High-Fidelity Load Identification Using Deformation Measurements for Static and Dynamic Problems

This work proposes an adjoint-sensitivities-based high-fidelity framework for load identification in structures subject to static and dynamic loads, utilizing displacement and/or strain measurements. The novelty of this work especially lies in identifying unknown loads acting on the structure or scenarios where direct load measurement may not be possible (e.g., in-flight conditions or inaccessible structural regions). The adjoint method for sensitivity calculation efficiently computes the gradients. The load identification problem is framed as an optimization task with the objective of minimizing the aggregated errors between numerical models and the sensor measurements. For dynamic loading cases, an aggregation of errors across all time steps is performed. Since the focus is on high-fidelity load recovery, the inverse problem is usually ill-conditioned, and regularization methods such as Vertex Morphing are employed to smooth the gradients. Three numerical examples (a Truss Bridge, a NACA 0012 Airfoil, and a 2D Beam) are shown to demonstrate the effectiveness of the proposed methodology. The examples are designed to investigate various aspects of the methodology, including the effect of Vertex Morphing on the identified load distribution, scalability with the number of identification variables, and a comparison of the computational effort and identification accuracy for the static and dynamic cases. In all the cases, the target load was recovered with sufficient accuracy.