The bearing-rotor system is prone to faults during operation, so it is necessary to analyze the dynamic characteristics of the bearing-rotor system to discuss the optimal structure of the convolutional neural network (CNN) in system fault detection and classification. The turbo expander is undertaken as the research object. Firstly, the hybrid magnetic bearing-rotor system is modeled into the form of four stiffness coefficients and four damping coefficients, so as to analyze and explain the dynamic characteristics of the system. Secondly, the ambient pressure is introduced to analyze the dynamic characteristics of the elastic foil gas bearing-rotor system based on the changes in the dynamic stiffness and dynamic damping of the gas bearing. Finally, the CNN is introduced to be applied in the detection of faults of bearing-rotor system through determining the parameters of the constructed CNN. The results show that the displacement of the rotor increases and the stiffness decreases with the acceleration of the speed of the electromagnetic bearing. The maximum displacement of the rotor can reach 135[mu]m, and the maximum stiffness can be reduced to 35x10.sup.5 N/m. Increase of ambient pressure causes enhancement of main stiffness of the gas bearing, and the main damping decreases accordingly. Analysis of the classification accuracy and loss function based on the CNN model shows that the convolution kernel size of 7*1 and the batch size of 128 can realize the best performance of CNN in fault classification. This provides a data support and reference for studying the dynamic characteristics of the bearing-rotor system and for the optimization of CNN structure in fault classification and detection.