Damage assessment through nonlinear structural identification

A procedure based on the minimum model error approach combined with correlation test and least squares fit is proposed to identify the location as well as severity of structural damage sustained during a severe loading episode.; In adapting the minimum model error estimation to the current problem formulation, a new approach utilizing Euler-Lagrange equations for the Bolza problem and the concept of dynamical programming is proposed to reduce the minimization problem to a two-point boundary value problem with jump discontinuity. An analytic form for the errors in estimated state and model error term is then presented. Statistical properties of the estimates are discussed. By introducing auxiliary state and auxiliary model error term, the minimum model error approach is modified to study identification with noisy input measurement and with absolute acceleration measurement.; The proposed identification procedure is evaluated and validated through numerical examples. Estimates for state and model error terms are robust in the presence of high measurement noise, correlation test supplemented by least square fit is numerically simple and parameter estimates obtained are reasonable. An experimental verification of the procedure is also carried out in the laboratory using a three-story model steel frame. In the experiment, an active control experiment using a nonlinear control algorithm is used to simulate the structure's transition from its undamaged state to a damage state, thus allowing a verification of the identification procedure.; High correlation coefficient and low least squares cost are necessary conditions when searching for the right non-linear function and its associated parameters from a prior library. Different nonlinear models or different parameter values within one nonlinear function form, depending on the form of nonlinearity, can all yield high correlation coefficient and low least square cost. Studies with experimental data show that there are shifts in both state and model error term estimates when using measurement of absolute acceleration. Simulation results reproduce this phenomenon when an incorrect measurement noise information is assumed.