Construction of a new Lorenz-like system with cubic nonlinearity and its application in weak signal detection

Abstract

To investigate the application value of the Lorenz system in weak signal detection for rolling bearing vibrations, this study innovatively proposes an improved Lorenz system model incorporating a cubic nonlinear term. This improvement not only enhances the system's performance in weak signal detection but also provides new research perspectives for a deeper understanding of nonlinear dynamic behaviors. The study focuses on analyzing the influence mechanism of the cubic nonlinear term on the system's chaotic characteristics and systematically examines the practical application effectiveness of this improved model in weak signal detection. Under constant parameter conditions, a systematic sensitivity analysis was conducted to evaluate the dynamical implications of introducing cubic nonlinearities into the first two governing equations of the system. Our research reveals that as one of the control parameters decreases, the system exhibits a singular degenerate heteroclinic cycles structure, whose collapse process establishes a crucial evolutionary pathway toward chaotic states. In the end, by utilizing the transient chaotic characteristics of the novel Lorenz-like system with cubic terms, we propose a method capable of detecting weak signals in strong noise environments and performing mechanical fault diagnosis. Its effectiveness has been verified through both simulations and experimental validation.