Compressive sensing-based construction of high-resolution mode shapes for updating bridge boundary constraints

In this study, a method of finite element model updating is proposed to quantitatively identify bridge boundary constraints using the high-resolution mode shapes of a bridge. The high-resolution mode shapes are first identified from the responses measured by few randomly distributed sensors using the compressive sensing theory, which is innovatively implemented in the spatial domain with a proposed basis matrix. To speed up finite element updating, the frequency and modal assurance criterion Kriging models are then established to approximate the implicit relation between boundary constraints and bridge modal parameters including frequencies and mode shapes, serving as surrogate models for the bridge finite element model. By adopting the surrogate models in finite element updating, the objective functions of frequencies and mode shape indicators are optimized by a multi-objective genetic algorithm. The numerical examples as well as an actual laboratory experiment have shown that the mode shapes and boundary constraints of a bridge can be identified precisely and efficiently by the proposed method, even for a continuous and variable cross-sectional bridge.