Structural damage identification with unknown external inputs based on the sparse constraint

Abstract

Abstract The strength and integrity of a structure are determined not only by the quality of its materials, but also by the health of its various components. In some cases, damaged cracks inside the structure will be generated from excessive loads, which may cause catastrophic failure of structures if undetected for a long period. However, at early stages, most of the damages are minor, and therefore difficult to detect by only visual inspection. Thus, in this paper, a damage estimation algorithm based on an unscented Kalman filter (UKF) is proposed, which can identify and locate the damage parameters in real time using a limited number of sensors. Meanwhile, using this algorithm, joint force-damage estimation can be achieved, which is very applicable to the structural system with unknown external inputs. On the other hand, for most structures, the distribution of damage parameters in the space domain is sparse. Therefore, the sparsity of the damage parameter vector is introduced to UKF as an l 1-norm constraint by the pseudo measurement (PM) technique. Thus, unconstrained optimization of the damage parameter estimation is transformed into an l1 -norm constrained optimization problem. With such improvement, the process of damage parameter estimation converges faster, and the false damage parameters can be effectively restrained. Moreover, to solve the force drift problem during force identification if only acceleration data is used, the sparse constraint of the force vector is also introduced to the UKF framework by the PM technique. Finally, the performance of the proposed algorithm is validated by two case studies, including numerical simulations of a ten-story shear building and experiments of a three-story shear structure. The results indicate that the proposed algorithm can accurately identify the damage, and successfully resolve the common force drift problem.