Sparse space-heterogeneous, physics-constrained PDE reconstruction for defect identification through low-frequency mechanics

This contribution explores an application of automatic PDE identification for nondestructive
testing. Defect localization is traditionally performed via the identification of the
spatial distribution of a well-chosen physical property, which is assumed to be impacted by the
defect in question. Defects whose impact on physical properties is unclear may thus cause the
identification approach to fail. This contribution tries to leverage automatic PDE identification
methods like [1] to overcome this limitation. In the context of physics-constrained identification
in mechanics, the equations of forces equilibrium is known and the relation between cinematic
and statical variables is the only part of the PDE that requires identification [3]. The idea of the
contribution is to identify a space-dependent PDE instead of a single space-dependent
parameter. In practice, the PDE in question is defined in this work through a high-dimensional set
of parameters and the method consists in identifying a scalar field for each of those parameters.
As expected, the e iciency of the method relies on regularizing tricks, among which sparsitypromoting
penalization is key. The method is evaluated on experimental data coming from the
dynamical solicitation of a composite beam