Construction and identification of a stochastic computational dynamical model using experimental modal data

This research is devoted to the construction and the identification of a stochastic computational model (SCM) using experimental eigenfrequencies and mode shapes measured on a family of real structures with slight differences inducing a significant experimental variability. Concerning the construction of the SCM, the two sources of uncertainties are taken into account: (1) model-parameter uncertainties and (2) model uncertainties induced by the modeling errors. The SCM must have the capability of representing all the configurations of this family, that is to say, the variability of the experiments. The SCM is constructed using a generalized probabilistic approach of uncertainties which allows us to take into account the two sources of uncertainties in a separate way. To facilitate the identification of the SCM, the prior probability distributions of the uncertain model parameters are constructed using the Maximum Entropy principle and the model uncertainties are taken into account with the nonparametric probabilistic approach. The statistical properties of the SCM are thus controlled by a small number of hyperparameters such as mean values, coefficients of variation, etc. The hyperparameters are identified using the first experimental natural frequencies and the associated experimental mass-normalized mode shapes, which are measured for the family of real structures. The methodology proposed here introduces a random transformation of the computational modal quantities (computational eigenfrequencies and associated computational mode shapes) in order to make them almost surely in correspondence with the experimental modal data of each measured real structure. Thus this methodology automatically takes into account the mode crossings and mode veerings which can take place between the experimental configurations and the computational realizations of the SCM. An adapted observation is constructed in order to compare the random computational outputs calculated using the SCM to the experimental outputs. Finally, the hyperparameters are identified using the maximum likelihood method. The proposed methodology is applied to a booster pump of thermal units for which experimental modal data have been measured on several sites. [1]A. Batou, C. Soize, S. Audebert, Identification of a stochastic computational model using experimental modal data, Mechanical systems and Signal Processing, 50-51 (-), 307-322 (2015).