Stochastic Modeling of Structural Uncertainty/Variability from Ground Vibration Modal Test Data

The focus of this investigation is on the formulation and validation of a methodology for the estimation of a stochastic linear modal model of a structure from measurements of a few of its natural frequencies and mode shapes on a few nominally identical samples of the structure. The basis for the modal model is composed of the modes of an approximate representation of the structure, e.g., a nonupdated or preliminary finite element model. Furthermore, the variability or uncertainty in the structure is assumed to originate from stiffness properties (e.g., Young's modulus, boundary conditions, attachment conditions) so that the mass matrix of the uncertain linear modal model is identity but the corresponding stiffness matrix is random. The nonparametric stochastic modeling approach is adopted here for the representation of this latter matrix; thus, the quantities to be estimated are the mean stiffness matrix and the uncertainty level. This effort is accomplished using the maximum likelihood framework using both natural frequencies and mode shapes data. The successful application of this approach to data from the Air Force Institute of Technology joined wing is demonstrated.