On the use of AR models for SHM: A global sensitivity and uncertainty analysis framework

This paper proposes a complete sensitivity analysis of the use of Autoregressive models (AR) and Mahalanobis Squared Distance in the field of Structural Health Monitoring (SHM). Autoregressive models come from econometrics and their use for modelling the response of a physical system has been well established in the last twenty years. However, their aware application in engineering should be supported by knowledge about how they describe phenomena which are well defined by physics. Since autoregressive models are estimated by a least square minimization, statistical tools like Global Sensitivity Analysis and uncertainty propagation are powerful methods to investigate the performance of AR models applied to SHM. These methodologies allow one to understand the role of the uncertainty and uncorrelated noise by a rigorous approach based on statistical motivations. Moreover, it is possible to quantify the link between the mechanical properties of a system and the AR parameters, as well as the Mahalanobis Squared Distance. By fixing a factor prioritization among the variables of a AR model, it is possible to understand which are the parameters playing a main role in damage detection and which type of structural changes is possible to efficiently detect.