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.

In intelligent fault diagnosis, the success of artificial intelligence (AI) models is highly dependent on labeled training samples, which may not be obtained in real-world applications. Recently, a finite element method (FEM) simulation-based personalized diagnosis method was developed to overcome the problems of insufficient and incomplete labeled training samples. However, the simulation signals obtained using the FEM and measured signals actually have a certain deviation. To supplement the FEM simulation-based personalized diagnosis method, a fault diagnosis method using domain adaptation (DA) is proposed to bridge the gap between simulation signals and measured signals. First, the FEM is adopted to obtain sufficient and complete simulation samples of all the fault categories as the original fault samples in the source domain. Second, the original simulation fault samples are adjusted using a generative adversarial network (GAN)-based DA network to make them similar to the measured samples through the adversarial training of the refiner and domain discriminator. Last, credible adjustment fault samples and measured fault samples obtained in machinery are applied to a convolutional neural network (CNN) for training and testing to complete the fault classification. The data obtained from rolling element bearing and gear test rigs are utilized to explore the feasibility of the proposed method, and the classification accuracies reach 99.44% and 99.58%, respectively. The comparison investigations using experimental data of gears and bearings indicate that the present method can accurately classify faults in machinery.