Vibration-based damage precise localization in three-dimensional structures: Single versus multiple response measurements

The goal of this study is vibration-based damage precise localization on three-dimensional structures through the vector version of an advanced Functional Model–Based Method. This version, which constitutes an extension of the original scalar method, is equipped with a Functional Model form that may simultaneously exploit multiple structural responses and incorporate the damage coordinates within its parameters through an appropriate operating parameter vector. Based on this model form, precise estimation of the damage coordinates is achieved within a nonlinear optimization framework with constraints representing the three-dimensional structural topology, and corresponding damage confidence intervals are constructed. The effectiveness of the method is assessed through damage precise localization for numerous damage scenarios in a three-dimensional truss structure, as well as through detailed comparisons with the previous, scalar method, demonstrating significant reduction in the localization error.