A general approach to construct full-field responses and high-resolution mode shapes of bridges using sparse measurements

The full-field responses and high-resolution mode shapes are of paramount importance in the detection of bridge damage and finite element model updating. As enlightened by the Fourier series expansion of the mode shapes for a bridge, this study proposes an approach for compressive sensing-based reconstruction of the full-field responses and identification of high-resolution mode shapes, in which a general basis matrix is newly formulated, with particular application to beam-like continuous or non-uniform bridges. The merits of the proposed approach are model-free, output-only, and easy to implement, especially the need of a few sensors. The effectiveness of the approach is validated through both numerical and experimental examples by considering various bridge boundary conditions and non-uniform cross-sections, from which the potential application of this general approach is foreseeable.