Gaussian basis function fitting for stationary solutions of a double-flag hysteretic nonlinear oscillator under colored noise excitation

The double-flag hysteretic nonlinear model is widely used in industrial applications, particularly for describing the stress-strain constitutive relationship of shape memory alloys (SMAs). This study investigates the vibrational response of a double-flag hysteretic nonlinear oscillator under Gaussian colored noise excitation. A semi-analytical method, Gaussian basis function (GBF) fitting, is employed to approximate the system’s steady-state probability density function (PDF) as a weighted sum of Gaussian basis functions. A loss function is constructed using stochastic sampling, and optimal weight coefficients are determined through minimization. The method yields the steady-state joint PDF of displacement and velocity, as well as their marginal PDFs. The results show good agreement with Monte Carlo simulation (MCS) data.