Narrow Results

Multiscale entropy (MSE) discloses the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. Most of these research results are pure experimental search, till Costa et al. made the first attempt to the theoretical basis of MSE. However, the analysis only supports the Gaussian distribution [Phys. Rev. E71, 021906 (2005)]. In this paper, we present the theoretical basis of MSE under the inverse Gaussian distribution, which is a typical model for physiological, physical and financial data sets. The analysis is applicable to uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, providing a reliable foundation for potential applications of MSE to explore complex physical and physiological time series.

Considering the effects of time-varying meshing stiffness, time-varying support stiffness, transmission errors, tooth side clearance and bearing clearance, a nonlinear dynamics model of the coupled gear-rotor-bearing transmission system of a new energy vehicle is constructed. Firstly, the fourth-order Runge–Kutta integral method is used to solve the differential equations of the system dynamics, and the time-varying meshing force diagram, time history diagram, phase diagram, FFT spectrum diagram, Poincaré map and bifurcation diagram of the system are obtained to study the influence of the external load excitation frequency on the dynamics characteristics of the system. In addition, the multiscale method is used to analyze the main resonance characteristics of the system and to determine the main resonance stability conditions of the system. The effect of time lag control parameters and external load excitation frequency on the main resonance of the system is analyzed by numerical methods. The results show that the gear-rotor-bearing coupled transmission system of the new energy vehicle has obviously nonlinear characteristics, avoiding the system instability interval reasonable selection of external load excitation frequency, meshing damping, time lag parameters and load fluctuations, which can be used to improve the stability of the transmission system of the new energy vehicle.