Identification of structural damage based on a "weak" formulation of locally perturbed structural vibration

The recently developed pseudo-excitation (PE) technique [1, 2] was proven capable of characterizing structural damage under steady vibration. Relying on partial differential equations that characterize the local dynamic equilibrium of the inspected structural components, the PE technique in its primary form, however, presents high susceptibility to measurement noise. In this study, the technique was improved by establishing a "weak" formulation in which a multitude of damage indices, involving derivatives of the structural deflection from lower- to higher-order, as a result of different integration steps, were proposed. The multi-order derivatives in the "weak" formulation provide flexibility for optimally selecting the weight functions, integration intervals and other measurement parameters, to create multi-detection strategies with different levels of precision and noise immunity capabilities. As a representative example, the continuous Gaussian smoothing (CGS) was demonstrated, revealing stronger noise immunity than original PE technique. The effectiveness of the CGS was then validated experimentally by detecting multi-cracks in an irregular beam-like structure, showing satisfactory detection accuracy which could not be achieved by the original PE technique.