Interval process model and non-random vibration analysis

• An interval process model is proposed for time-varying uncertainty analysis.
• The dependent interval process can be transformed into an independent one.
• A non-random vibration method is developed for both SDOF and MDOF systems.
• The upper and lower bounds of structural responses can be expressed analytically.

This paper develops an interval process model for time-varying or dynamic uncertainty analysis when information of the uncertain parameter is inadequate. By using the interval process model to describe a time-varying uncertain parameter, only its upper and lower bounds are required at each time point rather than its precise probability distribution, which is quite different from the traditional stochastic process model. A correlation function is defined for quantification of correlation between the uncertain-but-bounded variables at different times, and a matrix-decomposition-based method is presented to transform the original dependent interval process into an independent one for convenience of subsequent uncertainty analysis. More importantly, based on the interval process model, a non-random vibration analysis method is proposed for response computation of structures subjected to time-varying uncertain external excitations or loads. The structural dynamic responses thus can be derived in the form of upper and lower bounds, providing an important guidance for practical safety analysis and reliability design of structures. Finally, two numerical examples and one engineering application are investigated to demonstrate the feasibility of the interval process model and corresponding non-random vibration analysis method.