Physics-informed deep operator networks for structural damage identification via damage function

Accurate identification of structural damage remains a challenging inverse problem, particularly due to the difficulties in mathematically representing arbitrary damage shapes and spatially distributed damage fields without explicit parameterization. This study proposes a physics-informed deep operator network (PI-DeepONet) framework coupled with a parametric damage function for structural damage identification. Unlike element-wise stiffness updates, the spatial distribution of stiffness degradation is described by a damage function constructed using compactly supported radial basis functions. This approach significantly reduces the number of unknown parameters while ensuring high-order continuity and physical consistency with locally abrupt damage fields. To accommodate irregular geometries, a Non-Uniform Rational B-Spline-based coordinate transformation is employed to map the physical domain onto a regular parametric space, facilitating the accurate imposition of boundary conditions. A branched neural network architecture is developed, in which parametric coordinates and damage function coefficients are introduced through separate input branches and fused to predict the structural displacement field. Furthermore, a bilevel alternating optimization strategy is employed to decouple training: network weights are optimized to satisfy physical equilibrium, while damage parameters are updated by minimizing strain residuals. Numerical validations demonstrate that the proposed framework accurately captures both the location and severity of stiffness degradation, showing strong potential for structural health monitoring applications.