Identification procedure for epistemic uncertainties using inverse fuzzy arithmetic

For the mathematical representation of systems with epistemic uncertainties, arising, for example, from simplifications in the modeling procedure, models with fuzzy-valued parameters prove to be a suitable and promising approach. In practice, however, the determination of these parameters turns out to be a non-trivial problem. The identification procedure to appropriately update these parameters on the basis of a reference output (measurement or output of an advanced model) requires the solution of an inverse problem. Against this background, an inverse method for the computation of the fuzzy-valued parameters of a model with epistemic uncertainties is presented. This method stands out due to the fact that it only uses feedforward simulations of the model, based on the transformation method of fuzzy arithmetic, along with the reference output. An inversion of the system equations is not necessary. The advancement of the method presented in this paper consists of the identification of multiple input parameters based on a single reference output or measurement. An optimization is used to solve the resulting underdetermined problems by minimizing the uncertainty of the identified parameters. Regions where the identification procedure is reliable are determined by the computation of a feasibility criterion which is also based on the output data of the transformation method only. For a frequency response function of a mechanical system, this criterion allows a restriction of the identification process to some special range of frequency where its solution can be guaranteed. Finally, the practicability of the method is demonstrated by covering the measured output of a fluid-filled piping system by the corresponding uncertain FE model in a conservative way.