Identification of gradually varying physical parameters based on discrete cosine transform using partial measurements

Structural physical parameters often vary gradually due to the degradation of material properties or effects of environment. In this paper, two novel approaches are proposed to identify the gradually varying physical parameters based on the discrete cosine transform (DCT) using partial measurements of structural responses. Approach I is proposed for the circumstance of known excitations. The gradually varying physical parameters are first located by the fading‐factor extended Kalman filter (FEKF) and then identified by the proposed DCT integrated with Kalman filter (KF) method. Approach II is proposed for the identification of gradually varying physical parameters under unknown excitations. The gradually varying physical parameters are first localized by the proposed fading‐factor extended Kalman filter under unknown input (FEKF‐UI) and then identified by the proposed DCT integrated with Kalman filter under unknown input (KF‐UI). Numerical examples demonstrate that the proposed approaches can identify the gradually varying physical parameters accurately with incomplete measurement data. Moreover, the identification of time‐varying cable force in cable‐stayed bridge is also discussed as a case study of the proposed approach I. Experimental verification shows that it provides a new path to identify the time‐varying cable force by only using one acceleration response measurement of the cable.