Response and reliability analysis of a nonlinear VEH systems with FOPID controller by improved stochastic averaging method and LBFNN algorithm

In engineering, it is an important issue to guarantee the normal working of a vibration energy harvesting (VEH) device to harvest electricity. However, the determination of the system dynamics is a huge challenge due to random excitation, nonlinear structure, and control force. This paper aims to study the response and reliability of a kind of nonlinear and coupled VEH system with an FOPID controller. The stationary response is analyzed by an improved stochastic averaging method, in which an amplitude-dependent frequency is taken into account during the averaging procedure in the case of the strongly nonlinear system. Time-varying reliability in the VEH system is analyzed by using a new LBFNN algorithm, and weight coefficients at each time in this algorithm is obtained through an iteration procedure. Numerical results show that there are essential differences between the weakly nonlinear system and the strongly nonlinear one in terms of averaging procedure and response probability. The fractional orders in the FOPID controller are critical parameters to bring stochastic bifurcations. In addition, strongly nonlinear structure together with lower-order fractional derivative and higher-order fractional integration in FOPID controller are helpful to enhance the reliability performance of the VEH system.