Support tensor machine with dynamic penalty factors and its application to the fault diagnosis of rotating machinery with unbalanced data

The fault diagnosis methods of rotating machinery based on machine learning have been developed in the past years, such as support vector machine (SVM) and convolutional neural networks (CNN). SVM just can be only used for the classification of the vector space in which the feature data extracted from raw signals are input data in vector form, so SVM loses its functions while the input feature data are high order tensors which can contain rich feature information of rotating machinery. Moreover, a large number of data are needed in CNN, but it's hard to get large numbers of fault samples of rotating machinery under different conditions. Recently, a kind of tensor classifier called support tensor machines (STM) can solve the problems in the above methods. But when the input samples of STM are unbalanced data, the hyper-plane obtained by the training of STM may not be the optimal hyper-plane and it may reduce the overall classification rate. Therefore, in this paper, a novel tensor classifier called support tensor machine with dynamic penalty factors (DC-STM) is proposed and applied to the fault diagnosis of rotating machinery. In this method, for linear separable case, linear support tensor model with dynamic penalty factors (DC-LSTM) is proposed, which does not ignore the impact of rare support vectors of a class with less training samples on the structural risk. Subsequently, for nonlinear separable case, a tensor kernel function is introduced into DC-LSTM, and nonlinear support tensor model with dynamic penalty factors (DC-NSTM) is proposed. In order to verify the performance of DC-STM in unbalanced data classification, it is applied to fault classification of rotating machinery with unbalanced data. The experimental results show that the proposed method can achieve better classification results when the training samples of rotating machinery are unbalanced data. (C) 2019 Elsevier Ltd. All rights reserved.