Port-Hamiltonian Structural Consistency Residual Damage Detection in Discrete Timoshenko Beams

Structural damage detection in flexible beam structures requires methods that combine physical interpretability with fault localization. This paper proposes an energy-based framework for damage detection, localization, and severity estimation in discrete Timoshenko cantilever beams, grounded in port-Hamiltonian system theory. The beam is formulated in explicit port-Hamiltonian form using finite elements, HRZ mass lumping, and Rayleigh proportional damping. The central contribution is the port-Hamiltonian Structural Consistency Residual, a power-balance violation metric that decomposes analytically into element-level damage signatures, enabling localization through a matched-filter least-squares estimator without prior knowledge of damage location or magnitude. The framework is validated numerically on a cantilever beam across four configurations (uniform and non-uniform cross-section, each with 0% and 1% measurement noise) and fifty idealized stiffness-loss damage scenarios per configuration (10 elements × 5 severity levels, 2–30% stiffness reduction). Overall localization accuracy ranges from 86% (uniform, noiseless) to 66% (non-uniform, 1% noise), with exact identification reaching 100% at 30% severity for mid-span elements across all configurations.