Autoregressive model extrapolation using cubic splines for damage progression analysis

The application of Structural Health Monitoring (SHM) methods focuses mainly on its initial levels of the hierarchy of damage identification. The contribution of this paper is to propose a new strategy that allows going further, predicting the progression of the damage indices through the extrapolation of Autoregressive (AR) models with one-step-ahead prediction estimated at early-stage damage conditions using piecewise cubic splines. A trending curve capable of predicting the damage progression can be determined, and it allows the extrapolation to future structural conditions based on some assumptions. The data sets of a benchmark involving a three-story building structure are investigated to illustrate the proposed methodology. The extrapolated coefficients in the most severe condition are implemented to identify an extrapolated AR model, and the results are encouraging by adequately reproducing the structure’s future behavior if the damage is initially detected and not repaired immediately.