Fuzzy identification of dynamic loads in presence of structural epistemic uncertainties

The interval identification of dynamic loads for uncertain structures was performed primarily by the interval perturbation method (IPM). Influences of structural epistemic uncertainties on unknown loads cannot be effectively quantified for now and the interval inversion needs to be furtherly investigated. In this paper, Tikhonov regularized technique for the inverse analysis is integrated into a non-intrusive de/re-uncertainty procedure, i.e. the dimension-wise analysis, to reconstruct unknown loads under structural epistemic uncertainties. The proposed method transforms the interval identification model at zero-cut of fuzzy inputs into a finite number of classical ones with crisp parameters, regularized solutions to which are adopted to construct a polynomial approximation of each slice of the unknown load. The extreme point set of each approximation at zero-cut is derived to calculate its minimum/maximum (min/max) points at any alpha-cut with respect to the corresponding uncertain parameter, from which the min/max input vectors of the unknown load are assembled in a dimension-wise manner. Subsequently, the interval bounds of the unknown load at each alpha-cut can thus be evaluated by Tikhonov regularized inversion, based on which the fuzzy description is obtained. The effectiveness of the proposed method is validated by the inclusion of the unknown load in the identified result and a tighter identified interval suggests its accuracy advantage over the IPM if the same regularization method is adopted.