A Methodology for Discriminant Time Series Analysis Applied to Microclimate Monitoring of Fresco Paintings

The famous Renaissance frescoes in Valencia's Cathedral (Spain) have been kept under confined temperature and relative humidity (RH) conditions for about 300 years, until the removal of the baroque vault covering them, carried out in 2006. In the interest of longer-term preservation and in order to maintain these frescoes in good condition, a unique monitoring system was implemented to record both air temperature and RH. Sensors were installed in different points at the vault of the apse, during the restoration process. The present study proposes a statistical methodology for analyzing a subset of RH data recorded in 2008 and 2010, from the sensors. This methodology is based on fitting different functions and models to the time series, in order to classify the sensors. The methodology proposed, computes classification variables and applies a discriminant technique to them. The classification variables correspond to estimates of parameters of the models and features such as mean and maximum, among others. These features are computed using values of the functions such as spectral density, sample autocorrelation (sample ACF), sample partial autocorrelation (sample PACF), and moving range (MR). The classification variables computed were structured as a matrix. Next, Sparse Partial Least Squares Discriminant Analysis (sPLS-DA) was applied in order to discriminate sensors according to their position in the vault. It was found that the classification of sensors derived from Seasonal ARIMA-TGARCH showed the best performance (i.e., lowest classification error rate). Based on these results, the methodology applied here can be useful for characterizing the differences in RH, measured at different positions in a historical building.