This section is structured in three parts:
Section 3.1 shows the outcomes of T and RH data pre-processing, while
Section 3.2 and
Section 3.3 show the results from the statistical methods applied to objectively identify similarities, if any, among rooms. Finally,
Section 3.4 is devoted to the discussion of the a posteriori deployment of microclimate sensors based on the previous results.
3.2. Univariate Statistical Method
Figure 6a,b shows the box-and-whisker plots of T and RH data, respectively, recorded in each room and outside (data retrieved from ERA5 database, labelled as “out”) over the selected period.
Table 2 and
Table 3 synthetically report the main statistical parameters for the interpretation of box-and-whisker plots. Outliers were visible only in RH plots (
Figure 6b, black dots), although they were not excluded in the following analyses. In general, it can be noted that T boxes overlap in all rooms, whereas RH boxes behave differently among the rooms.
Box-and-whisker plots provide a synthetic visualisation of the hygrothermal behaviour, but this information does not provide a microclimate classification, except for adjoining locations such as Rooms 38 and 39 in the basement, which might be reasonably characterised by similar indoor climate conditions.
Moreover,
Figure 6 illustrates a different performance for TRH28, which was deployed in a semi-confined attic where no artworks are exhibited or preserved (personal communication of the museum curator). In such location, observations collected by TRH28 were highly similar to the external conditions, also characterised by a higher IQR with respect to values collected in the other rooms.
3.3. Multivariate Statistical Methods
Room 28 was initially included in the following analysis. However, both
Figure 6 and multivariate methods proved to be effective in identifying that the microclimate conditions measured in this room were not comparable with those of the other rooms, always revealing an isolated microclimate pattern.
Principal Component Analysis. PCA was carried out on the hourly T and RH data, separately. The main results are shown below.
Regarding temperature,
Table 4 shows that PC1 is the only component with an eigenvalue > 1, which explains 95% of the total data variance.
Figure 7a shows the contribution of temperature sensors to PC1 and PC2 (loadings), which together explain 97.8% of the total data variability. PC1 loadings range between 0.328 and 0.338. This low variability could be ascribed to the high similarity in time evolution (i.e., parallel trajectories). Considering PC2 loadings, PCA seems to reveal two clusters of rooms based on the height with respect to the ground floor: a group established with Rooms 38, 39, and 52 (in the basement, with PC2 loadings ≥ 0.4) and another group containing all the rest (PC2 loadings ranging between −0.1 and −0.3).
In the case of RH,
Table 4 reports that the two first components (PC1 and PC2) have an eigenvalue > 1 and explain 66.5% and 16.8% of the data variability, respectively. In
Figure 7b, PC1 loadings range between 0.2 and 0.4, highlighting that the time evolution of RH observations is not markedly parallel in the rooms. PC2 loadings, instead, range between −0.5 and 0.5. Once again, on the basis of floor height, rooms in the basement form a cluster with some peculiarities: RH in Room 52 differs in terms of time evolution of relative humidity (PC2, see
Figure 7b), whereas Rooms 38 and 39 appear extremely similar to each other. The other rooms seem to be characterised by a different microclimate pattern.
PCA highlights that one microclimate pattern is clearly attributable to rooms in the basement and another for Rooms 7 and 6 (ground floor), whereas the remaining rooms might be singularly grouped in other microclimate patterns.
Cluster Analysis. Cluster analysis (CA) was applied to indoor monthly averages of T and RH observations following the workflow in
Figure 4 and considering a number of clusters (k) from 2 to 5.
Figure 8 shows the time evolution of temperature and relative humidity both indoors (based on the clustering k) and outdoors (extracted from the ERA5 database [
24]).
Cluster 1 was characterised by the lowest monthly T (T = 6.0 °C) occurring in March (
Figure 8a,c,e,g, blue lines) and the highest monthly RH (RH = 70.0%) occurring in September (
Figure 8b,d,f,h, solid blue lines). Both indoor variables were highly correlated with the outdoor ones (dashed black lines). When k ≥ 3, Cluster 3 identified a microclimate pattern characterised by higher T and lower RH values compared the others, especially in winter months. Cluster 4 was characterised by a peculiar microclimate pattern recorded on average in May: it yields the lowest T (16.0 °C) and the highest RH (67.0%) in the castle (
Figure 8e–h, solid violet lines). This microclimate behaviour was in contrast with outdoor conditions and those reflected by other clusters.
Regardless of the k value, Room 7 (cluster 1) is always characterised by a peculiar microclimate pattern (Cluster 1), showing that this room is the most sensitive to the infiltration of external air masses due to its proximity to an entrance door. Similarly, Rooms 38 and 39 are always included in the same cluster and, in case of k = 5, they are strongly in accordance with each other at S = 0.9 (cluster 3). The microclimate in these rooms is the least affected by the outdoor climate conditions due to the high thermal inertia related to the heavy masonries (wall thickness 1.5 m) compared to the other rooms (wall thickness 1.0 m): the average monthly T is equal to 19.4 °C, whereas RH = 52.0%.
Table 5 summarises the representative outcomes of the cluster analysis for k = 2, k = 3, k = 4 and k = 5, respectively. When k > 3, microclimate conditions in Room 52 are presented by a unique cluster with T = 15.9 °C and RH = 54.7% on average. Looking at the average TRH conditions for each k, it is evident that the clustering is temperature-driven, ranging between 14.4 °C (Cluster 1, Room 7, ground floor) and 19.4 °C (Cluster 3, k = 5, Rooms 38 and 39, basement).
According to the Silhouette index (S), k = 3 has the lowest median S score (S = 0.4, ranging between −0.2 and 1.0) whereas k = 2 yields the highest (S = 0.8 ranging between 0.5 and 1.0). A negative individual S score occurs only in Room 21T (S = −0.2 for k = 3, S = −0.1 for k = 4) meaning that, although similar, Room 21T is not well clustered with other rooms belonging to the same cluster. When k = 3, individual S scores of Cluster 3 range between −0.2 and 0.3, meaning that the similarity among TRH of these rooms is not highly significant, especially in Room 21T. This result seems reasonable, as Rooms 38, 39, and 52 are located in the basement, whereas Room 21T is on the second floor. Individual S scores of Cluster 2 in k = 5 range between 0.2 and 0.3, meaning that Rooms 29 and 34, located in the two towers, are not well clustered with Room 6 on the ground floor. Considering the S median, four clusters (k = 4) were found to be effective in the climate-room classification.
3.4. A-Posteriori Deployment of Microclimate Sensors
The location of microclimate sensors according to the first-guess configuration, along with the position of climate-sensitive artworks selected by the museum conservators, are shown in
Figure 2a,b. Based on the classifications derived from the three methods, three a posteriori deployments of microclimate sensors are shown in
Figure 9a–c. For each method, the number of sensors to relocate was equal to the number of sensors that collected similar microclimate patterns, and, for this reason, may be moved to other positions. It is worth noticing that the relocation of these redundant sensors followed the priority provided by conservators, i.e., considering the climate-sensitivity of the selected artworks. In addition, the sensor in Room 28 (attic where no artworks are exhibited or preserved) was relocated in all the cases to Room 3. It has to be borne in mind that periodic calibration of sensors should be performed not only on a regular basis but also repeated every time a sensor is moved.
According to the climate-room classification resulting from the interpretation of box-and-whisker plots, it was found that Rooms 38 and 39 had a similar microclimate behaviour over the year. For this reason, the microclimate sensor originally located in Room 39 was moved to Room 15 (
Figure 9a). This configuration would allow collection of microclimate data for two additional artworks.
From the principal component analysis, a similar microclimate behaviour was identified between Rooms 38 and 39, as well as between Rooms 6 and 7. For this reason, the microclimate sensors originally located in Rooms 39 and 7 could be moved to Rooms 15 and 3 (
Figure 9b). This configuration would allow to collect microclimate data for four additional artworks.
From the k-means cluster analysis, four clusters were identified as representative of the four microclimate patterns in the Castle (
Table 5). The sensors originally located in Rooms 6, 21T, 29, 34, and 39 could be relocated. The microclimate sensor in Room 6 was moved to the opposite side of the room, closer to the selected climate-sensitive artworks, in order to study whether microclimate conditions differed from the original sampling point in the proximity of artworks. The others were moved to Rooms 3, 13, and 15 (
Figure 9c). This new configuration would allow to collect microclimate data for nine additional artworks.
To sum up,
Table 6 summarises the results obtained by the three statistical approaches providing objectively the number of sensors that can be moved from the original location to another location close to artworks following the decision of conservators. Finally, the k-means cluster analysis has proven to be more sensitive to the intrinsic common characteristics of microclimate behaviour, identifying four microclimate patterns.