Displacement-based structural identification using differentiable physics

Infrastructure is at constant risk of failure due to internal or hidden damage resulting from environmental conditions, variability in building materials, and fabrication errors. These risks can be mitigated by structural health monitoring, but it is difficult to monitor the state of the entire structure using discrete measurements. In this study, we propose a scheme for estimating spatially varying elastic modulus fields of a structural element using differentiable physics to support structural health monitoring efforts. Our approach is evaluated on two numerical model systems, a cantilever beam and a simply supported beam, and systematically evaluated for its sensitivity to initialization, boundary conditions, and a wide variety of spatially varying modulus fields. The results demonstrate the effectiveness of this approach in finding structures with matching displacement responses, while also highlighting its limitations in recovering accurate material properties, as is common in with all inverse methods. To address these limitations, we employ regularization techniques including blur filters and Heaviside projection to mitigate degeneracy and recover more complex fields. This work lays the foundation for more informed decision-making in structural health monitoring, with especially close applications to digital image correlation based approaches.