Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parameters

The uncertainty present in many practical engineering analysis and design problems can be modelled using probabilistic or non-probabilistic interval analysis methods. One motivation for using non-probabilistic interval analysis models rather than probabilistic models for uncertain variables is the general dearth of information in characterizing the uncertainties. Non-probabilistic interval analysis methods are less information-intensive than probabilistic models, since no density information is required. Instead of conventional optimization studies, where the minimum possible response is sought, here an uncertainty model is developed as an anti-optimization problem of finding the least favourable response and the most favourable response under the constraints within the set-theoretical description. Non-probabilistic interval analysis methods have been used for dealing with uncertain phenomena in a wide range of engineering applications. This paper is concerned with the problem of comparison between the non-probabilistic interval analysis method and the probabilistic approach in the static response problem of structures with uncertain-but-bounded parameters from mathematical proofs and numerical calculations. The results show that under the condition of the interval vector of the uncertain parameters determined from the probabilistic and statistical information, the width of the static displacement obtained by the non-probabilistic interval analysis method is larger than that by the probabilistic approach for structures with uncertain-but-bounded structural parameters. This is just the result that we expect, since according to the definition of probabilistic theory and interval mathematics, the region determined by the non-probabilistic interval analysis method should contain one predicted by the probabilistic approach.