Efficient structural impact localization via signal curvature energy and probabilistic error function

This study presents a novel probabilistic error function-based structural impact localization method that leverages curvature energy to extract Time of Arrival (TOA) values. By iteratively calculating cumulative and curvature energy across sensor signal time points, the first non-zero moment in the curvature energy curve is identified as the TOA. The method eliminates false signals, and using the predicted TOA, an error function encompassing the impact moment is minimized to compute the probability of impact locations within the structure. Experimental results demonstrate average localization error rates of 5.31% and 7.02% for steel plate without stiffeners, steel plate with stiffeners. The minimum localization error rate can reach 0.20%. Key advantages of the proposed method include: (a) an innovative automatic TOA extraction method based on energy curvature is proposed, eliminating the need for manual threshold setting and facilitating implementation; (b) an impact localization method based on a novel probabilistic error function enables the localization of impact sources and determination of impact occurrence time using at least three sensors; (c) elimination the need for wave velocity calculations in structures and removes dependence on preset databases or accurate wave velocity estimates; (d) applicable to both isotropic and anisotropic steel plate structures. The proposed approach demonstrates strong potential for real-time structural health monitoring and impact localization in diverse engineering applications, offering a practical and efficient alternative to conventional methods.