Use of the cointegration strategies to remove environmental effects from data acquired on historical buildings

The theory of cointegration, usually employed in econometric studies, has proved very powerful in the context of Structural Health Monitoring (SHM), where it can be used to distinguish operational and environmental changes of dynamic features from those related to the evolution of damage. The different nature of the effects imposed by operational and environmental variations on structural response required here an extension of the theory of cointegration from the linear to the nonlinear field. For this purpose, a nonlinear multivariate regression has been developed. This paper proposes a regression obtained through a particular class of machine learners, based on statistical learning theory and its Bayesian variants The algorithms considered, Support Vector Machines (SVMs) and Relevance Vector Machines (RVMs), are applied to data from the Sanctuary of Vicoforte, which was dynamically monitored over a period of four months and modelled with finite elements to simulate structural damage. The SVMs and the RVMs have the advantage of working well with sparse data sets. The algorithms also provide information about the most informative data points (support and relevance vectors) which could prove valuable in an active or query learning context.