Uncertainty-based experimental validation of nonlinear reduced order models

Abstract This paper presents the first results of a combined experimental–computational investigation focused on the validation of reduced order models of geometrically nonlinear structures in the presence of uncertainty. The validation approach considered here is based on the premise that the model is valid if the experimental results can be considered as random sample responses of the stochastic system of which the reduced order model is the mean. For the situation considered here, the power spectra of the experiments should lie within the 2nd and 98th percentiles of the response (forming the uncertainty band) of the stochastic model. Nominally clamped–clamped beams are considered to demonstrate the entire process. The construction of two mean reduced order models and their stochastic counterparts are first performed. Then, the validation effort is carried out by comparing experimentally obtained power spectra and their corresponding computational uncertainty bands. This process leads, for both reduced order models, to a very good representation of the important upper envelope (98th percentile) of the experimental data but a less good fit of the lower envelope (2nd percentile).