## 2 Materials and Methods
### Non-Invasive Analytical Investigation and Data Analysis  
A multi-analytical non-invasive approach was used to estimate the efficiency of each cleaning test in the removal of the artificial soiling. Photographic documentation under visible light was acquired with a Nikon D4 full-frame digital camera equipped with a 50 mm f.1.4 Nikkor objective using a Softbox LED lamp. Colorimetric measurements were accomplished using a portable Konica Minolta CM-2600d spectrophotometer (Chiyoda, Tokyo, Japan). The average of the SCE values was considered (10 repetitions in the SSw and Sw area before and after the application of the treatments, and 3 repetitions after cleaning in the tested area for each time of application), and the dataset was processed in the CIELab space (CIELAB 1976). The chromatic difference (expressed as \(\Delta\)E*) between the SSw and the Sw surfaces, and the corresponding cleaned ones, were considered. Moreover, L* difference (\(\Delta\)L*) values were used to evaluate the darkening and the bleaching of the surface due to the removal of black particles in the soiling mixture. Furthermore, the colorimetric parameters (L*, a*, and b*) were auto scaled and the dataset 3 \(\times\) 192 (variables \(\times\) objects) was explored by PCA. A differential value (\(\Delta\)PC1 and \(\Delta\)PC2 scores) was calculated subtracting the score values of the cleaned areas during the time from the respective soiled area or soiled and sweaty one. Those differential values were used to study the behavior of the chromatic features depending on the application time of each cleaning method. The portable ELIO XRF spectrometer produced by XGLab (Milano, Italy) with Rh anode was employed to collect XRF maps on the specimen surface (40 kV, 15 \(\mu\)A, 3 s per spectrum). The elemental distribution was pointed out by heat maps before and after the cleaning procedure. Ca, as part of the dry fraction of the soiling mixture, was considered a marker for the soiling presence/removal, and Si distribution was also taken into account to determine any residue of VelvesilTM Plus. No marker elements were detected in the sweaty area; in this case, in fact, the technique was slightly informative. Transflection mode FTIR spectra were recorded with the Alpha portable spectrometer (Billerica, MA, USA) equipped with R-Alpha module. Spectra were collected between 7500 cm\({}^{-1}\) and 400 cm\({}^{-1}\) at the resolution of 4 cm\({}^{-1}\) with an acquisition time of 1 min. The beam diameter measured 5 mm. Each spectrum resulted from the average of the three measurements in the same area, in order to assess the analytical reproducibility. The selected dataset employed for the processing consisted of 36 spectra collected in the central point of the areas previously described and corresponding to the different treatments: two points in V, one in SSw and one in Sw; four points in SSw; and four in Sw, respectively for each cleaning application time. Data were processed in OPUS 7.2 software (Billerica, MA, USA). In this study, diagnostic bands were identified for the inorganic fraction of the soiling mixture, mainly ascribable to the Portland cement (CaO 61-67%, SiO\({}_{2}\) 19-23%, Al\({}_{2}\)O\({}_{3}\) 2.5-6%, Fe\({}_{2}\)O\({}_{3}\) 0-6%, and SO\({}_{3}\) 1.5-4.5%) and the mineral kaolin. Variation in the absorbance intensity of the inorganic fraction bands was considered to evaluate the soiling removal. Moreover, diagnostic bands of the VelvesilTM Plus were identified and considered for the detection of the cleaning residues. FTIR spectra were reduced in the range 1800-490 cm\({}^{-1}\) (36 objects \(\times\) 702 variables) and transformed by smoothing (Savitzky-Golay, 3 wavelengths gap size) and mean center to be explored by PCA. Each cleaning method was investigated by independent scores plot to enable a clear understanding of each trajectory or behavior.