Improved learning algorithm for two-layer neural networks for identification of nonlinear systems

Performance for rotor system of hybrid electromagnetic bearing and elastic foil gas bearing with dynamic characteristics analysis under deep learning

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 135μm, and the maximum stiffness can be reduced to 35×10⁵N/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.

Externally Recurrent Neural Network based identification of dynamic systems using Lyapunov stability analysis

This paper proposes an Externally Recurrent Neural Network (ERNN) for approximating the unknown dynamics of complex nonlinear systems and time series prediction. The proposed model utilizes the present as well as delayed values of the system outputs as well as of the external input. The weight update equations are tested for their boundedness by applying the Lyapunov stability method. Further, the error convergence proof is also given. The proposed model is put to test by considering various nonlinear examples and its performance is also compared with other state of the art methods. The results obtained in the present study indicate that the method is efficient and has provided accurate results.