Stochastic dynamics and first-passage failure of wind turbine transmission system with time-varying stiffness under harmonic excitations using path integral methods

To reveal the dynamical behaviors of wind power transmission systems under complex external environments, this paper establishes a two-mass drivetrain model of the mechanical transmission chain with the time-varying stiffness under a combination of harmonic and Gaussian white noise excitations. Then the evolution of the stationary and transient probability density functions of the system is computed using the improved path integral method. Furthermore, the path integral results are used to evaluate the stability of the wind power transmission system with the first-passage failure theory. Meanwhile, the results of the improved path integral method are compared with those of the Monte Carlo simulations to verify its accuracy in predicting periodic behavior as well as tail peak values. Studies show that the damping coefficients and the time-varying stiffness amplitude can induce stochastic P-bifurcation, and larger damping coefficients, smaller time-varying stiffness amplitude, harmonic excitation and noise intensity are more favorable for the stability of the wind turbine drive shaft system.