Non-probabilistic interval process analysis of time-varying uncertain structures

In the engineering practices, the information or the sample data to construct the precise probabilistic characteristics are usually insufficient. Aim at this issue, a non-probabilistic interval process model, whose upper and lower bounds can be determined on the basis of limited data, is introduced to describe the time-varying uncertainties. To obtain the dynamic response bounds of the structure under the non-probabilistic interval process model, a numerical method is proposed, namely the interval Chebyshev surrogate model based on the Karhunen-Loève expansion (ICSM-KLE), are proposed. In this method, the time-dependency between the adjacent values of an interval process is quantified by the Karhunen-Loève expansion. And then, the structural dynamic response bounds of the time-varying uncertain structure is respectively approximated by the Chebyshev surrogate model. Two numerical examples, including a multi-degree-of-freedom linear vibration system and a continuum shell structure, verify that the accuracy of the ICSM-KLE is very high, when compared with the referenced results provided by the direct Monte Carlo method. Thus, the ICSM-KLE provides a good platform for the non-probabilistic interval process analysis of the time-varying uncertain structures with limited information.