# Intelligent Diagnosis of Bearing Failures Based on Recurrence Quantification and Energy Difference
## 1 Introduction  
With the rapid advancement of modern industry and science technology, mechanical equipment is swiftly progressing toward high-speed intelligence, precision systematization, high-efficiency automation, and deep cleanliness. As the structural complexity of mechanical equipment increases and the interdependencies among its components become more intricate, the safe, stable, and efficient operation of this equipment is directly tied to corporate economic interests and production safety. Component failures can result in substantial financial losses and potentially severe consequences, including environmental pollution and personal injuries. Consequently, real-time monitoring and the fault diagnosis of mechanical equipment are critically important. To improve fault diagnosis accuracy and understand fault reasons and types, many researchers have focused on this area. In 2009, [PERSON] [1], from the University of Science and Technology of China, undertook a detailed study and analysis of the application of uncertainty theory in the field of mechanical fault diagnosis. He developed a probability inference methodology based on the connection tree algorithm and a consultation diagnostic fusion model grounded in Dempster-Shafer (D-S) evidence theory. These contributions provided targeted and effective solutions to address the uncertainties inherentin mechanical fault diagnosis. In 2013, [PERSON] et al. [2] introduced the first graph-based neural network, formally applying convolutional neural network (CNN) models to the analysis and modeling of graph-structured data and their practical applications. This work garnered significant attention in the fields of machine vision and pattern recognition. In 2016, [PERSON] et al. [3] proposed a novel hierarchical learning rate adaptive deep convolutional neural network based on an improved algorithm and investigated its use for diagnosing bearing faults and determining their severity. In 2017, [PERSON]. [4], from Harbin Institute of Technology, conducted a study utilizing convolutional neural networks (CNNs) in the context of specific electromechanical equipment fault diagnosis. He proposed an enhanced CNN framework, referred to as WDCNN, specifically tailored for fault diagnosis in the components of rotating mechanical systems. Through additional research and analysis, [PERSON] improved the adaptive batch normalization algorithm, substantially enhancing the load adaptability and noise resilience of the designed WDCNN model. In 2017, [PERSON] et al. [5] proposed a novel bearing fault diagnosis algorithm, IDSCNN, based on an ensemble of deep convolutional neural networks and an improved evidence fusion algorithm based on [PERSON]'s theory, which achieved better fault diagnosis performance than the existing machine learning approaches by fusing compensating or conflicting evidence from different models and sensors and adapting to different load conditions. In 2017, [PERSON] et al. [6] performed continuous wavelet transform (CWT) on the vibration signals of rolling bearings to obtain time-frequency diagrams of the fault data, which were visualized as grayscale images. After resizing the time-frequency diagrams to appropriate dimensions, they served as feature maps and were fed into a CNN classifier model, enabling the intelligent fault diagnosis of different modes of rolling bearings. In 2018, [PERSON] et al. [7] proposed an \"end-to-end\" adaptive convolutional neural network (ACNN-FD) for fault diagnosis and monitoring. This approach constructs a deep network structure to enable the adaptive hierarchical extraction of features from raw vibration signals. In 2019, [PERSON] et al. [8] utilized a novel data preprocessing technique to transform raw time-domain signal data into two-dimensional grayscale images. By extracting features from the transformed images, they performed denoising on the fault dataset obtained through experimentation.