The spectral inversion model for electrical conductivity in mural plaster following phosphate erosion based on fractional order differentiation and novel spectral indices
Authors: Ren Yikang , Liu Fang 
Published: August 2024

Abstract
The Dunhuang murals are a precious treasure of China’s cultural heritage, yet they have long been affected by salt damage. Traditional methods for detecting salt content are costly, inefficient, and may cause physical harm to the murals. Among current techniques for measuring salt content in murals, hyperspectral remote sensing technology offers a non-invasive, circumventing issues of high costs, low efficiency. Building on this, the study constructs an inversion model for the Electrical Conductivity (EC) values of mural plaster subjected to phosphate erosion, through the integration of Fractional Order Differentiation (FOD), a novel three-band spectral index, and the Partial Least Squares Regression algorithm. The specific research contents include: (1) Initially, in preparation for the experiments, the materials used to create the samples underwent a rigorous desalting process, and phosphate solutions were prepared using deionized water to ensure uniform experimental conditions and the accuracy of the results. These meticulous preprocessing steps guaranteed that the measured EC values exhibited a clear correlation with the phosphate content. Subsequently, by employing qualitative experimental analysis techniques, this study was able to more accurately simulate the real-world scenarios of mural plaster affected by salt damage, enabling a deeper investigation into the mechanisms by which salts inflict microscopic damage to murals. (2) Explores the absorption mechanisms and characteristic spectral bands of the Electrical Conductivity (EC) values measured after the phosphate erosion of mural plaster. By integrating the optimal spectral indices, a univariate linear regression model is constructed, providing a basis for the rapid quantitative measurement of electrical conductivity in murals. (3) By comparing the accuracy of the Phosphate Simple Ratio (PSR) and Phosphate Normalized Difference Index (PNDI) spectral indices based on the linear regression model, the first six orders of the highest accuracy spectral index were selected as the optimal three-band spectral index combination, used as explanatory variables, with mural plaster electrical conductivity as the response variable, employing the PLSR method to construct the mural phosphate content high-spectral feature inversion model. The study’s findings include: (1) Surfaces of samples deteriorated by phosphate erosion formed numerous irregularly shaped crystal clusters, exhibiting uneven characteristics. (2) By comparing the outcomes of different orders of fractional differentiation, it was found that the model performance reached its optimum at a 0.3 order of differentiation for both PSR and PNDI data, with a determination coefficient (Q2) of 0.728. (3) Utilizing PLSR, this study employed the previously determined optimal six-order three-band spectral index combination as explanatory variables, with salt content as the response variable, successfully constructing the high-spectral feature inversion model for mural electrical conductivity with a determination coefficient (Q2) of 0.815. This provides an effective technical means for monitoring the salt damage conditions of precious cultural heritage such as murals.