Application of Mixture Density Network on solving Uncertainty Qualification Problem in Quasi-Zero Stiffness Vibration Isolator

Quasi-zero stiffness (QZS) vibration isolators, as a class of passive isolation devices, offer significant advantages for vibration attenuation in low-frequency applications. However, the inherent nonlinear characteristics of QZS systems can amplify parameter uncertainties, leading to substantial deviations in isolation performance, particularly near resonance. While previous studies have explored the uncertainty quantification (UQ) of QZS systems, many existing methods struggle to accurately predict the probabilistic behavior of the system’s response in the resonance region. This study proposes a Mixture Density Network (MDN) incorporating a Gaussian Mixture Model to address this challenge. The proposed framework enables a comprehensive UQ analysis of the system’s steady-state peak displacement response across the entire frequency domain, regardless of the underlying distribution of uncertain parameters. To further interpret the results, the MDN is coupled with Sobol’ sensitivity analysis to identify the dominant parameters contributing to response variability in different frequency ranges. Numerical results demonstrate that the MDN approach achieves comparable accuracy and computational efficiency to conventional methods in non-resonant regions, while significantly outperforming them in capturing the probability distribution of peak displacement in strongly nonlinear, resonant regimes.