A novel analysis method for vibration systems under time-varying uncertainties based on interval process model

Non-probabilistic models can quantify the uncertainties of engineering systems with limited data, which is significantly convenient and economical for engineering applications. However, a key issue in the application of non-probabilistic methods to vibration problems is how to address the time-varying uncertainties, especially when the correlation is involved. In this study, a novel analysis method based on the interval process model is proposed to obtain the dynamic response bounds of vibration systems under time-varying uncertainties, where uncertainties inherently existed in external excitations and system parameters are considered. Firstly, the interval process model is utilized for describing the uncertain-but-bounded variables, and the correlation function quantifies the correlation between the variables at different times. By solving two optimization problems, the dynamic response bounds concerning uncertain system parameters are obtained. Based on the response bounds, the first-order Taylor expansion is used to handle the uncertainties of system parameters, and a homogenization treatment is proposed to suppress the interval expansion. Thus the upper and lower bounds of the dynamic response under time-varying uncertainties can be determined. To quantify the reliability of vibration systems under time-varying uncertainties, the time-varying reliability indexes related to the proposed method are constructed. Finally, the proposed method is validated by the corresponding Monte Carlo simulation method and further applied in lunar soil coring. The findings from this study can provide an important tool for uncertainty and reliability analysis of vibration systems in practical engineering.

Automated summary

Non-probabilistic models provide a convenient and economical way to quantify the uncertainties of engineering systems with limited data. However, dealing with time-varying uncertainties remains a key issue in the application of non-probabilistic methods to vibration problems. This study proposes a novel analysis method based on the interval process model to obtain dynamic response bounds and reliability indexes of vibration systems under time-varying uncertainties.