Interval sensitivity theory and its application to frequency response envelope analysis of uncertain structures

This paper introduces the new concept of interval sensitivities applicable in the general context of numerical interval analysis. The interval sensitivities represent a measure for the individual influence of uncertain interval inputs on the range of the obtained interval outcome of the analysis. The approach differs from the classical sensitivity analysis in the fact that it does not focus on local first or second-order behaviour of the output function in a design point, but rather provides the analyst with information on the sensitivity of the full range of the result with respect to the defined finite interval uncertainties. After introduction of the concept, it is shown how interval sensitivities are calculated in the framework of general numerical interval analysis. Next, the procedure is applied to the envelope frequency response function analysis of uncertain mechanical structures, yielding the sensitivity of the bounds defining the response range to the width of each individual uncertain input parameter interval. The method is finally illustrated on a numerical example.