A time series generalized functional model based method for vibration-based damage precise localization in structures consisting of 1D, 2D, and 3D elements

• A vibration data-based damage precise localization methodology is introduced.
• The damage coordinates and their uncertainty bounds are estimated.
• The methodology may be applied to structures consisting of 1D, 2D, or 3D elements.
• Its effectiveness is experimentally demonstrated with a spatial truss structure.
• Localization achieved even with a single response signal (low & limited bandwidth).

This study focuses on the problem of vibration-based damage precise localization via data-based, time series type, methods for structures consisting of 1D, 2D, or 3D elements. A Generalized Functional Model Based method is postulated based on an expanded Vector-dependent Functionally Pooled ARX (VFP-ARX) model form, capable of accounting for an arbitrary structural topology. The FP model׳s operating parameter vector elements are properly constrained to reflect any given topology. Damage localization is based on operating parameter vector estimation within the specified topology, so that the location estimate and its uncertainty bounds are statistically optimal. The method׳s effectiveness is experimentally demonstrated through damage precise localization on a laboratory spatial truss structure using various damage scenarios and a single pair of random excitation - vibration response signals in a low and limited frequency bandwidth.