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

Abstract

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 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 at 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 by the sensors in 2008 and 2010. This methodology is based on fitting different functions and models to the time series, in order to classify the different sensors.The methodology proposed, computes classification variables and applies a discriminant technique to them. The classification variables correspond to estimates of model parameters of and features such as mean and maximum, among others. These features are computed using values of 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 could be useful for characterizing the differences in RH, measured at different positions in a historical building.

Multivariate Time Series Analysis of Temperatures in the Archaeological Museum of L’Almoina (Valencia, Spain)

“…However, results from the sPLS-DA and RF were better when using a common seasonal ARIMA, for all sensors in the same stage of the series. By contrast, the previous study [ 10 ] used a common ARIMA-GARCH model and did not compute forecasts for SH-W. Expanding the methods in this research, by using the Wold decomposition and predictions of T from SH-W, did not improve the results.…”

“…Moreover, the latter yielded better results than using M3, which in turn led to a better classification than with M4. Regarding the results from sPLS-DA, compared with those from the previous study [ 10 ], in both cases, the second best results were derived from the SH-W, possibly because it reliably generates the last level of the smoothing components for a wide range of time series. In the previous research, seasonal ARIMA-TGARCH yielded the best result, while in the present work it was achieved using different functions applied to the time series.…”

“…Furthermore, the sPLS-DA has been applied in a previous study for the classification of different time series of RH [ 10 ] using centroid distance. In addition, BER was used to compare the performance of various models.…”

“…Based on the two first components, the differences between the time series of RH in different positions in the apse were discussed. Ramírez et al [ 10 ] proposed a statistical methodology in order to classify different time series of RH, which pointed to those zones with moisture problems in the apse vault of the Cathedral of Valencia. Merello et al [ 11 ] analyzed 26 different time series of RH and T, recorded at Ariadne’s house (Pompeii, Italy), using graphical descriptive methods and Analysis of Variance (ANOVA), in order to assess the risks for long-term conservation of the mural paintings in the house.…”

“…The purpose was to classify the sensors according to features and variables extracted from the time series of T. Another target was to identify those variables that best discriminate the different time series per zone. For this purpose, a methodology was applied based on sparse partial least squares discriminant analysis (sPLS-DA) and random forest (RF) with models and functions of time series [ 10 , 13 ]. Another target was to identify a subset of representative sensors for a long-term monitoring of thermic air conditions in the museum, as well as to determine the best location recommended for these sensors.…”