Comparison of convex model and interval analysis from optimization viewpoint

The response sets of structures with uncertain-but-bounded structural parameters obtained by convex model and interval analysis were compared from the optimization point of the view. Our analysis indicates that the difference between these two models essentially comes from the difference in feasible regions of their corresponding optimization problems, which gives an intuitive explanation of why the response set obtained by convex model is smaller or larger than that by interval analysis under various circumstances. Specifically, when the hyperrectangle encloses or is enclosed by the hyperellipsoid, the response set obtained by convex model is smaller or larger than that by interval analysis. Otherwise, when no inclusion relation exists between these two parameters sets, which response set is smaller will be not self-evident. In this case, the upper and lower bounds of response sets should be calculated and then compared. Since the formula for convex model is well suited for general case, the one for interval analysis is suggested in this article. This optimization point of the view not only avoids comparing these two models through inequality derivation method, but also reveals that for structures with uncertain-but-bounded structural parameters, expanding the parameters set will result in a larger response set. For its generality, this idea could be applied in the comparison of static, dynamic and bulking responses of structures with uncertain-but-bounded structural parameters.