Efficient structural model updating with spatially sparse modal data: A Bayesian perspective

Abstract

Structural model updating was born from the need to adjust advanced finite element models to match with the observations of the real asset. An important branch of the discipline is dedicated to the development of Bayesian approaches to solving the updating problem. In the literature, Gibbs samplers were developed to assimilate modal data. This imposes both a forward model linearity in the parameters and a spatial reconstruction of the complete mode shapes from the partial observations. In this paper, a new forward model is constructed, based on a novel two-stage condensation technique. The latter allows one to recover the unobserved degrees of freedom from the observed ones while remaining linear in the parameters. To solve some ill-conditioning issues, a perturbed state of the problem is used that gives more flexibility in the inference. The perturbed two-stage condensation provides a more robust identifiability even in presence of spatially sparse observations. An illustrative numerical example from hydroelectric industry is proposed. Sensitivity analyses are performed to explore performances and limitations.