Transient response prediction of randomly excited vibro-impact systems via RBF neural networks

Systems exposed to random excitations may fail long before stationarity is achieved, which necessitates consideration of the transient responses of the system. On the other hand, the transient response prediction of non-smooth systems may face more obstacles than that of smooth systems. One of the foremost challenges lies in the handling of vector fields with singularities in non-smooth systems. In this work, the radial basis function neural networks (RBFNN) is utilized for the first time to analyze the transient response of randomly excited vibro-impact systems (VIS), a class of typical non-smooth systems. The solution of the system response is expressed in terms of a serious of Gaussian activation functions (GAFs) with time-dependent weights. These time-dependent weights are determined by minimizing a loss function, which involves the residual of the differential equations and constraint conditions. To avoid the singularity of the initial condition being a Dirac delta function, a strategy of short-time Gaussian approximation is presented to obtain the initial weights. Two typical VISs exposed to stochastic excitations are presented to verify the suggested scheme. Appropriate comparisons to the data obtained by digital simulation show that the method yields reliable results even for strongly nonlinear systems. With the merits of high computational accuracy and satisfactory efficiency, this approach is expected to be an effective method for solution of random vibration problems of high-dimensional complex non-smooth systems.