Hybrid uncertainty propagation analysis of nonlinear systems in the frequency domain based on multi-scale random interval moment method

To quantify the impact of hybrid uncertainty (random and interval parameters) on the frequency-domain nonlinear dynamic response, the multi-scale method (MSM) and the random interval moment method (RIMM) are combined to establish a new uncertainty propagation analysis method, called the multi-scale random interval moment method (MS-RIMM). RIMM is used to describe the hybrid uncertainty, while MSM is used to determine the frequency-domain nonlinear dynamic response. The statistical characteristics (i.e., the expectation value and variance) of the amplitude-frequency response of the nonlinear system with hybrid uncertainties are derived. Furthermore, the accuracy and effectiveness of the proposed method are verified by comparing the results with those obtained using the multi-scale Monte Carlo simulation method (MS-MCSM). Overall, the results of this study can serve as a useful reference for the hybrid uncertainty propagation analysis of nonlinear systems and for predicting the frequency-domain nonlinear dynamic response.