A local specific stiffness identification method based on a multi-scale “weak” formulation

This paper presents a novel local specific stiffness identification method based on a multi-scale “weak” formulation. Based on the local equation of motion, the specific stiffness of a structure can be extracted from its measured vibration displacement, which can further be used as an indicator of damage occurrence inside the structure. However, the estimation of the high order derivative of the measured displacement via a finite difference scheme is prone to the measurement noise. To tackle this problem, a weight function is utilized as a scanning window, which transforms a “point-by-point” identification strategy to a “region-by-region” paradigm. Through a proper parameter setting of the weight function, the final mathematical expression of the local specific stiffness allows avoiding the direct calculation of the high order derivative, thus improving the identification accuracy under noisy measurement conditions. As a proof-of-concept example, an aluminum cantilever beam is investigated for validating the proposed method. The influences of key parameters, such as measurement interval, scale factor and derivative order of the measured vibration displacement, are investigated. The effectiveness of the proposed method is demonstrated numerically and validated experimentally using a step-shaped beam.