and the deviation between amplitudes. In this paper, in order to effectively extract the fault characteristics of rolling bearings, multiscale amplitude-aware permutation entropy (MAAPE) is used to extract the fault features of rolling bearings. For fault type identification, high performance multi-classifier is used to identify the extracted fault features to determine the fault type or fault severity of rolling bearings. [PERSON] et al. presented an approach for motor rolling bearing fault diagnosis using neural networks and time-frequency domain bearing vibration analysis [28]. At present, the commonly used artificial neural network includes radical basis function (RBF) neural network and conventional back-propagation (BP) neural network. However, it is difficult to determine the structure of the neural network, since the number of hidden layers is usually selected according to experience. In order to ensure high identification accuracy, a large number of samples are required for training neural network. Support vector machine (SVM) is suitable for solving the classification problem under small sample conditions and has high classification accuracy and good generalization capabilities. Nonetheless, SVM is a kind of binary classifier that needs to use a suitable binary tree to realize multi-classification in the application of multi-classification [11]. Moreover, kernel function selection and kernel parameter setting of SVM have great influence on the identification results. Random forest classifier is an ensemble classifier with high performance that is composed of multiple decision trees [29]. It uses the classification results of all decision trees to determine categories through voting principle. Random forests require very little manual intervention. It does not need to do feature selection or data collation, that is to say, it can determine the features according to the data, so as to simplify the design process of random forest itself. In addition, it usually does not need to preprocess the data in observation data dimension, so it can resist and detect the gross errors that often exist in the form of outlier data. It can maintain a good accuracy when a large proportion of data is lost, and provide the estimation of lost data to simplify its engineering application. Random forests have very fast computing speeds. Since each node of the tree is mainly given by comparison operation, and the amount of calculation is proportional to the depth of a tree, it is very fast to do classification or regression on the well-grown trees. A fault diagnosis method of rolling bearings based on multiscale amplitude-aware permutation entropy and random forest is proposed in this paper. The vibration of rolling bearings presents the characteristics of periodic instantaneous impact, and the location of bearing failure will lead to different impact characteristics. In order to more fully extract the rolling bearing fault information contained in the vibration signal, using AAPE's sensitivity to the amplitude and frequency changes of vibration signals, the AAPE values at different time scales are calculated as the feature vector, which improves the effectiveness of fault feature extraction. A multiple classifier based on random forests is established by the feature vectors composed of multiscale amplitude-aware permutation entropy to identify the fault type and fault severity of rolling bearings. The contributions of this paper can be summarized as follows:  
1.