This work presents the development of novel convolutional neural network (NCNN) for effective identification of bearing defects from small samples. For effective feature learning from small training data, cost function of convolution neural network (CNN) is modified by adding additional sparsity cost in the existing cost function. A novel trigonometric cross-entropy function is developed to compute the sparsity cost. The proposed cost function introduces sparsity by avoiding unnecessary activation of neurons in the hidden layers of CNN. For identification of bearing defects from small training samples, NCNN-based transfer learning is applied in the following manner. First, the raw vibration signals as well as envelope signals from source domain machine are obtained. Thereafter, these envelope signals are applied to NCNN for the learning of features from the big training data acquitted from the source domain. After feature learning, knowledge gained from NCNN is transferred to do fine-tuning of NCNN from small training samples of target domain. Thereafter, defect identification is carried out by applying the test data of target domain to fine-tuned NCNN. The experimental result validates that the proposed cross-entropy function introduces sparsity in CNN and, hence, creates an effective deep learning which can even work under a situation when training data are not available in abundant.

Early identification of rolling element defects is always a topic of interest for researchers and the industry. For early fault identification, a simple and effective dynamic degradation monitoring method using variational mode decomposition (VMD) based trigonometric entropy measure is developed. First, vibration signals are obtained and are further decomposed using VMD to obtain various frequency modes. Second, a trigonometric entropy measure is developed to monitor the dynamic change occurring in the health of bearing. Third, trigonometric entropy measure of various VMD modes is computed. Fourth, the variance of measure is computed and two modes having the highest variance are selected for principal component analysis (PCA). Thereafter, PCA of selected measures is carried out. Finally, dynamic degradation monitoring is carried out by observing the trend in the principal component having the highest diverse information. The testing of newly developed VMD based trigonometric entropy measure is carried out on the two different types of data set. One is from XJTU-SY Bearing datasets and another is from the Centre for Intelligent Maintenance Systems. The experimental study reveals that the proposed method is capable of raising the alarm about the initiation of defects at a very early stage. Compared to existing indicators such as kurtosis, RMS, and Shannon entropy, the proposed method is superior while carrying out defect degradation monitoring.