A Multi-Objective DIRECT Algorithm Towards Structural Damage Identification with Limited Dynamic Response Information

Abstract: A major challenge in Structural Health Monitoring (SHM) is to accurately identify both the location and severity of damage using the dynamic response information acquired. While in theory the vibration-based and impedance-based methods may facilitate damage identification with the assistance of a credible baseline finite element model since the changes of stationary wave responses are used in these methods, the response information is generally limited and the measurements may be heterogeneous, making an inverse analysis using sensitivity matrix difficult. Aiming at fundamental advancement, in this research we cast the damage identification problem into an optimization problem where possible changes of finite element properties due to damage occurrence are treated as unknowns. We employ the multiple damage location assurance criterion (MDLAC), which characterizes the relation between measurements and predictions (under sampled elemental property changes), as the vector-form objective function. We then develop an enhanced, multi-objective version of the DIRECT approach to solve the optimization problem. The underlying idea of the multi-objective DIRECT approach is to branch and bound the unknown parametric space to converge to a set of optimal solutions. A new sampling scheme is established, which significantly increases the efficiency in minimizing the error between measurements and predictions. The enhanced DIRECT algorithm is particularly suitable to solving for unknowns that are sparse, as in practical situations structural damage affect only a small number of finite elements. A number of test cases using vibration response information are executed to demonstrate the effectiveness of the new approach.