Deep convolutional sparse dictionary learning for bearing fault diagnosis under variable speed condition

Dictionary learning is a usual method in the field of machinery fault diagnosis, but it requires that the rotating speed conditions of training set and test set are the same and constant. When the speed condition of test set is different from that of training set or one of them is time-vary, normal dictionary learning is difficult to get a precise sparse representation. A special dictionary model named convolutional sparse dictionary (CSD) can overcome the influence from variable speed conditions by atoms locally shifting in the sample's dimension, which is beneficial to capture the local fault features in the signal no matter how the speed changes. However, there are both large features and small features in the mechanical vibration signal, and several continuous small features can also form a large feature. The problem is that CSD can only locally optimize the signal at a fixed scale, so the features of other scales cannot be optimized. To solve this problem, this paper proposes a model named deep convolutional sparse dictionary (DCSD) to extract bearing fault features under variable speed conditions, which is improved from CSD. DCSD has multiple dictionary layers, where each layer is a CSD, but the atom's dimensions are different in each layer. The larger the number of layer is, the larger the atom's dimension is, and the sparse representation result of each layer is used to train the next dictionary layer. Through simulations cases and experimental cases under variable speed conditions, it is proved that DCSD has better performances than CSD in the fault diagnosis.