An efficient algorithm for simultaneous identification of time-varying structural parameters and unknown excitations of a building structure

• Develop a recursive least-squares estimation algorithm for system identification.
• Transform multivariate observation equation to simple linear regression equation.
• Introduce a time-varying correction factor matrix to reflect parametric variations.
• Numerical examples demonstrate the feasibility and accuracy of the proposed method.

When a structure is being damaged under unknown excitations, structural parameters of the damaged elements are actually varying with time. Hence, the simultaneous identification of time-varying structural parameters and unknown excitations is an important task in structural health monitoring. Although some analytical methods for such identifications are available in the literature, they are complicated, time-consuming, or restrained by special requirements. This paper presents an efficient algorithm for identifying time-varying structural parameters of a building structure under unknown excitations. By projecting on to the column space of influence matrix of unknown excitations, the observation equation of the structural system with unknown excitations is transformed from a multiple linear regression equation to a simple linear regression equation. By further introducing a time-varying correction factor matrix, an analytical recursive least-squares estimation algorithm is developed for identifying unknown excitations and time-varying structural parameters such as stiffness and damping. The feasibility and accuracy of the proposed algorithm are finally demonstrated through numerical examples and comparison with the existing methods. The results clearly exhibit that the proposed algorithm can simultaneously identify unknown excitations and time-varying structural parameters efficiently and accurately.