Method for retrieving concentration of sodium sulfate in fresco considering temperature and humidity by hyperspectral

Abstract

The application discloses a method for hyperspectral inversion of sodium sulfate concentration in murals considering temperature and humidity, and belongs to the technical field of cultural relic protection and spectral analysis. The method comprises the following steps: preparing simulated mural samples with sodium sulfate concentration of 0% to 1%, and temperature and humidity ranges of-14 DEG C to 38 DEG C and 15% RH to 100% RH; collecting 350nm to 2500nm spectral reflectance data and recording environmental parameters by using a ground object spectrometer; after data preprocessing, screening characteristic wave bands based on Pearson correlation analysis, constructing a multivariate data set containing characteristic wave band reflectance, temperature and humidity, dividing a training set and a test set, and establishing a prediction model by using a regression algorithm; and finally inputting characteristic wave band reflectance and real-time temperature and humidity of a mural to be tested, and outputting a sodium sulfate concentration prediction value. The method can accurately invert the sodium sulfate concentration in the mural, and provides technical support for mural salt damage monitoring and protection.

Description

Technical Field

[0001] This invention relates to the fields of cultural relic preservation and spectral analysis technology. More specifically, this invention relates to a method for hyperspectral inversion of sodium sulfate concentration in murals, taking into account temperature and humidity. Background Technology

[0002] Murals are a type of painting art created on walls for decorative and aesthetic purposes, possessing immense research value. However, in humid environments, sodium sulfate migrates to the surface of murals through capillary channels. Repeated dissolution and crystallization weaken the bonding in the ground layer structure, leading to loosening, flaking, or peeling of the pigment layer, as well as common damage such as efflorescence, blisters, and salt blooms. Therefore, salt content testing of murals is crucial for preventing salt damage and preserving the murals. Temperature changes cause phase transitions in sodium sulfate hydrates (such as the conversion between sodium sulfate decahydrate and anhydrous sodium sulfate), while humidity fluctuations affect its hygroscopic dissolution and crystallization processes. These two factors combined alter the spectral reflectance characteristics of the material. Traditional methods, such as ion chromatography (IC), high-density electrochemical staining, and Raman spectroscopy, typically rely on chemical analysis and professional personnel, and often treat temperature and humidity as static interference variables or simply exclude their influence, failing to establish a dynamic coupling relationship between environmental parameters and spectral characteristics. This results in decreased accuracy of inversion models under complex environments. Due to the aforementioned problems, the inversion accuracy of existing methods fluctuates significantly under different temperature and humidity conditions, making it difficult to meet the actual needs of long-term monitoring of murals. Summary of the Invention

[0003] This invention provides a hyperspectral method for retrieving sodium sulfate concentration in murals that takes into account temperature and humidity. This method can accurately retrieve the sodium sulfate concentration in murals, providing technical support for the monitoring and protection of mural salt damage.

[0004] One objective of this invention is to address the shortcomings of traditional methods in effectively integrating temperature and humidity parameters with spectral characteristics, lacking multivariate joint modeling, and making it difficult to accurately capture the coupling relationship between environment, spectrum, and salt content.

[0005] Another objective of this invention is to address the problem that existing simulated mural samples do not accurately reproduce the layered structure and salt distribution characteristics of actual murals, resulting in discrepancies between the collected spectral data and the actual murals, which affects the universality of the inversion model.

[0006] Another objective of this invention is to address the issue that spectral reflectance data is susceptible to interference from noise, baseline drift, and scattering effects during the acquisition process.

[0007] Another objective of this invention is to address the issue that if a reasonable correlation coefficient threshold is not set, low-correlation bands may not be effectively filtered, affecting the model's prediction accuracy and computational efficiency.

[0008] Another objective of this invention is to address the problem that traditional partitioning methods (such as random partitioning) do not consider the joint similarity of multiple variables such as spectral reflectance, sodium sulfate concentration, temperature and humidity, which may lead to an unbalanced distribution of the dataset, poor generalization ability of the model under unknown environmental conditions, and affect the reliability of model evaluation.

[0009] Another objective of this invention is to provide a single regression algorithm that takes into account both the nonlinear characteristics of spectral data and the dynamic effects of temperature and humidity.

[0010] Another objective of this invention is to address the issue that correlation analysis based solely on a single band for feature selection, without considering the interaction between adjacent bands (such as normalized difference index and ratio index), may miss combined features reflecting differences in absorption peaks of substances, thereby reducing the model's ability to discriminate sodium sulfate concentration.

[0011] Another objective of this invention is to address the fact that existing models do not consider the driving effect of the dynamic rate of change of temperature and humidity (such as temperature gradient ΔT and humidity gradient ΔH) on salt migration, as well as the spectral standardization requirements for different temperature and humidity ranges, which makes the models unable to adapt to the temporal changes and spatial heterogeneity of environmental parameters.

[0012] Another objective of this invention is to address the difficulty of achieving high-precision predictions in complex environments by using a single regression algorithm that fails to integrate local details of spectral features (such as local spectral patterns extracted by convolutional neural networks), temporal environmental features (such as the temporal effects of temperature and humidity in random forest fusion), and physical constraints (such as Fick's diffusion law).

[0013] To achieve these objectives according to the present invention, a method for hyperspectral inversion of sodium sulfate concentration in murals, taking into account temperature and humidity, is provided, comprising:

[0014] Simulated mural samples with sodium sulfate concentrations ranging from 0% to 1% were prepared. The ambient temperature range for the samples was -14℃ to 38℃, and the humidity range was 15%RH to 100%RH. Spectral reflectance data of the simulated mural samples were collected at multiple time points using a ground-based spectrometer. The ambient temperature and humidity at the time of collection were also recorded. The spectral wavelength range was 350nm to 2500nm, and the sampling intervals were 1.4nm and 2nm.

[0015] Preprocessing and enhancement of spectral reflectance data were performed. Based on Pearson correlation analysis, the relationship between reflectance and salt content was extracted band by band, and characteristic bands were screened.

[0016] A multivariate dataset containing characteristic band reflectance, ambient temperature and ambient humidity was constructed, and a training set and a test set were divided. A sodium sulfate concentration prediction model was established using a training regression algorithm. The training set data was input into the model for training, and the coefficient of determination and root mean square error were calculated using the test set data to select the optimal model.

[0017] The characteristic band reflectivity of the mural to be tested, the real-time ambient temperature, and the real-time ambient humidity are input into the optimal model, and the predicted value of sodium sulfate concentration is output.

[0018] Preferably, the sample comprises a coarse mud layer and a fine mud layer, wherein sodium sulfate is distributed in the fine mud layer. The coarse mud layer is formed by mixing loess, silt, coarse sand, wheat straw, and water in a mass ratio of 20:30:20:20:30 and then air-drying. The fine mud layer is formed by mixing yellow clay, silt, fine sand, hemp fiber, and a sodium sulfate-containing solution in a mass ratio of 10:55:35:3:35 and then air-drying.

[0019] Preferably, the preprocessing and enhancement of the spectral reflectance data includes: removing data breakpoints, averaging four spectral data of the same order, scattering correction by transforming the standard normal variable, smoothing the spectral curve with a third-order Savitzky-Golay convolution with a third-order polynomial and a window width of 5 to reduce spectral noise, and using spectral differentiation for baseline correction.

[0020] Preferably, bands with an absolute correlation coefficient greater than 0.6 are extracted as feature bands.

[0021] Preferably, the training set and test set are divided based on the XY joint distance algorithm. The XY joint distance algorithm determines the data similarity by calculating the sum of the Euclidean distances of spectral reflectance, sodium sulfate concentration, ambient temperature, and ambient humidity. The total distance is calculated using four distances as the measurement standard: the Euclidean distance between ambient temperatures, the Euclidean distance between ambient humidity, the Euclidean distance between spectral reflectance, and the Euclidean distance between sodium sulfate concentration. The total distance between each pair of data is calculated separately, and the two data with the greatest distance are selected as the seeds for clustering. Then, clustering is performed based on the minimum Euclidean distance until the number of samples in the test set reaches 30% of the total number of samples. At this point, the test set is divided, and all the remaining data are assigned to the training set.

[0022] Preferably, the training regression algorithm is one of the following: linear partial least squares regression, random forest, or convolutional neural network.

[0023] Preferably, after the step of screening feature bands based on Pearson correlation analysis, the method further includes supplementing feature bands based on band interaction feature extraction and fusion technology, specifically including:

[0024] For all adjacent band combinations with continuous wavelengths less than 50nm in the wavelength range of 350nm to 2500nm and without any interval, calculate the normalized difference index and the ratio index. The normalized difference index is defined as the difference between the reflectance of the first band and the reflectance of the second band, divided by the sum of the reflectances of the two bands. The ratio index is defined as the reflectance of the first band divided by the reflectance of the second band.

[0025] Band combinations with an absolute value greater than 0.6 in the normalized difference index or ratio index and the Pearson correlation coefficient of sodium sulfate concentration are selected as supplementary feature bands;

[0026] The normalized difference index and ratio index data corresponding to the supplementary feature bands are merged with the reflectance data of the feature bands selected based on Pearson correlation analysis to form a fused feature dataset, which is used for subsequent model training and prediction.

[0027] Preferably, the following steps are included after the step of constructing the multivariate dataset:

[0028] For each sample, based on the ambient temperature and humidity data recorded at consecutive time points, the rate of change of temperature ΔT and the rate of change of humidity ΔH at adjacent time points are calculated to form a two-dimensional gradient vector [ΔT, ΔH]. The calculation interval of the gradient vector is an integer multiple of the data acquisition time interval and does not exceed 2 hours.

[0029] The gradient vector is input into a Bi-LSTM network containing 32 hidden units, which outputs a dynamic modulation coefficient matrix with the same dimension as the number of feature bands. This matrix is ​​then compared with the feature band reflectance data according to formula R'. λ =R λ ×(1+tanh( W λ Multiply by band, R' λ Indicates the modulated reflectivity. l Indicates the band number, R λ Represents the reflectivity of the original characteristic band. W λ This represents the coefficient corresponding to each band in the dynamic modulation coefficient matrix, and tanh is the hyperbolic tangent function, which restricts the modulation coefficient to the range of (-1, 1).

[0030] The temperature range is defined as 11 intervals divided in 5°C increments within the range of -14°C to 38°C, and the humidity range is defined as 9 intervals divided in 10%RH increments within the range of 15%RH to 100%RH. For each sample, based on its temperature interval t and humidity interval h, the pre-stored mean spectral reflectance μ of all samples within that interval in the characteristic band is retrieved. t,h With standard deviation σ t,h According to formula R norm =(R-μ t,h ) / σ t,h Standardization, R norm R represents the normalized reflectance, and R represents the original reflectance.

[0031] During the model training phase, the loss function L is defined as L=α·MSE+(1-α)·|ρ|, where MSE is the mean square error between the predicted concentration and the true value, ρ is the sum of the absolute values ​​of the Pearson correlation coefficients of the predicted concentration change rate and ΔT and ΔH, and α is set to 0.7. Backpropagation is used to simultaneously optimize the prediction accuracy and the consistency with the physical laws of salt migration.

[0032] Preferably, an integrated model is used to establish a sodium sulfate concentration prediction model, including the following steps:

[0033] The reflectance data of the fused feature dataset is input into a one-dimensional convolutional neural network. The one-dimensional convolutional neural network contains 3 convolutional layers, each with 64 to 128 convolutional kernels, a kernel size of 3 to 5, a stride of 1, and the activation function is ReLU. The output is a local spectral feature vector.

[0034] The local spectral feature vector is concatenated with the time-series data of ambient temperature and humidity according to the timestamp, and then input into the random forest regression model. The random forest contains 150 to 200 decision trees, each with a maximum depth of 12 to 15 and a minimum number of samples per node of 5 to 10. The output is an environment-spectral joint feature vector.

[0035] The environmental-spectral joint feature vector is input into a partial least squares regression model, and a salt migration constraint equation is constructed based on Fick's diffusion law, in the form ∂C / ∂t = γ(D·∇ 2 C)+β(ΔTΔH), where C represents the sodium sulfate concentration and D represents the diffusion coefficient, with a measured calibrated value of 1.5×10. -5 m 2 / s to 2.0×10 -5 m 2 / s, γ and β represent weighting coefficients and satisfy γ+β=1, γ is based on empirical values, β is based on empirical values, ΔT represents the rate of temperature change, and ΔH represents the rate of humidity change; by minimizing the weighted sum of the predicted concentration residual and the physical equation residual, the final predicted value of sodium sulfate concentration is output.

[0036] When the number of newly added mural samples reaches 50 to 100 sets, a sliding window mechanism is used to retain 80% of the latest data. The weight parameters of the convolutional neural network and partial least squares regression model are updated online, with an update cycle of no more than 15 days. The loss function is defined as L = 0.7MSE + 0.3|∇C pred -∇C phys |, where ∇C pred Represents the predicted concentration gradient, ∇C phys Calculate the gradient for the physical equations.

[0037] The present invention has at least the following beneficial effects:

[0038] First, this invention is the first to deeply integrate ambient temperature, humidity (static value and dynamic rate of change) with hyperspectral reflectance to construct a multivariate joint dataset. It considers the dynamic influence of environmental factors on salt migration in murals, and solves the problem that traditional methods ignore the influence of temperature and humidity on the phase transition and migration process of sodium sulfate. This enables the model to accurately capture the coupling relationship between environment, spectrum and salt content, significantly improve the inversion accuracy in complex environments, and accurately invert the sodium sulfate concentration in murals, providing technical support for the monitoring and protection of salt damage in murals.

[0039] Secondly, this invention effectively mines the inter-band interaction information in spectral data by extracting the normalized difference index and ratio index of adjacent bands as supplementary feature bands. Traditional single-band correlation analysis only focuses on the relationship between a single wavelength and sodium sulfate concentration, while band interaction features can reflect the relative differences and synergistic changes between spectral absorption peaks. This information is of great value for accurately determining sodium sulfate concentration. The addition of supplementary feature bands enriches the dimensionality of the feature dataset, enabling the model to acquire more comprehensive spectral information and making up for the shortcomings of single feature selection. The model trained based on the fused feature dataset has a significantly enhanced ability to distinguish sodium sulfate concentration, and can more accurately capture the complex relationship between spectrum and salt content, further improving the accuracy and reliability of sodium sulfate concentration inversion in murals.

[0040] Third, this invention effectively addresses the problem of traditional models failing to consider dynamic changes in temperature and humidity and physical constraints by calculating the environmental temperature and humidity gradient vector, constructing a dynamic coupling model, implementing conditional standardization, and adding physical driving constraints. The introduction of the temperature and humidity gradient vector and the Bi-LSTM network enables the model to capture the impact of temperature and humidity changes over time on the spectrum, dynamically modulating spectral reflectance. Conditional standardization eliminates spectral differences under different temperature and humidity conditions, making the data comparable. The physical driving constraints ensure that the model's predictions conform to the physical laws of salt migration. These measures work together to significantly improve the model's stability and physical interpretability in complex environments, making the model more accurate.

[0041] Fourth, this invention achieves spectral feature extraction, environmental time series fusion, and physical law constraint through a three-layer architecture. Spectral feature extraction utilizes a one-dimensional convolutional neural network (1D-CNN) to automatically capture local band correlation features of spectral data (such as absorption peak positions and slope changes), avoiding the subjectivity of manual feature selection. Environmental feature fusion integrates spectral features with temperature and humidity time series data through random forest (RF), processes nonlinear mapping relationships, and outputs joint features containing environmental-spectral coupling information. Physical constraint regression introduces Fick's diffusion law as a regularization term, constraining the model prediction results to conform to the physical laws of salt migration (temperature / humidity changes drive salt diffusion or crystallization), improving generalization ability. Dynamic incremental updates retain the latest data through a sliding window mechanism, updating model parameters online to adapt to long-term changes in the mural environment.

[0042] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating one technical solution of the present invention. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0045] It should be understood that terms such as “having,” “comprising,” and “including” as used herein do not exclude the presence or addition of one or more other elements or combinations thereof.

[0046] It should be noted that, unless otherwise specified, the experimental methods described in the following embodiments are conventional methods, and the reagents and materials mentioned are commercially available. In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "setting" should be interpreted broadly. For example, they can refer to fixed connection or setting, detachable connection or setting, or integral connection or setting. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. The terms "lateral," "longitudinal," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention and simplifying the description. They do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0047] like Figure 1 As shown, this invention provides a method for hyperspectral inversion of sodium sulfate concentration in murals that takes into account temperature and humidity, comprising:

[0048] Step 1: Prepare simulated mural samples with a sodium sulfate concentration of 0% to 1%, possessing similar physicochemical properties to real murals. These samples will be used for spectral data acquisition and model training under laboratory conditions. The ambient temperature range for the samples is -14℃ to 38℃, and the humidity range is 15%RH to 100%RH. A ground-based spectrometer will be used to measure the spectral reflectance of the objects in the visible-near-infrared band. Spectral reflectance data of the simulated mural samples will be collected at multiple consecutive time points, while simultaneously recording the ambient temperature and humidity. The spectral wavelength range is 350nm to 2500nm, with sampling intervals of 1.4nm (visible-near-infrared short wave) and 2nm (near-infrared long wave).

[0049] Based on research of relevant literature from temples and monasteries such as the Huapen Guandi Temple in Yanqing, Beijing, the Princess Temple in Wutaishan, Shanxi, the Dayu Temple in Pingshun, Shanxi, and the Guandi Temple in Fenyang, Shanxi, areas with severe salt damage to murals all had Na ion content exceeding 1%. Content below 1% generally did not cause salt damage. Furthermore, simulation samples of the murals revealed that samples with a salt content above 1% exhibited salt damage or precipitation reactions, while samples with Na2SO4 content below 1% did not show either salt damage or precipitation reactions, allowing for laboratory simulation. Therefore, sodium sulfate was prepared in the range of 0% to 1%, with 0.05% increments, resulting in a total of 21 samples.

[0050] The mural structure is layered and complex, with sodium sulfate concentrated in the fine clay layer. Existing simulation samples often ignore the differences in materials and salt distribution characteristics between the coarse and fine clay layers, resulting in low matching between spectral data and actual murals. Preferably, the sample includes a coarse clay layer and a fine clay layer, with sodium sulfate distributed in the fine clay layer. The coarse clay layer is formed by mixing loess, silt, coarse sand, wheat straw, and water in a mass ratio of 20:30:20:20:30 and then air-drying. The fine clay layer is formed by mixing yellow clay, silt, fine sand, hemp fibers, and a sodium sulfate-containing solution in a mass ratio of 10:55:35:3:35 and then air-drying. The materials required for the experiment are yellow clay with a diameter less than 5 micrometers, local silt with a diameter less than 75 micrometers, fine sand, coarse sand, wheat straw, hemp fibers, analytical grade sodium sulfate, and deionized water.

[0051] Pretreatment: ① Add water to locally sourced silt, stir, filter to remove larger stones, and allow to settle for 24 hours. Then remove the supernatant and floating matter. ② Add sufficient deionized water to cover the silt and stir for at least 10 minutes to fully dissolve the soluble salts in the water. After settling for 24 hours, pour off the supernatant. Allow the material surface to air dry and measure the cation content on the dried material surface using an XRF fluorescence spectrometer. ③ Repeat step ② until the cation content no longer changes. ④ Perform steps ② and ③ on the yellow clay, fine sand, and coarse sand for deionization. ⑤ Allow the deionized soil to air dry and grind it using a mortar and pestle. Pass the silt and yellow clay through a 200-mesh sieve (200 mesh corresponds to a diameter of 75 micrometers). Since the diameter of the yellow clay was confirmed to be less than 5 micrometers when purchased, it only needs to be passed through a 200-mesh sieve to break it up. ⑥ Cut the wheat straw to less than 4 cm and use a hemp knife to pound and roughen it, while removing impurities.

[0052] The coarse clay layer simulates the underlying structure of the mural, primarily serving as support and initial reinforcement. It is composed of a mixture of various materials, providing a stable foundation for the upper layers. The fine clay layer simulates the surface layer of the mural that is in direct contact with the external environment and where salt easily accumulates. Its composition and structure have a significant impact on the distribution and spectral characteristics of sodium sulfate.

[0053] Preparation of the coarse mud layer: For each sample, take 20g of loess, 30g of silt, 20g of coarse sand, 20g of wheat straw, and 30g of water. Add water in several batches, stirring evenly. Fill the mud into the sample mold, compact and smooth it with a tool, and place the sample block in a cardboard box at a temperature of about 20 degrees Celsius and a humidity of 40% to 50% to air dry. During this period, monitor the environment with a thermometer and hygrometer until the sample quality no longer changes.

[0054] Preparation of the fine mud layer: The fine mud layer is the main measurement target of the experiment. The mixture consists of 10 g yellow clay, 55 g silt, 35 g fine sand, 5 g hemp fiber, and 35 g water. Sodium sulfate is poured into the water and stirred until completely dissolved. This solution is then added to the well-mixed clay and hemp fiber mixture to form a uniform mud ball. This salt-containing mud ball is filled into a mold containing the coarse mud layer, compacted and smoothed with a tool. The sample block is placed in a cardboard box at approximately 20°C and 40% to 50% humidity to air dry. The environment is monitored with a thermometer and hygrometer during this period until the sample quality no longer changes.

[0055] By clearly defining the material ratios and preparation processes for the coarse and fine clay layers, the simulated mural samples more closely resemble real murals in terms of physical structure and chemical composition. In particular, the directional distribution of sodium sulfate in the fine clay layer accurately replicates the salt enrichment state in actual murals. The collected spectral data accurately reflects the occurrence characteristics of sodium sulfate in the actual scene, effectively improving the authenticity and reliability of subsequent hyperspectral inversion model training data and laying the foundation for accurate inversion of sodium sulfate concentration in murals.

[0056] Instruments required for data acquisition: Spectral data acquisition utilized an ASD-FieldSpec4 Hi-Res ground object spectrometer manufactured by Analytical Spectroscopy Equipment, USA. The instrument's wavelength range is 350 to 2500 nm, with sampling intervals of 1.4 nm (350 to 1000 nm) and 2 nm (1001 to 2500 nm). The light source was solely a 70W quartz-tungsten-halogen lamp integrated into the contact probe. Temperature and humidity monitoring was performed using a calibrated HTC-1 thermometer and hygrometer. Literature review indicated that temple murals are directly exposed to the environment, with temperatures ranging from -14°C to 38°C and humidity from 15%RH to 100%RH. Therefore, environmental data was recorded whenever the ambient temperature changed by 5°C or the humidity changed by 8%, and spectral data acquisition was then organized accordingly.

[0057] Spectral data acquisition process: The instrument is preheated for at least 30 minutes. First, a white board is placed on a black flannel cloth, and the contact probe is vertically placed on the white board. After the curve stabilizes, the reflectance data of the standard white board is collected. After calibration, the white board data is a nearly stable horizontal line, and the white board is recalibrated every 15 minutes. The simulated mural is processed using the same method. The sample is placed on a black flannel cloth, and the contact probe is vertically placed on the surface of the sample mural. After the spectrum stabilizes, data is collected once, and then the probe is rotated 90° and measured again. Each position is measured four times.

[0058] Step 2: Preprocessing and enhancement of spectral reflectance data, specifically including: preprocessing to remove data gaps caused by instrument malfunction, signal interruption, etc.; averaging four spectral curves from the same sample acquired in the same session to improve data quality; data enhancement in Matlab using Standard Normal Variable Transform (SNV) scattering correction to effectively eliminate scattering interference caused by uneven particle size and distribution in coarse / fine mud layers; smoothing the spectral curves using a third-order Savitzky-Golay convolution with a window width of 5 using a third-order polynomial; smoothing the spectral curves using polynomial fitting to reduce spectral noise, improve the signal-to-noise ratio, and preserve the original features of the data to the greatest extent; finally, baseline correction using spectral differential; calculating the derivative of spectral reflectance to correct spectral baseline drift, eliminating the influence of baseline drift, revealing features that are not easily noticeable in the original spectral curves, improving the correlation between spectral data and salt content, and laying the foundation for feature extraction.

[0059] In the spectral preprocessing process, issues such as noise interference and baseline drift, if not handled properly, can obscure effective features. Removing data breakpoints ensures data integrity, averaging reduces random noise, standard normal variable transformation unifies the data benchmark, Savitzky-Golay convolution smooths the curves, and spectral differential correction corrects the baseline, significantly improving the quality and stability of the spectral data. High-quality spectral data can more accurately reflect the spectral characteristics of sodium sulfate, improving the accuracy of feature band selection and the reliability of subsequent model training, reducing inversion errors caused by data quality issues, and providing strong data support for the accurate inversion of sodium sulfate concentration in murals.

[0060] During feature selection, the Pearson correlation coefficient between reflectance and sodium sulfate concentration for each spectral band is calculated, with a closer absolute value to 1 indicating a stronger correlation. Specifically, the mean values ​​of spectral reflectance and sodium sulfate concentration are first calculated separately. Then, using the Pearson correlation coefficient formula, the covariance of reflectance and sodium sulfate concentration at each wavelength is calculated, divided by the product of their standard deviations to obtain the correlation coefficient for that wavelength. Based on Pearson correlation analysis, the relationship between reflectance and salt content is extracted band by band. A two-sided significance test is used to screen statistically significant results. Bands with an absolute correlation coefficient greater than 0.6 are selected as feature bands, and their corresponding reflectance data are used for subsequent regression modeling. By setting a screening criterion of an absolute Pearson correlation coefficient greater than 0.6, feature bands highly correlated with sodium sulfate concentration are accurately extracted from a large number of spectral bands. These feature bands exhibit a strong linear correlation between spectral reflectance and sodium sulfate concentration, effectively reflecting the spectral information of changes in sodium sulfate concentration. This screening process removed bands with weak correlation to sodium sulfate concentration, retained key spectral features, reduced data dimensionality, and improved the efficiency and accuracy of subsequent data analysis and model training.

[0061] Step 3: Construct a multivariate dataset containing characteristic band reflectance, ambient temperature, and ambient humidity. Specifically, summarize the spectral reflectance data and the corresponding ambient temperature, ambient humidity, and sodium sulfate concentration data to form a complete dataset. Each data point in the complete dataset contains the spectral reflectance corresponding to the characteristic band, the sodium sulfate concentration of the corresponding simulated mural, and the temperature and humidity conditions at the time the spectrum was acquired.

[0062] The training and test sets are divided. Preferably, the training and test sets are divided based on the XY joint distance algorithm. The XY joint distance algorithm determines data similarity by calculating the sum of the Euclidean distances of spectral reflectance, sodium sulfate concentration, ambient temperature, and ambient humidity. The total distance is calculated using four distances as the standard: the Euclidean distance between ambient temperatures, the Euclidean distance between ambient humidity, the Euclidean distance between spectral reflectance, and the Euclidean distance between sodium sulfate concentration. The total distance between each pair of data is calculated separately, and the two data pairs with the greatest distance are selected as the seeds for clustering. Then, clustering is performed based on the minimum Euclidean distance, using equal weights. During the clustering process, the number of samples in the test set is continuously monitored until the number of samples in the test set reaches 30% of the total number of samples. At this point, the test set is divided, the clustering operation is stopped, and all remaining data are assigned to the training set.

[0063] The XY joint distance algorithm achieves a scientific partitioning of the training and test sets by comprehensively considering the joint similarity of multiple key factors such as spectral reflectance, sodium sulfate concentration, temperature, and humidity. This ensures a reasonable distribution of the training and test sets across multiple dimensions, including spectral reflectance, sodium sulfate concentration, temperature, and humidity. The test set effectively covers samples under different temperature and humidity conditions and sodium sulfate concentration levels, avoiding model evaluation bias caused by imbalanced dataset partitioning. This improves the effectiveness of model training and the reliability of test evaluation, enabling the established sodium sulfate concentration prediction model to have better generalization ability under different environmental conditions and more accurately predict the sodium sulfate concentration in actual murals.

[0064] The model was built using a variety of training regression algorithms, including linear algorithms such as Partial Least Squares Regression (PLSR), nonlinear machine learning algorithms such as Random Forest (RF), and deep learning methods such as Convolutional Neural Network (CNN) to predict sodium sulfate concentration. The dependent variable was sodium sulfate concentration, and the independent variables were spectral reflectance, temperature, and humidity data. The training set data was input into the model for training, and the coefficient of determination (R²) was calculated using the test set data. 2 The model's coefficient of determination and root mean square error (RMSE) are calculated using the predicted and true values ​​of the dependent variable. The former represents the confidence level used to evaluate the model. 2 A value less than 0.5 indicates the model lacks predictive ability; a value between 0.5 and 0.7 represents preliminary predictive ability; and a value greater than 0.7 indicates good predictive ability. RMSE represents model accuracy; a smaller value indicates higher prediction accuracy. Comparing both parameters, the model with the strongest predictive ability and highest prediction accuracy is selected as the final model, i.e., Rm. 2 The model with the highest RMSE and the smallest RMSE is selected as the optimal model.

[0065] If partial least squares regression is chosen, firstly, principal components are extracted from the independent variable data such as characteristic band reflectance, ambient temperature, and ambient humidity in the training set. An appropriate number of principal components is determined so that the extracted principal components can explain the variance information of the independent and dependent variables (sodium sulfate concentration) to the greatest extent possible. Then, based on the extracted principal components, a linear regression equation is established between the principal components and the sodium sulfate concentration. The regression coefficients are then solved using the least squares method to complete model training.

[0066] If the random forest algorithm is chosen, multiple decision trees are first constructed based on the training set data. When constructing each decision tree, a subset of samples and features are randomly selected from the training set for splitting. The dataset is recursively divided into different child nodes until a stopping condition is met (e.g., the number of samples in a node is less than a threshold or the Gini index reaches its minimum). Each decision tree makes predictions independently. Finally, the predictions from all decision trees are voted on or averaged to obtain the final predicted sodium sulfate concentration, completing the model training.

[0067] If a convolutional neural network is chosen, the reflectance data of the characteristic bands in the training set should be preprocessed to conform to the network input format (e.g., adjusted to a one-dimensional vector sequence). A network structure containing three convolutional layers should be constructed, with each layer having 64 to 128 convolutional kernels, a kernel size of 3 to 5, a stride of 1, and ReLU as the activation function. Local features of the spectral data should be automatically extracted through the convolutional layers, and then mapped to the predicted sodium sulfate concentration using fully connected layers. The network parameters should be trained using backpropagation and an optimizer (e.g., stochastic gradient descent), continuously adjusting the network weights to minimize the prediction error on the training set.

[0068] The training algorithm does not restrict the regression model. Partial least squares regression is suitable for handling cases where independent variables exhibit multicollinearity. Principal component extraction effectively simplifies the data structure and establishes a linear relationship model. Random forest algorithm, by integrating multiple decision trees, enhances the model's ability to handle nonlinear data and its resistance to interference, enabling it to adapt to complex spectral-concentration relationships. Convolutional neural networks, with their powerful feature extraction capabilities, automatically capture the band features and potential patterns of spectral data. This diverse selection of algorithms improves the applicability of the method, enabling the established sodium sulfate concentration prediction model to achieve high-precision predictions under different data conditions, meeting the practical application needs of sodium sulfate concentration inversion in murals.

[0069] Step 4: Prediction of sodium sulfate concentration in real murals: Input the characteristic band reflectivity of the mural to be tested, the real-time ambient temperature, and the real-time ambient humidity into the optimal model, and output the predicted value of sodium sulfate concentration.

[0070] The above technical solution is the first to deeply integrate ambient temperature, humidity (static value and dynamic change rate) and hyperspectral reflectance to construct a multivariate joint dataset. It considers the dynamic influence of environmental factors on salt migration in murals, solves the problem that traditional methods ignore the influence of temperature and humidity on the phase transformation and migration process of sodium sulfate, and enables the model to accurately capture the coupling relationship between environment, spectrum and salt content. It significantly improves the inversion accuracy in complex environments and can accurately invert the sodium sulfate concentration in murals, providing technical support for the monitoring and protection of salt damage in murals.

[0071] Feature band selection relies solely on single spectral correlation analysis, failing to uncover inter-band interactions and thus losing potential discriminative features. In another approach, after the feature band selection step based on Pearson correlation analysis, supplementary feature bands are added using band interaction feature extraction and fusion techniques, specifically including:

[0072] For all adjacent band combinations with continuous wavelengths less than 50 nm in the wavelength range of 350 nm to 2500 nm and without any interval, the normalized difference index and the ratio index are calculated. The normalized difference index is defined as the difference between the reflectance of the first band and the reflectance of the second band, divided by the sum of the reflectances of the two bands. It is an index that highlights the spectral differences of ground objects and is used to mine the interactive information between bands. The ratio index is defined as the reflectance of the first band divided by the reflectance of the second band. It is an index that enhances the spectral characteristics of specific ground objects and reflects the relative change relationship between bands.

[0073] Based on the actual sampling interval of the spectrometer, with sampling intervals of 1.4 nm (visible to near-infrared short wave, 350-1000 nm) and 2 nm (near-infrared long wave, 1000-2500 nm), then the "continuous and uninterrupted" adjacent bands can be:

[0074] 350-1000nm range: band pairs are ( l 1 , l 1 +1.4nm), such as (350nm, 351.4nm), (351.4nm, 352.8nm), etc.;

[0075] 1000-2500nm range: band pairs are ( l 2 , l 2 +2nm), such as (1000nm, 1002nm), (1002nm, 1004nm), etc.

[0076] Since the interval between the aforementioned adjacent bands is only 1.4 nm or 2 nm (both much less than 50 nm), all consecutive adjacent band pairs satisfy the condition. The final number of adjacent band combinations generated is approximately:

[0077] In the 350 to 1000 nm range: (1000-350) / 1.4 ≈ 464 band pairs;

[0078] In the 1000 to 2500 nm range: (2500-1000) / 2 = 750 band pairs;

[0079] There are a total of approximately 1214 adjacent band combinations.

[0080] For each adjacent band combination ( ᵢ , λⱼ ),in ᵢ < λⱼ Furthermore, for consecutive adjacent bands, calculate the Normalized Difference Index (NDI) and the Ratio Index (RI):

[0081]

[0082]

[0083] in, R λi and R λj bands ᵢ and λⱼ The reflectivity value.

[0084] Band combinations with an absolute value greater than 0.6 in the Pearson correlation coefficient between the normalized difference index or ratio index and the sodium sulfate concentration are selected as supplementary feature bands. These band combinations or correlation indices can further improve model performance based on the single-band correlation screening.

[0085] For each adjacent band combination ( ᵢ , λⱼ ):

[0086] Extract the NDI values ​​of all samples (denoted as NDI) k , k =1,2,…, n , n (total number of samples)

[0087] Extract the sodium sulfate concentration values ​​of all samples (denoted as ). C k );

[0088] calculate r (NDI, C):

[0089]

[0090] Similarly, calculate r (RI, C).

[0091] The normalized difference index and ratio index data corresponding to the supplementary feature bands are merged with the reflectance data of the feature bands selected based on Pearson correlation analysis to form a fused feature dataset. This fused feature dataset contains direct relevant information of a single band and interaction information between bands, which is used for subsequent model training and prediction.

[0092] In the above technical solution, by extracting the normalized difference index and ratio index of adjacent bands as supplementary feature bands, the interactive information between bands in the spectral data is effectively mined. Traditional single-band correlation analysis only focuses on the relationship between a single wavelength and sodium sulfate concentration, while band interaction features can reflect the relative differences and synergistic changes between spectral absorption peaks. This information is of great value for accurately determining sodium sulfate concentration. The addition of supplementary feature bands enriches the dimensionality of the feature dataset, enabling the model to acquire more comprehensive spectral information and making up for the shortcomings of single feature selection. The model trained based on the fused feature dataset has a significantly enhanced ability to distinguish sodium sulfate concentration, and can more accurately capture the complex relationship between spectrum and salt content, further improving the accuracy and reliability of sodium sulfate concentration inversion in murals.

[0093] Failure to comprehensively consider the joint similarity of spectrum, concentration, temperature, and humidity during data partitioning may lead to an imbalance between the training and test sets, affecting model robustness. Following the step of constructing the multivariate dataset, the following steps are also included:

[0094] Calculate the ambient temperature and humidity gradient vector: For each sample, based on the ambient temperature T and ambient humidity data H recorded at consecutive collection time points, calculate the temperature change rate ΔT and humidity change rate ΔH at adjacent time points to form a two-dimensional gradient vector [ΔT, ΔH]. The calculation interval of the gradient vector is an integer multiple of the data collection time interval and does not exceed 2 hours, reflecting the dynamic change trend of temperature and humidity of the sample during the collection period.

[0095] Constructing an environment-spectral dynamic coupling model: Bi-LSTM, a recurrent neural network capable of capturing the temporal variations of temperature and humidity, outputs dynamic modulation coefficients to quantify the impact of temperature and humidity changes on reflectance in various wavelength bands (range (-1,1)). Sodium sulfate crystals (anhydrous sodium sulfate / sodium sulfate decahydrate) in the fine mud layer rapidly dissolve into a solution. Because the sodium sulfate solution has stronger light absorption capabilities in the 1450nm and 1940nm wavelength bands than the crystalline state (weaker intermolecular forces in the solution result in more significant absorption peaks for infrared light), the reflectance in these bands decreases (by 10%-15%). However, in the 700-900nm visible light band, the reflectance increases slightly (by <5%) due to reduced light scattering by the solution. This band-specific change needs to be quantified and corrected using dynamic modulation coefficients (Bi-LSTM output) to accurately reflect the dissolution state of sodium sulfate. The gradient vector is input into a Bi-LSTM network containing 32 hidden units. The network captures contextual information of the data through forward and backward memory units, analyzes the time-varying characteristics of temperature and humidity, and outputs the dimension and number of feature bands. N Same dynamic modulation coefficient matrix W =[ W 1 , W 2 ,…, W N ],in W λ ∈(-1,1) (constrained by the tanh function), used to dynamically adjust the original characteristic band reflectance. This matrix and the characteristic band reflectance data are combined according to formula R' λ =R λ ×(1+tanh( W λ Multiply by band, R' λ Indicates the modulated reflectivity. l Indicates the band number, R λ Represents the reflectivity of the original characteristic band. W λ This represents the coefficients corresponding to each band in the dynamic modulation coefficient matrix, where tanh is the hyperbolic tangent function. The modulation coefficients are restricted to the range (-1, 1), and the modulated reflectivity R' is... λ The original spectral information was preserved, and the effects of dynamic changes in temperature and humidity were incorporated (e.g., when humidity rises rapidly, the reflectance of certain bands may increase due to salt dissolution, through...). W λ Dynamic adjustment integrates dynamic temperature and humidity changes into spectral data, achieving dynamic coupling between the environment and the spectrum.

[0096] Standardization of implementation conditions: The temperature range is defined as 11 intervals divided in 5°C increments within the range of -14°C to 38°C; the humidity range is defined as 9 intervals divided in 10%RH increments within the range of 15%RH to 100%RH. For each sample, based on its temperature interval t and humidity interval h, the pre-stored mean spectral reflectance μ of all samples within that interval in the characteristic band is retrieved. t,h With standard deviation σ t,h According to formula R norm =(R-μ t,h ) / σ t,h Standardization, R norm R represents the normalized reflectance, and R represents the original reflectance.

[0097] Add a physical driving constraint: During the model training phase, the loss function L is defined as L=α·MSE+(1-α)·|ρ|, where MSE is the mean square error between the predicted concentration and the true value, ρ is the sum of the absolute values ​​of the Pearson correlation coefficients of the predicted concentration change rate and ΔT and ΔH, and α is set to 0.7. Through backpropagation, the consistency between prediction accuracy and the physical laws of salt migration is optimized at the same time.

[0098] The above technical solution effectively addresses the problem of traditional models failing to consider dynamic changes in temperature and humidity and physical constraints by calculating the environmental temperature and humidity gradient vector, constructing a dynamically coupled model, implementing conditional standardization, and adding physical driving constraints. The introduction of the temperature and humidity gradient vector and the Bi-LSTM network enables the model to capture the impact of time-varying temperature and humidity on the spectrum, dynamically modulating spectral reflectance. Conditional standardization eliminates spectral differences under different temperature and humidity conditions, making the data comparable. Physical driving constraints ensure that the model's predictions conform to the physical laws of salt migration. These measures work together to significantly improve the model's stability and physical interpretability in complex environments, making the model more accurate.

[0099] Traditional regression algorithms do not integrate the driving mechanism of dynamic changes in temperature and humidity (such as temperature gradients and humidity gradients) on salt migration, lack physical constraints, and have limited model generalization ability. An ensemble model is used to establish a sodium sulfate concentration prediction model, which includes the following steps:

[0100] The reflectance data from the fused feature dataset is input into a one-dimensional convolutional neural network. The reflectance data includes the reflectance of selected single feature bands (M bands) and supplementary interactive features (Q bands), forming a matrix of dimension (n, M+Q) (n is the number of samples). The reflectance data is standardized (mean 0, standard deviation 1) to ensure the stability of CNN training. The one-dimensional convolutional neural network contains 3 convolutional layers with 64, 96, and 128 kernels respectively, kernel sizes of 3, 5, and 3 respectively, stride of 1, and ReLU activation function. The three-dimensional features are compressed into a two-dimensional vector through a global average pooling layer, outputting a local spectral feature vector.

[0101] Each sample contains a time series of temperatures. T ( t ),humidity H ( t ), temperature change rate Δ T ( t ), humidity change rate Δ H ( t The local spectral feature vector is concatenated with the environmental data (environmental temperature and humidity) time series data at each time point according to the timestamp, and then input into the random forest regression model. The random forest contains 150 to 200 decision trees, each with a maximum depth of 12 to 15 and a minimum number of samples per node of 5 to 10. The environment-spectral joint feature vector is output through majority voting (mean for regression task).

[0102] The salt migration rate (∂C / ∂t) is determined by diffusion (γD∇). 2 C (related to concentration gradient) and environmental driving forces (βΔTΔH, the product of temperature and humidity change rates) are jointly determined. The environmental-spectral joint feature vector is input into a partial least squares regression (PLSR) model. At the same time, a salt migration constraint equation is constructed based on Fick's diffusion law, in the form ∂C / ∂t = γ(D·∇ 2 C)+β(ΔTΔH), where C represents the sodium sulfate concentration and D represents the diffusion coefficient. The measured calibration value is 1.5×10⁻⁶, obtained through laboratory simulations of salt migration under different temperature and humidity conditions. -5 m 2 / s to 2.0×10 -5 m 2 / s, γ and β represent weighting coefficients and satisfy γ+β=1, γ is based on empirical values, β is based on empirical values, ΔT represents the rate of temperature change, and ΔH represents the rate of humidity change; by minimizing the weighted sum of the predicted concentration residual and the physical equation residual, the final predicted value of sodium sulfate concentration is output.

[0103] When the number of newly added mural samples reaches 50 to 100 sets, a model update is triggered to ensure that the model focuses on recent environmental features. If this number is not reached, a forced update is performed every 15 days, using a sliding window mechanism to retain 80% of the latest data. The weight parameters of the convolutional neural network and partial least squares regression model are updated online, fixing the weights of the first-layer CNN convolutional kernels and updating only the parameters of the fully connected layers. Principal components are re-extracted using PLSR (due to changes in data distribution), with an update cycle not exceeding 15 days. The loss function is defined as L = 0.7MSE + 0.3|∇C pred -∇C phys |, where ∇C pred Represents the predicted concentration gradient, ∇C phys Calculate the gradient for the physical equation, emphasizing the prediction of the concentration gradient (∇C). pred ) and the gradient (∇C) calculated by the physical equation phys To ensure consistency and prevent the model from losing physical constraints due to overfitting to new data.

[0104] In the above technical solution, a three-layer architecture is used to achieve spectral feature extraction, environmental time series fusion, and physical law constraints. Spectral feature extraction uses a one-dimensional convolutional neural network (1D-CNN) to automatically capture local band correlation features of spectral data (such as absorption peak position and slope changes), avoiding the subjectivity of manual feature selection. Environmental feature fusion integrates spectral features with temperature and humidity time series data through random forest (RF), processes nonlinear mapping relationships, and outputs joint features containing environmental-spectral coupling information. Physical constraint regression introduces Fick's diffusion law as a regularization term, constraining the model prediction results to conform to the physical laws of salt migration (temperature / humidity changes drive salt diffusion or crystallization), improving generalization ability. Dynamic incremental update retains the latest data through a sliding window mechanism, updates model parameters online, and adapts to long-term changes in the mural environment.

[0105] The number of devices and processing scale described herein are for the purpose of simplifying the description of the invention. Applications, modifications, and variations of the invention will be readily apparent to those skilled in the art.

[0106] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity, characterized in that, include: Step 1: Prepare simulated mural samples with a sodium sulfate concentration of 0% to 1%. The ambient temperature range of the samples is -14℃ to 38℃ and the humidity range is 15%RH to 100%RH. Collect spectral reflectance data of the simulated mural samples at multiple time points using a ground object spectrometer. Record the ambient temperature and humidity at the time of collection. The spectral wavelength range is 350nm to 2500nm, and the sampling interval is 1.4nm for visible light-near infrared short wave and 2nm for near infrared long wave. Step 2: Preprocess and enhance the spectral reflectance data. Based on Pearson correlation analysis, extract the relationship between reflectance and salt content band by band and screen characteristic bands. Step 3: Construct a multivariate dataset containing characteristic band reflectivity, ambient temperature, and ambient humidity, divide it into training and test sets, use a regression algorithm to establish a sodium sulfate concentration prediction model, input the training set data into the model for training, and calculate the coefficient of determination and root mean square error using the test set data to select the optimal model. Step 4: Input the characteristic band reflectivity of the mural to be tested, the real-time ambient temperature, and the real-time ambient humidity into the optimal model, and output the predicted value of sodium sulfate concentration.

2. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 1, characterized in that, The sample comprises a coarse mud layer and a fine mud layer, wherein sodium sulfate is distributed in the fine mud layer. The coarse mud layer is formed by mixing loess, silt, coarse sand, wheat straw and water in a mass ratio of 20:30:20:20:30 and then air-drying. The fine mud layer is formed by mixing yellow clay, silt, fine sand, hemp fiber and a sodium sulfate-containing solution in a mass ratio of 10:55:35:3:35 and then air-drying.

3. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 1, characterized in that, Step two involves preprocessing and enhancing the spectral reflectance data, including: removing data breakpoints and averaging four spectral curves from the same sample collected in the same session; performing data enhancement in Matlab; correcting scattering through standard normal variable transformation; smoothing the spectral curves using a third-order polynomial and a third-order Savitzky-Golay convolution with a window width of 5; smoothing the spectral curves using polynomial fitting to reduce spectral noise; and finally, baseline correction using spectral differentiation.

4. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 1, characterized in that, Bands with an absolute correlation coefficient greater than 0.6 are extracted as characteristic bands.

5. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 1, characterized in that, Step 3, which involves dividing the training and test sets, is based on the XY joint distance algorithm. This includes: determining data similarity by calculating the sum of Euclidean distances for spectral reflectance, sodium sulfate concentration, ambient temperature, and ambient humidity; calculating the total distance using four distances as metrics: Euclidean distance between ambient temperatures, ambient humidity, spectral reflectance, and sodium sulfate concentration; calculating the total distance between each pair of data points; selecting the two data points with the greatest distance as the seeds for clustering; and then clustering based on the minimum Euclidean distance. The division of the test set is stopped when the number of test set samples reaches 30% of the total number of samples, and all remaining data are assigned to the training set.

6. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 1, characterized in that, In step four, a regression algorithm is used to establish a sodium sulfate concentration prediction model. The regression algorithm used is one of partial least squares regression, random forest, or convolutional neural network.

7. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 1, characterized in that, Step two involves extracting the relationship between reflectance and salt content band by band based on Pearson correlation analysis. After screening characteristic bands, it also includes supplementing characteristic bands based on band interaction feature extraction and fusion technology, specifically including: For all adjacent band combinations with continuous wavelengths less than 50nm in the wavelength range of 350nm to 2500nm and without any interval, calculate the normalized difference index and the ratio index. The normalized difference index is defined as the difference between the reflectance of the first band and the reflectance of the second band, divided by the sum of the reflectances of the two bands. The ratio index is defined as the reflectance of the first band divided by the reflectance of the second band. Band combinations with an absolute value greater than 0.6 in the normalized difference index or ratio index and the Pearson correlation coefficient of sodium sulfate concentration are selected as supplementary feature bands; The normalized difference index and ratio index data corresponding to the supplementary feature bands are merged with the reflectance data of the feature bands selected based on Pearson correlation analysis to form a fused feature dataset, which is used for subsequent model training and prediction.

8. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 7, characterized in that, Step three, after constructing a multivariate dataset containing characteristic band reflectance, ambient temperature, and ambient humidity, also includes the following steps: For each sample, based on the ambient temperature and humidity data recorded at consecutive time points, the rate of change of temperature ΔT and the rate of change of humidity ΔH at adjacent time points are calculated to form a two-dimensional gradient vector [ΔT, ΔH]. The calculation interval of the gradient vector is an integer multiple of the data acquisition time interval and does not exceed 2 hours. The gradient vector is input into a Bi-LSTM network containing 32 hidden units, which outputs a dynamic modulation coefficient matrix with the same dimension as the number of feature bands. This matrix is ​​then compared with the feature band reflectance data according to formula R'. λ =R λ ×(1+tanh( W λ Multiply by band, R' λ Indicates the modulated reflectivity. λ Indicates the band number, R λ Represents the reflectivity of the original characteristic band. W λ This represents the coefficient corresponding to each band in the dynamic modulation coefficient matrix, and tanh is the hyperbolic tangent function, which restricts the modulation coefficient to the range of (-1, 1). The temperature range is defined as 11 intervals divided in 5°C increments within the range of -14°C to 38°C, and the humidity range is defined as 9 intervals divided in 10%RH increments within the range of 15%RH to 100%RH. For each sample, based on its temperature interval t and humidity interval h, the pre-stored mean spectral reflectance μ of all samples within that interval in the characteristic band is retrieved. t,h With standard deviation σ t,h According to formula R norm =(R-μ t,h ) / σ t,h Standardization, R norm R represents the normalized reflectance, and R represents the original reflectance. During the model training phase, the loss function L is defined as L=α·MSE+(1-α)·|ρ|, where MSE is the mean square error between the predicted concentration and the true value, ρ is the sum of the absolute values ​​of the Pearson correlation coefficients of the predicted concentration change rate and ΔT and ΔH, and α is set to 0.

7. Backpropagation is used to simultaneously optimize the prediction accuracy and the consistency with the physical laws of salt migration.

9. The method for hyperspectral inversion of sodium sulfate concentration in murals taking into account temperature and humidity as described in claim 8, characterized in that, Step three involves using a regression algorithm to establish a sodium sulfate concentration prediction model, which includes the following steps: The reflectance data of the fused feature dataset is input into a one-dimensional convolutional neural network. The one-dimensional convolutional neural network contains 3 convolutional layers, each with 64 to 128 convolutional kernels, a kernel size of 3 to 5, a stride of 1, and the activation function is ReLU. The output is a local spectral feature vector. The local spectral feature vector is concatenated with the time-series data of ambient temperature and humidity according to the timestamp, and then input into the random forest regression model. The random forest contains 150 to 200 decision trees, each with a maximum depth of 12 to 15 and a minimum number of samples per node of 5 to 10. The output is an environment-spectral joint feature vector. The environmental-spectral joint feature vector is input into a partial least squares regression model, and a salt migration constraint equation is constructed based on Fick's diffusion law, in the form of: Where C represents the sodium sulfate concentration, and D represents the diffusion coefficient, with a measured calibrated value of 1.5 × 10⁻⁶. -5 m 2 / s to 2.0×10 -5 m 2 / s, γ and β represent weighting coefficients and satisfy γ+β=1, γ is based on empirical values, β is based on empirical values, ΔT represents the rate of temperature change, and ΔH represents the rate of humidity change; by minimizing the weighted sum of the predicted concentration residual and the physical equation residual, the final predicted value of sodium sulfate concentration is output. When the number of newly added mural samples reaches 50 to 100 sets, a sliding window mechanism is used to retain 80% of the latest data. The weight parameters of the convolutional neural network and partial least squares regression model are updated online, with an update cycle not exceeding 15 days. The loss function is defined as... ,in Predicting concentration gradients, Calculate the gradient for the physical equations.

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