A trajectory method for vibration based damage identification of underdetermined problems

The problem of structural damage identification based on vibration measurements (eigenfrequencies and incomplete mode shapes) is generally formulated as an inverse problem aiming to identify changes encountered on the global stiffness matrix. In most cases, the measured quantities are less than the damage parameters to be identified; thus, an infinite number of possible damage configurations are expected to satisfy the measurements. Therefore, damage identification problems are often proven to be ill-conditioned. The problem becomes more complex when measurements' noise and model uncertainties are considered. Therefore, depending on the structural system, damage scenario and available vibration measurements, additional eigenmode data may need to be considered in order to increase the robustness of the damage identification procedure. In this work, a new two-loop trajectory method is presented, that relies on an iterative nonlinear sensitivity analysis procedure. The main advantage of the proposed method is its ability to identify damage scenarios that match the measured data with high accuracy as well as to explore effectively the solution space. This feature can be exploited in order to assess the adequacy of the measurements in noisy and/ or uncertain environment. Copyright (C) 2016 John Wiley & Sons, Ltd.