Mining area copper pollution monitoring method and system based on multi-order fusion high-dimensional spectral index

Abstract

The invention relates to the technical field of mining area copper pollution monitoring, in particular to a mining area copper pollution monitoring method and system based on multi-order fusion high-dimensional spectral indexes. The method comprises the following steps: extracting pixel spectral data and copper element content corresponding to a quadrat based on a soil sample; performing multi-order fractional derivative transformation on the pixel spectrum to generate a plurality of groups of fractional derivative spectrums; calculating a plurality of three-dimensional spectral indexes according to the fractional derivative spectrum, screening a core three-dimensional spectral index from the three-dimensional spectral indexes, and fusing the core three-dimensional spectral indexes to obtain a multi-order fused high-dimensional spectral index; and constructing a data set by combining the multi-order fusion high-dimensional spectral index and the copper element content, training a mining area copper pollution monitoring model by using the data set, and completing mining area copper pollution monitoring through the trained mining area copper pollution monitoring model. According to the invention, through multi-order fractional derivative transformation, three-dimensional spectral index construction and multi-order fusion high-dimensional spectral index generation, accurate monitoring of copper pollution in the mining area is realized.

Description

Technical Field

[0001] This invention relates to the field of copper pollution monitoring technology in mining areas, specifically to a method and system for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices. Background Technology

[0002] The mining and smelting processes of copper deposits expose deep underground minerals to the surface environment, significantly increasing the release of copper into the environment. Copper pollutants enter the geochemical cycle system through surface runoff, groundwater infiltration, and atmospheric deposition, eventually integrating into the food chain. This not only pollutes crops and groundwater but may also accumulate through the food chain, posing a threat to human health. Therefore, accurately identifying copper-contaminated areas in the soil surrounding copper mining areas and monitoring the real-time spread of pollution are crucial for ensuring ecological and environmental safety.

[0003] Traditional soil copper pollution monitoring relies on fixed-point field sampling and laboratory chemical analysis, which is time-consuming, labor-intensive, costly, and lacks sufficient spatial coverage, making it difficult to meet the needs of large-area, dynamic monitoring. In recent years, hyperspectral remote sensing technology has been gradually applied to soil heavy metal pollution monitoring, but existing technologies still have many limitations: most studies are based on ground-based or UAV remote sensing platforms, which are limited by the observation range and data acquisition costs, making it impossible to achieve wide-area, real-time, and continuous monitoring; some studies use one-dimensional raw reflectance spectra or their transformations to construct models, which are not only structurally complex but also ignore the synergistic effects between different bands; models based on two-dimensional spectral indices are prone to signal saturation problems, affecting estimation accuracy; a few studies using three-dimensional spectral indices are limited to a single spectral form and do not fully integrate the advantages of multiple spectral transformations; therefore, existing technologies lack a mature scheme to deeply integrate high-dimensional spectral indices with spaceborne hyperspectral imagery, making it difficult to achieve large-scale, high-precision monitoring of copper pollution in mining areas. Summary of the Invention

[0004] To address the shortcomings of existing methods and the needs of practical applications, and in order to solve the aforementioned problems, this invention provides a method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices, comprising the following steps: Based on the spectral data of corresponding pixels and copper content extracted from soil samples, multi-order fractional derivative transformations are performed on the pixel spectra to generate multiple sets of fractional derivative spectra. Various three-dimensional spectral indices are calculated based on these fractional derivative spectra. Core three-dimensional spectral indices are selected from these indices, and the core three-dimensional spectral indices are fused to obtain a multi-order fused high-dimensional spectral index. A dataset is constructed by combining the multi-order fused high-dimensional spectral index and the copper content. A copper pollution monitoring model for the mining area is trained using this dataset, and the trained copper pollution monitoring model is used to complete the monitoring of copper pollution in the mining area.

[0005] This invention integrates soil sample spectral data with copper content information, employing spectral preprocessing, multi-order fractional derivative transformation, three-dimensional spectral index construction and core screening, and multi-order fusion high-dimensional spectral index generation. Combined with training and optimization using various machine learning models, it achieves precise monitoring of copper pollution in mining areas. By leveraging multi-order fractional derivatives to mine fine spectral features, and enhancing feature representation capabilities through three-dimensional spectral index construction and fusion, coupled with rigorous feature screening and model evaluation, monitoring accuracy is guaranteed. This effectively overcomes the limitations of traditional monitoring methods, such as low efficiency and narrow coverage, providing scientific and reliable technical support for rapid investigation, dynamic monitoring, and ecological restoration of copper pollution in mining soils. It has significant practical value for maintaining the ecological environment safety of mining areas and promoting soil pollution prevention and control.

[0006] Optionally, the method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices further includes preprocessing the extracted pixel spectral data, including: Low-quality bands with a signal-to-noise ratio below 30 below 400 nm were removed; bands with strong water vapor absorption, including those in the ranges of 1300.25~1450.83nm and 1800.50~1950.32nm, were eliminated; the remaining bands were averaged and resampled in groups of three adjacent bands to obtain standardized spectral data.

[0007] By deleting low signal-to-noise ratio and low-quality bands and eliminating bands with strong water vapor absorption interference, the impact of noise and non-target interference on spectral characteristics is effectively reduced. Furthermore, data standardization is achieved through average resampling of three adjacent bands, improving the stability and consistency of the spectral data. This provides a high-quality data foundation for subsequent key steps such as multi-order fractional derivative transformation and three-dimensional spectral index construction, ensuring the accuracy and effectiveness of subsequent feature extraction. Ultimately, this enhances the precision and reliability of the copper pollution monitoring model in the mining area, laying a solid data foundation for the scientific implementation of the entire monitoring method.

[0008] Optionally, the step of performing multi-order fractional derivative transformation on the pixel spectrum to generate multiple sets of fractional derivative spectra satisfies: in, This indicates the order of the fraction. Let represent the fractional wavelength, and n represent the difference between the upper and lower limits of the fractional derivative. This represents the gamma function.

[0009] Optionally, the fractional order calculation range is 0.1 to 2.0, with an interval of 0.05.

[0010] By processing pixel spectra using a specific fractional derivative transformation formula, multiple sets of fractional derivative spectra are generated within a reasonable parameter range of 0.1 to 2.0 orders with intervals of 0.05. The core function is to deeply mine fine features from spectral data. Compared to integer derivatives, fractional derivatives can more flexibly capture subtle spectral changes. Multi-order transformations can comprehensively cover low, medium, and high-order spectral information, avoiding feature omissions. This provides a rich and accurate feature data source for the subsequent construction of three-dimensional spectral indices, strengthens the correlation between spectra and copper content, lays a solid foundation for core spectral index selection and high-dimensional index fusion, and ultimately improves the accuracy of copper pollution monitoring in mining areas.

[0011] Optionally, the calculation of multiple three-dimensional spectral indices based on the fractional derivative spectrum includes the following steps: Construct various types of three-dimensional spectral index calculation models; Based on the fractional derivative spectrum, various three-dimensional spectral indices are calculated using the three-dimensional spectral index calculation model.

[0012] Optionally, the three-dimensional spectral index calculation model includes: The first three-dimensional spectral index calculation model satisfies: The second three-dimensional spectral index calculation model satisfies: The third three-dimensional spectral index calculation model satisfies: The fourth three-dimensional spectral index calculation model satisfies: The fifth three-dimensional spectral index calculation model satisfies: The sixth three-dimensional spectral index calculation model satisfies: in, They represent the bands respectively. The reflectivity, and the band satisfy The band spacing is ≥20nm.

[0013] By constructing six differentiated three-dimensional spectral index calculation models and combining them with specific band selection requirements (400~2500nm, λ1<λ2<λ3, interval ≥20nm), various three-dimensional spectral indices are calculated based on fractional derivative spectroscopy. This transforms the high-dimensional and complex fractional derivative spectral features into more targeted quantitative indices. The multi-model design comprehensively captures the coupling relationship and response law of reflectance in different bands, strengthens the correlation between spectral information and copper contamination, provides a rich candidate set for subsequent core index screening, improves the effectiveness of feature extraction, and lays the foundation for high-dimensional index fusion and the construction of precise monitoring models.

[0014] Optionally, the step of selecting core three-dimensional spectral indices from the three-dimensional spectral indices includes the following steps: Calculate the Pearson correlation coefficient r between all three-dimensional spectral indices and copper content, and screen out candidate spectral indices with an absolute value of |r|>0.5 and a significance level of p<0.01; The candidate spectral indices were subjected to a multicollinearity test. Highly collinear indices with a variance inflation factor > 10 were eliminated, and multiple core three-dimensional spectral indices from low-order, mid-order, and high-order fractional derivative spectra were retained.

[0015] Candidate spectral indices strongly correlated with copper content were screened using Pearson correlation coefficients. Highly redundant indices were then eliminated through multicollinearity testing, while core indices covering low, medium, and high-order fractional derivative spectra were retained. This process selected spectral features that combine strong correlation, low redundancy, and comprehensiveness, avoiding interference from invalid information and multicollinearity issues. This provides high-quality core materials for the subsequent construction of multi-order fusion high-dimensional spectral indices, ensuring the characterization ability of high-dimensional indices and thus improving the stability and accuracy of subsequent pollution monitoring models.

[0016] Optionally, the fusion of the core three-dimensional spectral indices yields a multi-order fused high-dimensional spectral indices, satisfying: in, Indicates a multi-order fusion high-dimensional spectral index. Indicates the number of core three-dimensional spectral indices. This represents the weight of the t-th core three-dimensional spectral index. This represents the t-th core three-dimensional spectral index.

[0017] The selected core three-dimensional spectral indices are fused using a weighted summation formula to generate multi-order fused high-dimensional spectral indices. The core function is to integrate high-quality features from low, medium, and high-order fractional derivative spectra, highlight the contribution of each core index through weight allocation, eliminate the limitations of single index representation being one-sided and incomplete in information coverage, and form high-dimensional feature indicators that are both comprehensive and targeted. This strengthens the correlation between spectral information and copper pollution in mining areas, provides high-quality input parameters for subsequent monitoring model training, and thus improves the accuracy and stability of the model in monitoring copper pollution.

[0018] Optionally, the step of constructing a dataset by combining the multi-order fused high-dimensional spectral index and the copper element content, and using the dataset to train a copper pollution monitoring model for the mining area, includes the following steps: The multi-level fused high-dimensional spectral index data were randomly divided into training and test sets at a ratio of 3:1. Stratified sampling was used to ensure that the copper content distribution characteristics of the two sets of data were consistent. Three copper content estimation models, namely partial least squares regression, random forest and support vector machine, were constructed respectively. The training set was used to train the models and the model parameters were optimized by 5-fold cross-validation. The performance of the models was comprehensively evaluated by the coefficient of determination, mean absolute error, relative root mean square error and relative analysis error, and the optimal model was selected.

[0019] By employing stratified sampling, the multi-level fused high-dimensional spectral index data was divided into training and testing sets at a ratio of 3:1 to ensure consistent copper content distribution between the two sets. Three models—partial least squares regression, random forest, and support vector machine—were constructed. Parameters were optimized through 5-fold cross-validation, and the optimal model was selected through comprehensive evaluation using multiple indicators. This effectively ensured the scientific rigor and effectiveness of model training, avoiding data distribution bias and parameter overfitting issues. Consequently, a high-precision and stable copper pollution monitoring model for mining areas was generated, providing reliable technical support for rapid and accurate monitoring of copper pollution and enhancing the credibility and practicality of monitoring results.

[0020] Secondly, to efficiently execute the copper pollution monitoring method for mining areas based on multi-order fusion high-dimensional spectral indices provided by this invention, this invention also provides a copper pollution monitoring system for mining areas based on multi-order fusion high-dimensional spectral indices, including a processor, an input device, an output device, and a memory. The processor, input device, output device, and memory are interconnected. The memory stores a computer program containing program instructions. The processor is configured to call the program instructions to execute the copper pollution monitoring method for mining areas based on multi-order fusion high-dimensional spectral indices as described in the first aspect of this invention. The copper pollution monitoring system for mining areas based on multi-order fusion high-dimensional spectral indices of this invention has a compact structure and stable performance, and can stably execute the copper pollution monitoring method for mining areas based on multi-order fusion high-dimensional spectral indices provided by this invention, further improving the overall applicability and practical application capability of this invention. Attached Figure Description

[0021] Figure 1 A flowchart of a method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices provided in this embodiment of the invention; Figure 2 This is a framework diagram of a copper pollution monitoring system in a mining area based on multi-order fusion high-dimensional spectral indices, provided for an embodiment of the present invention. Detailed Implementation

[0022] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0023] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0024] Please see Figure 1 To address the aforementioned problems, this invention provides a method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices, such as... Figure 1 As shown, in one embodiment, the method includes the following steps: S1. Based on the spectral data of corresponding pixels and copper content of soil sample plots.

[0025] In this embodiment, a 1.5m×1.5m quadrat design was adopted. Five surface soil samples (0-20cm) were collected at the four inflection points and the center of each quadrat. After being mixed evenly, 1kg was taken as the representative sample of the sampling point. The center coordinates of the quadrat were recorded using a high-precision GPS receiver (error ≤2m). Then, the copper content of the samples was determined using a Thermo Scientific Niton XL5t980 portable X-ray fluorescence spectrometer (pXRF). The instrument was set to the "Precise Detection of Heavy Metals (Cu / Pb / Zn)" mode, and the measurement time was set to 150s. Each sample was measured four times, and the average value was taken after removing outliers as the final copper content data.

[0026] Furthermore, high-resolution hyperspectral imagery data of the mining area with complete coverage and no cloud cover (cloud coverage rate ≤5%) was obtained through the National Integrated Earth Observation Data Sharing Platform; The image data was subjected to joint atmospheric correction using the QUAC fast atmospheric correction module in ENVI 5.6 software and the MODTRAN 6 radiative transfer model to eliminate the effects of atmospheric scattering and absorption, thus obtaining surface reflectance images. Then, using the 1:10,000 topographic map of the mining area as a reference, and combining GPS coordinates, more than 15 ground control points (GCPs) were selected to perform a second polynomial geometric correction on the atmospherically corrected image. The root mean square error (RMSE) after correction was ≤0.5 pixels. Based on GPS coordinates, bilinear interpolation was used to extract the spectral data of corresponding sample pixels in the geometrically corrected image.

[0027] In another embodiment, the method further includes preprocessing the extracted pixel spectral data, including: Remove low-quality bands with a signal-to-noise ratio below 30 below 400 nm; The wavelengths with strong water vapor absorption are excluded, including those in the ranges of 1300.25~1450.83nm and 1800.50~1950.32nm. The remaining bands are averaged and resampled in groups of three adjacent bands to obtain standardized spectral data.

[0028] S2. Perform multi-order fractional derivative transformation on the pixel spectrum to generate multiple sets of fractional derivative spectra.

[0029] Specifically, the Riemann-Liouville method is used to perform multi-order fractional derivative transformations on the pixel spectra, generating multiple sets of fractional derivative spectra that satisfy: in, This indicates the order of the fraction. Let represent the fractional wavelength, and n represent the difference between the upper and lower limits of the fractional derivative. This represents the gamma function.

[0030] Furthermore, the fractional derivative calculation range is 0.1 to 2.0, with an interval of 0.05. According to the above calculation formula, a total of 39 sets of fractional derivative spectral data were obtained by calculating the fractional derivative spectrum with a range of 0.1 to 2.0 and an interval of 0.05, covering three intervals: low order (0.1 to 0.6), middle order (0.7 to 1.4), and high order (1.5 to 2.0).

[0031] S3. Calculate multiple three-dimensional spectral indices based on the fractional derivative spectrum, select core three-dimensional spectral indices from the three-dimensional spectral indices, and fuse the core three-dimensional spectral indices to obtain multi-order fused high-dimensional spectral indices.

[0032] Specifically, the calculation of various three-dimensional spectral indices based on the fractional derivative spectrum includes the following steps: S31. Construct various types of three-dimensional spectral index calculation models.

[0033] In this embodiment, the three-dimensional spectral index calculation model includes: The first three-dimensional spectral index calculation model satisfies: The second three-dimensional spectral index calculation model satisfies: The third three-dimensional spectral index calculation model satisfies: The fourth three-dimensional spectral index calculation model satisfies: The fifth three-dimensional spectral index calculation model satisfies: The sixth three-dimensional spectral index calculation model satisfies: in, They represent the bands respectively. The reflectivity, and the band satisfy The band spacing is ≥20nm.

[0034] In other embodiments, more three-dimensional spectral index calculation models can be constructed.

[0035] S32. Based on the fractional derivative spectrum, calculate various three-dimensional spectral indices using the three-dimensional spectral index calculation model.

[0036] In this embodiment, implemented using Python 3.9 and incorporating the NumPy 1.24 and SciPy 1.10 scientific computing libraries, the specific steps include: Loaded standardized spectral data and 39 sets of fractional derivative spectral data; Develop a library of functions for calculating three-dimensional spectral indices, including: Set the band selection criteria: λ1, λ2, and λ3 are non-overlapping bands, and the band interval is ≥20nm; Define the band index generation function: def generate_band_index(band_num, min_gap=20): index_list = [] band_wls = np.linspace(400, 2500, band_num) # Band wavelength sequence for i in range(band_num): for j in range(i+1, band_num): for k in range(j+1, band_num): if band_wls[j]-band_wls[i]≥min_gap and band_wls[k]-band_wls[j]≥min_gap: index_list.append([i, j, k]) return np.array(index_list) ``` Based on the index function, calculation functions for six three-dimensional spectral indices were written, as shown in the following example (TBSI3): def calculate_TBSI3(spectral_data, band_index): n_sample = spectral_data.shape[0] n_index = band_index.shape[0] tbsi3_result = np.zeros((n_sample, n_index)) for idx in range(n_index): i, j, k = band_index[idx] tbsi3_result[:, idx] = spectral_data[:, i] - 3*spectral_data[:, j] + 2*spectral_data[:, k] return tbsi3_result Call the function library to calculate all three-dimensional spectral indices corresponding to the 39 sets of fractional derivative spectra.

[0037] Furthermore, the step of selecting core three-dimensional spectral indices from the three-dimensional spectral indices includes the following steps: Calculate the Pearson correlation coefficient r between all three-dimensional spectral indices and copper content, and screen out candidate spectral indices with an absolute value of |r|>0.5 and a significance level of p<0.01; The candidate spectral indices were subjected to a multicollinearity test. Highly collinear indices with a variance inflation factor > 10 were eliminated, and multiple core three-dimensional spectral indices from low-order, mid-order, and high-order fractional derivative spectra were retained.

[0038] In the embodiment, the three-dimensional spectral indices corresponding to the two largest correlation coefficients r are selected for the low-order, mid-order, and high-order fractional derivative spectra.

[0039] Furthermore, the fusion of the core three-dimensional spectral indices yields a multi-order fused high-dimensional spectral indices, satisfying: in, Indicates a multi-order fusion high-dimensional spectral index. Indicates the number of core three-dimensional spectral indices. This represents the weight of the t-th core three-dimensional spectral index. Let t represent the t-th core three-dimensional spectral index. The weights of the core three-dimensional spectral indices are determined using the entropy weighting method.

[0040] S4. Construct a dataset by combining the multi-level fusion high-dimensional spectral index and the copper element content, train a copper pollution monitoring model for the mining area using the dataset, and complete the copper pollution monitoring of the mining area using the trained copper pollution monitoring model.

[0041] Specifically, the step of constructing a dataset by combining the multi-order fused high-dimensional spectral index and the copper element content, and using the dataset to train a copper pollution monitoring model for the mining area, includes the following steps: The multi-level fused high-dimensional spectral index data were randomly divided into training and test sets in a 3:1 ratio, and stratified sampling was used to ensure that the copper content distribution characteristics of the two sets of data were consistent. Three copper content estimation models—partial least squares regression, random forest, and support vector machine—were constructed. The training set was used to train the models, and the model parameters were optimized through 5-fold cross-validation. Using the coefficient of determination (R) 2 The model performance is comprehensively evaluated using mean absolute error (MAE), relative root mean square error (RRMSE), and relative analysis error (RPD) to select the optimal model.

[0042] Furthermore, spectral data corresponding to each pixel in the Gaofen-5 image were extracted and MFSI was calculated; the selected optimal model was applied to the MFSI data of the image pixels to obtain a spatial distribution map of copper content in the entire mining area; based on the "Soil Environmental Quality Standard for Agricultural Land Soil Pollution Risk Control" (GB15618-2018), the copper content was divided into four levels: "clean (≤100mg / kg), slightly polluted (100~200mg / kg), moderately polluted (200~300mg / kg), and heavily polluted (>300mg / kg)," and a distribution map of copper pollution levels in the mining area was drawn.

[0043] Please see Figure 2 In an embodiment, to efficiently execute the copper pollution monitoring method for mining areas based on multi-order fusion high-dimensional spectral indices provided by this invention, this invention also provides a copper pollution monitoring system for mining areas based on multi-order fusion high-dimensional spectral indices, comprising: an input device, an output device, a processor, and a memory, wherein the input device, output device, processor, and memory are interconnected, and the memory contains program instructions for the steps of the copper pollution monitoring method for mining areas based on multi-order fusion high-dimensional spectral indices. The copper pollution monitoring system for mining areas based on multi-order fusion high-dimensional spectral indices of this invention has a compact structure and stable performance, and can stably execute the copper pollution monitoring method for mining areas based on multi-order fusion high-dimensional spectral indices of this invention, further improving the overall applicability and practical application capability of this invention.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the present invention.

Claims

1. A method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices, characterized in that, Includes the following steps: Based on the spectral data of corresponding pixels and copper content of soil sample plots; Perform multi-order fractional derivative transformations on the pixel spectrum to generate multiple sets of fractional derivative spectra; Calculate multiple three-dimensional spectral indices based on the fractional derivative spectrum, select core three-dimensional spectral indices from the three-dimensional spectral indices, and fuse the core three-dimensional spectral indices to obtain a multi-order fused high-dimensional spectral index. A dataset is constructed by combining the multi-level fusion high-dimensional spectral index and the copper element content. The dataset is then used to train a copper pollution monitoring model for the mining area. The trained copper pollution monitoring model is then used to complete the monitoring of copper pollution in the mining area.

2. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 1, characterized in that, It also includes preprocessing of the extracted pixel spectral data, including: Remove low-quality bands with a signal-to-noise ratio below 30 below 400 nm; The wavelengths with strong water vapor absorption are excluded, including those in the ranges of 1300.25~1450.83nm and 1800.50~1950.32nm. The remaining bands are averaged and resampled in groups of three adjacent bands to obtain standardized spectral data.

3. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 1, characterized in that, The pixel spectrum is subjected to a multi-order fractional derivative transformation to generate multiple sets of fractional derivative spectra, satisfying the following: in, This indicates the order of the fraction. Let represent the fractional wavelength, and n represent the difference between the upper and lower limits of the fractional derivative. This represents the gamma function.

4. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 3, characterized in that, The fractional order is calculated in the range of 0.1 to 2.0, with an interval of 0.

05.

5. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 1, characterized in that, The calculation of various three-dimensional spectral indices based on the fractional derivative spectrum includes the following steps: Construct various types of three-dimensional spectral index calculation models; Based on the fractional derivative spectrum, various three-dimensional spectral indices are calculated using the three-dimensional spectral index calculation model.

6. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 5, characterized in that, The three-dimensional spectral index calculation model includes: The first three-dimensional spectral index calculation model satisfies: The second three-dimensional spectral index calculation model satisfies: The third three-dimensional spectral index calculation model satisfies: The fourth three-dimensional spectral index calculation model satisfies: The fifth three-dimensional spectral index calculation model satisfies: The sixth three-dimensional spectral index calculation model satisfies: in, They represent the bands respectively. The reflectivity, and the band satisfy The band spacing is ≥20nm.

7. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 1, characterized in that, The process of selecting core three-dimensional spectral indices from the three-dimensional spectral indices includes the following steps: Calculate the Pearson correlation coefficient r between all three-dimensional spectral indices and copper content, and screen out candidate spectral indices with an absolute value of |r|>0.5 and a significance level of p<0.01; The candidate spectral indices were subjected to a multicollinearity test. Highly collinear indices with a variance inflation factor > 10 were eliminated, and multiple core three-dimensional spectral indices from low-order, mid-order, and high-order fractional derivative spectra were retained.

8. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 1, characterized in that, The fusion of the core three-dimensional spectral indices yields a multi-order fused high-dimensional spectral indices that satisfy: in, Indicates a multi-order fusion high-dimensional spectral index. Indicates the number of core three-dimensional spectral indices. This represents the weight of the t-th core three-dimensional spectral index. This represents the t-th core three-dimensional spectral index.

9. The method for monitoring copper pollution in mining areas based on multi-order fusion high-dimensional spectral indices according to claim 1, characterized in that, The process of constructing a dataset by combining the multi-level fused high-dimensional spectral index and the copper element content, and then using the dataset to train a copper pollution monitoring model for the mining area, includes the following steps: The multi-level fused high-dimensional spectral index data were randomly divided into training and test sets in a 3:1 ratio, and stratified sampling was used to ensure that the copper content distribution characteristics of the two sets of data were consistent. Three copper content estimation models—partial least squares regression, random forest, and support vector machine—were constructed. The training set was used to train the models, and the model parameters were optimized through 5-fold cross-validation. The model performance is comprehensively evaluated using the coefficient of determination, mean absolute error, relative root mean square error, and relative analysis error to select the optimal model.

10. A copper pollution monitoring system for mining areas based on multi-order fusion high-dimensional spectral indices, characterized in that, The copper pollution monitoring system for mining areas based on multi-order fusion high-dimensional spectral indices includes: an input device, an output device, a processor, and a memory. The input device, output device, processor, and memory are interconnected. The memory includes program instructions, which are used to execute the copper pollution monitoring method for mining areas based on multi-order fusion high-dimensional spectral indices as described in any one of claims 1-9.

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