Response of an oscillator with SMA spring under Gaussian white noise excitation based on RBFNN

This study investigates the stochastic vibration of shape memory alloy (SMA) spring oscillators under Gaussian white noise, employing two hysteresis models (two-flag and piecewise polynomial). While piecewise models complicate stochastic averaging analysis, we propose an efficient solution via a radial basis function neural network (RBFNN)-based semi-analytic method—Gaussian RBFs approximate the steady-state joint PDF of displacement and velocity, optimized via Lagrange multipliers to minimize error. Simulations confirm identical results to Monte Carlo methods (MCS) while requiring significantly less computation, demonstrating the RBFNN method as a practical alternative for stochastic analysis of hysteretic systems.