A Deep Echo State Network With Scaling Factor Activation Functions for Fault Diagnosis of Electrical Drive Systems

Deep echo state networks (Deep-ESNs) play an important role in fault diagnosis. However, due to its limitation in the iterative process of dealing with nonlinear data, the accuracy of fault diagnosis is relatively low. In order to improve the fault diagnosis accuracy of electrical drive systems, this article proposes a novel Deep-ESN based on the synergistic effect of golden jackal optimization (GJO), variational mode decomposition (VMD), and scaling factor activation function, called GVSD-ESN. The main work of this study contains: 1) the novel scaling factor activation function is proposed to solve the gradient vanishing problem in the Deep-ESN model; 2) GJO is used to solve high-dimensional optimization problems of VMD; 3) the power spiral curve is proposed to optimize the position update equation of GJO, which solves the problem of falling into the local optimal; and 4) adding a sparse regularization layer between reservoirs can enhance the class definition of GVSD-ESN. Finally, the effectiveness of the proposed method is verified in electrical drive systems.