# Intelligent Diagnosis of Bearing Failures Based on Recurrence Quantification and Energy Difference
## 1 Introduction
They also adjusted the adaptive learning rate of the gradient descent algorithm in the convolutional neural network, effectively optimizing the algorithm's performance. In 2019, [PERSON] et al. [9] proposed a motor fault diagnosis method based on transfer learning. The main framework of the model consists of a VGG-16 model based on a convolutional neural network. This method first trains the fault diagnosis model on a dataset from the ImageNet image database, and then transfers the trained model. The specific method is to freeze the parameters of some layers of the network model after the pre-training is completed, then update some parameters for the motor dataset, and finally realize the rapid adaptation for the motor fault dataset. In 2023, [PERSON] et al. [10] introduced the hybrid information convolutional neural network (MIXCNN), which constitutes an efficient and compact framework for end-to-end fault diagnosis classification. A distinguishing characteristic of MIXCNN is its uniform output dimensionality across all convolutional layers, ensuring a consistent feature space representation. [PERSON] et al. [11] introduced an innovative fault diagnosis paradigm for rotor systems, anchored in an enhanced parallel convolutional neural network (PCNN) framework, complemented by an attention mechanism (termed AMPCNN). This structure leverages convolutional kernels of heterogeneous sizes across parallel pathways to process raw data inputs. Subsequently, a feature fusion phase integrates diverse feature maps to generate a more holistic representation, while the amalgamation of the attention mechanism facilitates reciprocal information exchange among parallel channels. When considering the idea of dynamics and stability in modeling a defect mechanical system, the Floquet theory and first-order approximation from the averaging method [12] can be referenced. For accurate bearing fault diagnosis, recurrence quantity spectrums are defined for a comprehensive dataset with enhanced features. Activation functions in the activation layer are optimized for better fault diagnosis. Feature matrices are specifically defined to identify the subtlest defects of bearings accurately. This research develops a more efficient fault detection procedure and algorithms that can serve as a universal model for practical bearing fault diagnosis in engineering. Regarding the techniques of bearing fault diagnosis, the extraction of features from raw data is a critical component. This research commences by introducing the characteristic frequencies of rolling bearings alongside pertinent theoretical knowledge in Section 2. It explores feature extraction methods implemented through programming, elucidates the meaning and specific application of recurrence plots, and highlights the advantages of quantitative analysis using metrics in recurrence quantification analysis (RQA) in the subsections. The application of data washing techniques is provided in Section 3, accompanied by a bearing fault diagnosis technique based on machine learning. A comparison of the proposed procedures with other methods is given in Section 4. The last section summarizes this research.