System Identification in Structures Subject to Dynamic Loading

In this work, a high-fidelity adjoint-based framework for system identification in structures subject to dynamic loading, using displacement and/or strain measurements, is proposed. The novelty of this work lies in extending the high-fidelity system identification approach from static to transient cases. Accordingly, the system identification problem is formulated as an optimization problem, minimizing the aggregated errors between sensor measurements and numerical models, also aggregating over time. The gradients for the optimization are computed using the adjoint method, which requires solving the adjoint equation system backwards in time. To mitigate the ill-conditioning of the inverse problem a simple gradient smoothing is employed to obtain meaningful solutions. The effectiveness of the proposed methodology is demonstrated using three numerical examples of increasing complexity: a 1D cantilever beam, a 3D beam, and a wing using the NACA 0012 airfoil example. The results show that in every case, a precise localization of weakness was obtained. The examples show clearly the difference in dynamic behavior between the undamaged and the damaged structures. The 3D beam example demonstrates the effectiveness of the method for multiple load cases. The wing using NACA 0012 airfoil example results show that the inverse problem is challenging in terms of obtaining the true global minimum. However, the obtained solutions are close to the true global minimum, as inferred from the small differences between the obtained and the target distributions.