Quantification and localization of added masses under varying mass distribution based on a functionally pooled auto-regressive framework

The application of data-driven models derived from structural health monitoring (SHM) systems has emerged as an effective alternative for structural damage diagnosis, requiring a reduced amount of information and enabling direct implementation. Among these approaches, autoregressive (AR) models stand out for their simplicity and low computational cost, as they employ a single input signal to represent the dynamic behavior of the structure. This study proposes a hybrid methodology that integrates AR models for damage detection and functionally pooled autoregressive (FP-AR) models for damage quantification and localization. The framework is developed as a continuous workflow that enables a complete structural diagnosis using only one output signal. The adverse condition analyzed corresponds to the addition of mass, considered as structural modified condition, applied in different configurations and locations along the structural element. Accordingly, the model is trained using variable spatial mass distributions and evaluated against untrained combinations through an exhaustive search based on genetic algorithms. The case study involves a steel beam tested under laboratory conditions, with added masses ranging from 0.5% to 17% of the total beam weight. The results demonstrate reliable detection across all damage scenarios, while the quantification and localization results remain consistent with the applied conditions. Overall, the proposed methodology demonstrates strong potential for real-world applications in which additional masses on structural elements exhibit variable spatial distributions, as it allows the model to be trained with known data and to diagnose new configurations using a single sensor and at a low computational cost.