Probabilistic response analysis of nonlinear vibration energy harvesting system driven by Gaussian colored noise

A new quasi-conservative stochastic averaging method is proposed to analyze the Probabilistic response of nonlinear vibration energy harvesting (VEH) system driven by exponentially correlated Gaussian colored noise. By introducing a method combining a transformation and the residual phase, the nonlinear vibration electromechanical coupling system is equivalent to a single degree of freedom system, which contains the energy-dependent frequency functions. Then the corresponding drift and diffusion coefficients of the averaged Ito^ stochastic differential equation for the equivalent nonlinear system are derived, which are dependent on the correlation time of Gaussian colored noise. The probability density function (PDF) of stationary responses is derived through solving the associated Fokker–Plank–Kolmogorov (FPK) equation. Finally, the mean-square electric voltage and mean output power are analytically obtained through the relation between the electric voltage and the vibration displacement, and the output power has a linear square relationship with the electric voltage, respectively. The main results on probabilistic response of VEH system are obtained to illustrate the proposed stochastic averaging method, and Monte Carlo (MC) simulation method is also conducted to show that the proposed method is quite effective.