Statistical model-based optimization for damage extent quantification.

• Damage quantification is proposed considering data-based uncertainties in model optimization. • Statistical properties of MAC are derived to evaluate mode shape match between data and model in the optimization. • An objective function and a stopping criterion are developed incorporating the variance estimates of modal parameters. • Damage localization is used to reduce the optimization parameter space. • The resulting framework is applied to quantify damage of a simulated beam experiment. Damage localization and quantification constitute different aspects of structural damage diagnosis, which are of particular interest in the Structural Health Monitoring field. Therein, a classical solution is model updating, where the parameters of a finite element model of the possibly damaged structure are optimized to match with the corresponding parameters estimated from its vibration responses. To avoid ill-posedness of the classical finite element updating problem, damage localization and quantification can be treated separately. First, the information about regions or clusters of possibly damaged elements in the structure is obtained by a damage localization method. Then, this information is used to reduce the number of parameters for damage quantification. A framework combining the advantages of methods for damage localization with model optimization is proposed in this paper. For the exploration of the clustered physical model space, a stochastic optimization algorithm is coupled with the evaluation of the statistical properties of the MAC and frequency differences between the numerical model and the estimated modes for an adequate treatment of the data-based uncertainties. Herein, the development of the statistical properties of the MAC estimate is an important step, which is based on a recent quadratic framework that is adapted to the context of the inner product between an estimated mode shape and a numerical mode shape. This statistical information is used in the formulation of the objective function as well as in a data-driven stopping criterion for the optimization search. The proposed framework is validated on numerical simulations of a beam model, where damage at multiple locations is quantified up to the clustering precision. [ABSTRACT FROM AUTHOR]