Linear maximum margin tensor classification based on flexible convex hulls for fault diagnosis of rolling bearings

The fault diagnosis of rolling bearings methods based on machine learning have been developed in the past years, such as neutral network (NN), support vector machine (SVM) and convolutional neural networks (CNN). The first two methods just can be used for the classification of the vector space in which the feature data extracted from raw signals are input in vector form, so they lose their functions when the input feature data are high order tensors which can contain rich feature information of rolling bearing vibration signals. Moreover, a large number of data are needed in CNN, but it is hard to get large numbers of fault samples of rolling bearings under different conditions. Recently, a kind of tensor classifier called support tensor machines (STM) can solve the problems in the above methods. These classifiers can be regarded as maximum margin tensor classification based on convex hulls methods. But convex hull is typically a substantial under-approximation to the class region. Therefore, in this paper, a novel linear maximum margin tensor classification based on flexible convex hulls(MMTC-FCH) is proposed and applied to the fault diagnosis of rolling bearings. In this method, firstly, for binary classification problems, MMTC-FCH is aimed at finding an optimal separating hyperplane that generates the maximum margin between flexible convex hulls of two tensor sample sets. Subsequently, for linearly inseparable cases, the reduction factor is used to improve the robustness of MMTC-FCH when there are outliers in the training samples. Finally, MMTC-FCH is extended to deal with the multi-class classification problems by using the strategies in SVM. To train a MMTC-FCH classifier, wavelet time–frequency grayscale images as second-order tensors input are constructed from raw vibration signals by continuous wavelet transform (CWT). The experimental results show that the proposed method not only recognizes different rolling bearing faults but also can achieve the best results when the classifier is lack of severe fault training samples and there are outliers in the training sample.