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Currently, deep-learning-based methods have been widely used in fault diagnosis to improve the diagnosis efficiency and intelligence. However, most schemes require a great deal of labeled data and many iterations for training parameters. They suffer from low accuracy and over fitting under the few-shot scenario. In addition, a large number of parameters in the model consumes high computing resources, which is far from practical. In this paper, a multi-scale and lightweight Siamese network architecture is proposed for the fault diagnosis with few samples. The architecture proposed contains two main modules. The first part implements the feature vector extraction of sample pairs. It is composed of two lightweight convolutional networks with shared weights symmetrically. Multi-scale convolutional kernels and dimensionality reduction are used in these two symmetric networks to improve feature extraction and reduce the total number of model parameters. The second part takes charge of calculating the similarity of two feature vectors to achieve fault classification. The proposed network is validated by multiple datasets with different loads and speeds. The results show that the model has better accuracy, fewer model parameters and a scale compared to the baseline approach through our experiments. Furthermore, the model is also proven to have good generalization capability.

Nowadays a large number of mechanical equipment working in harsh working environment will lead to strong background noise, which makes it difficult to extract feature information related to equipment fault. Bolt joint looseness inevitably occurs in engineering, which occupies a large proportion of all types of mechanical equipment faults. Therefore, it is quite difficult to extract the bolt looseness feature information. Based on this problem, a method based on subharmonic resonance and adaptive stochastic resonance method is proposed to recognize weather the bolt is loose. Firstly, a typical single bolted joint model is carried out dynamic analysis and numerical simulation, which verifies the specific conditions for the generation of subharmonic frequency related to bolt looseness. Then, a bolt looseness identification method based on adaptive stochastic resonance and coherence resonance is proposed. A quality factor index is defined, which is used to identify stochastic resonance and coherence resonance for bolt looseness identification. Finally, the effectiveness of this method is successfully verified by experiment, which effectively identifies bolt looseness under strong noise background.

Vibrational resonance (VR) shows great advantages in signal enhancement. Nonlinear frequency modulated (NLFM) signals widely exist in various fields，so it is of great significance to enhance a NLFM signal. However, for the complex NLFM signal, where its instantaneous frequency of the signal varies nonlinearly, the traditional VR method is no longer applicable. To solve this problem, a rescaled VR method by a real-time scale transformation method is proposed. Its basic principle is to use the real-time scale coefficient and auxiliary signal parameters to match a NLFM signal in a nonlinear system. The corresponding numerical simulation is carried out to process three kinds of typical NLFM signals. The results manifest the excellent performance of the proposed method for the signal enhancement of NLFM signals. The method can process NLFM signals with an arbitrary frequency variation. Consequently, it has certain theoretical and practical values in some fields.