The influence of model and measurement uncertainties on damage detection of experimental structures through recursive algorithms

In this work, we developed a framework for identifying frame-type structures regarding the measurement uncertainty and the uncertainty involved in inherent and structural parameters. The identification process is illustrated and examined on a one-eight-scale four-story moment-resisting steel frame under seismic excitation using two well-known recursive schemes: the Extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) methods. The nonlinear system equations were assessed by applying a first-order instantaneous linearization approach through the EKF method. In contrast, the UKF algorithm employs several sample points to estimate moments of random variables' nonlinear transformations. A nonlinear transformation is applied to distribute sample points to derive the precise mean and covariance up to the second order of any nonlinearity. Accordingly, it is theoretically expected that the UKF algorithm is more capable of identifying the nonlinear systems and determining the unknown parameters than the EKF algorithm. The capability of the EKF and UKF algorithms was assessed by considering a 4-story moment-resisting steel frame with several inherent uncertainties, including the material behavior model, boundary conditions, and constraints. In addition to these uncertainties, the combination of acceleration and displacement responses of different structural levels is employed to evaluate the capability of the algorithms. The information entropy measure is used to investigate further the uncertainty of a group of established model parameters. As highlighted, a good agreement is observed between the results using the information entropy measure criterion and those using the UKF and EKF algorithms. The results illustrate that using the responses of fewer levels placed in the proper positions may lead to improved outcomes than those of more improperly positioned levels.