A red layer soil thermal conductivity prediction method based on data enhancement and machine learning

Abstract

The application provides a red layer soil thermal conductivity prediction method based on data enhancement and machine learning, comprising the following steps: S1, obtaining red layer soil sample data, and constructing an original sample data set; S2, performing feature correlation analysis on the original sample data set to determine input features affecting the thermal conductivity k of the red layer soil; S3, using a two-stage data enhancement strategy to expand the original sample data set to generate an enhanced data set; S4, performing standardization processing on the enhanced data set, constructing a plurality of candidate machine learning prediction models, training and verifying the models by using the enhanced data set, and screening a final prediction model; S5, obtaining the saturation, porosity n, water content and dry density of the red layer soil to be predicted, performing standardization processing, and inputting the target prediction model to obtain the thermal conductivity k of the red layer soil to be predicted. The application breaks the small sample bottleneck, greatly improves the prediction accuracy and model generalization ability, and solves the applicability defects of the general model to the red layer soil.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering thermal property analysis technology, specifically to a method for predicting the thermal conductivity of red soil based on data augmentation and machine learning. Background Technology

[0002] Red bed soils are widely distributed in southwestern my country and are a special geological material frequently encountered in water conservancy, hydropower, and geotechnical engineering construction. Red bed soils are characterized by high clay content, weak cementation, and significant hydrophilicity. Their thermal conductivity is a key parameter for measuring the heat transfer capacity of soils, and it has important guiding significance for engineering practices such as the design of ground source heat pump systems, the calculation of buried cable current carrying capacity, and the thermal stability analysis of roadbeds in permafrost areas. Accurately obtaining the thermal conductivity of red bed soils is a prerequisite for conducting related engineering thermodynamic analysis and design.

[0003] Currently, methods for determining soil thermal conductivity mainly fall into three categories: laboratory testing, empirical model calculation, and numerical simulation. While laboratory testing (such as the steady-state heat source method and the transient thermal probe method) can directly obtain soil thermal conductivity, it is time-consuming, costly, and involves significant challenges in sampling and preparing samples of red soil, making it difficult to conduct extensive and repeated tests to cover the varied working conditions in actual engineering projects. Empirical models (such as the Johansen model) are typically based on specific soil types and have poor applicability to red soil with high clay content and weak cementation, resulting in insufficient prediction accuracy. Numerical simulation methods rely on accurate reconstruction of soil microstructure and precise setting of boundary conditions, making them complex to operate and computationally intensive.

[0004] In recent years, machine learning methods have shown great potential in soil parameter prediction due to their powerful nonlinear mapping capabilities. However, the performance of machine learning models is highly dependent on the quality and quantity of training data. Limited by the difficulty of field sampling and the cost of laboratory experiments, only a few dozen sets of high-quality measured samples of thermal conductivity of red soil are typically available. This limited sample data is insufficient to support the adequate training of complex machine learning models, easily leading to overfitting and insufficient generalization ability. Data augmentation techniques, through reasonable interpolation and noise injection to generate reasonable simulated data, are an effective strategy for expanding sample size and improving dataset quality; however, their application in the prediction of thermal conductivity of red soil is still lacking.

[0005] To address the aforementioned issues, this invention proposes a method for predicting the thermal conductivity of red soil based on data augmentation and machine learning, which significantly improves the prediction accuracy and generalization ability of the thermal conductivity of red soil under small sample conditions. Summary of the Invention

[0006] The main objective of this invention is to provide a method for predicting the thermal conductivity of red soil based on data augmentation and machine learning, thereby solving the problems of low prediction accuracy and poor generalization ability of machine learning models due to the scarcity of measured samples.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for predicting the thermal conductivity of red soil based on data augmentation and machine learning includes the following steps: S1. Obtain red soil sample data and construct the original sample dataset; S2. Perform feature correlation analysis on the original sample dataset to determine the input features that affect the thermal conductivity k of red soil. S3. A two-stage data augmentation strategy is adopted to expand the original sample dataset and generate an augmented dataset. S4. Enhance the normalization of the dataset, construct multiple candidate machine learning prediction models, use the enhanced dataset for model training and validation, and select the final prediction model. S5. Obtain the saturation of the red soil to be predicted. Porosity n, water content and dry density After standardization, the thermal conductivity k of the red soil to be predicted is obtained by inputting it into the target prediction model.

[0008] In the preferred embodiment, in S2, the feature correlation analysis uses the Pearson correlation coefficient to assess the strength of the linear correlation between each input feature and the thermal conductivity. The formula for calculating the Pearson correlation coefficient r is: ; in, and These represent the i-th observation values ​​of the two variables, and These represent the means of the two variables, respectively. Based on the Pearson correlation coefficient analysis results, the parameters with the most significant correlation with thermal conductivity were selected as the input features of the prediction model.

[0009] In the preferred scheme, the key input features selected in S2 include saturation. Porosity n, water content and dry density .

[0010] In the preferred embodiment, S3 includes: Phase 1: Establish equidistant interpolation coordinates along the sample dimensions, and use the same interpolation coordinates to perform cubic spline interpolation on the input features and corresponding thermal conductivity, expanding the 42 sets of samples into 100 sets of interpolation samples. Second stage: Select the first 50 samples from the 100 interpolated samples, add Gaussian noise with an intensity of 5% of the original sample's corresponding variable range, and generate 50 noisy samples. The interpolated samples are merged with the noisy samples, and the feature bias of the merged samples is verified. Samples with a bias of more than 15% for any variable are removed. When the number of valid samples is less than 150, samples are drawn from the original sample dataset to supplement it, forming an augmented sample dataset with 150 samples.

[0011] In the preferred scheme, cubic spline interpolation is performed using the following formula: ; In the formula, This represents the cubic spline interpolation result at the interpolation coordinate x; x represents the coordinate to be interpolated. Represents the coordinates of the left endpoint of the i-th interpolation interval; This represents the coordinates of the right endpoint of the i-th interpolation interval; i represents the interpolation interval index. , , and Let represent the cubic spline coefficients in the i-th interpolation interval; This represents the coordinate difference between the coordinates to be interpolated and the left endpoint of the interpolation interval; Gaussian noise injection is performed using the following formula: ; In the formula, x represents the interpolated sample variable value before noise is added; This represents the variable value after noise has been added; represents a Gaussian random perturbation; N represents a normal distribution; 0 represents that the mean of the Gaussian random perturbation is 0; This represents the variance of the Gaussian random perturbation.

[0012] In the preferred scheme, the t-SNE method is used to map the original sample dataset and the augmented sample dataset to a two-dimensional space respectively, and the sample distributions of the two are compared. The enhanced samples were used to determine that they maintained the main distribution characteristics of the original samples.

[0013] In the preferred scheme, in S4, the constructed machine learning prediction model includes four types: support vector machine, random forest, artificial neural network, and long short-term memory network; the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination are used. Evaluate the predictive performance of candidate machine learning models.

[0014] In the preferred embodiment, in S5, based on saturation The theoretical relationship between porosity n and thermal conductivity k of red soil was used to qualitatively verify the overall variation law of the predicted thermal conductivity.

[0015] In the preferred scheme, the theoretical relationships used for qualitative verification include: ; ; ; ; ; ; ; ; In the formula, k represents the thermal conductivity of the red soil; This represents the thermal conductivity of soil under saturated conditions. This represents the thermal conductivity of soil in a dry state. Represents the dimensionless Kersten coefficient; Indicates the thermal conductivity of soil particles; This represents the thermal conductivity of water; This indicates parameters related to soil type; T represents temperature, in °C. Indicates saturation; Indicates moisture content; Indicates the specific gravity of soil particles; n represents porosity; Indicates dry density; This indicates the density of water.

[0016] In the preferred scheme, the theoretical relationship is used to characterize the overall increase in thermal conductivity as saturation increases and the overall decrease in thermal conductivity as porosity increases.

[0017] This invention provides a method for predicting the thermal conductivity of red soil based on data augmentation and machine learning. By adopting the above scheme, the following beneficial effects are achieved: To address the core challenges of difficult sampling and preparation of red soil samples and the scarcity of measured thermal conductivity samples, which can easily lead to overfitting and poor generalization ability in machine learning models, a two-stage data augmentation strategy of "cubic spline interpolation + Gaussian noise injection" is adopted to expand the effective sample to 150 groups. Simultaneously, an outlier removal mechanism with a 15% deviation threshold and a t-SNE dimensionality reduction distribution verification method are implemented to ensure that the augmented samples always closely match the distribution characteristics of the original data, and that the input features maintain a physical correspondence with the thermal conductivity, avoiding the generation of invalid and distorted samples. Comparative verification shows that the optimal random forest model has the highest determination coefficient. The value improved from 0.622 to 0.782, and the root mean square error (RMSE) increased from 0.223 W / (m²). K) decreased to 0.142 W / (m K) significantly improves prediction accuracy and model generalization ability under small sample conditions.

[0018] Based on measured data of red soil, this method uses Pearson correlation analysis to screen out four key influencing characteristics: saturation, porosity, water content, and dry density. It establishes a nonlinear prediction mapping relationship specific to red soil, which is more in line with the thermal property variation law of red soil and solves the applicability defects of general models to red soil.

[0019] Simultaneously construct four candidate machine learning models: random forest, support vector machine, artificial neural network, and long short-term memory network. Use mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (CQD) as the evaluation criteria. The model performance is evaluated using three indicators, and the random forest model with the best fit is selected. This avoids the limitations of selecting a single model and ensures the stability and reliability of the prediction results.

[0020] Compared with indoor steady-state heat source method and transient thermal probe method, this method does not require complicated test equipment and sample preparation process. It only requires input of four easily obtainable conventional physical parameters: saturation, porosity, moisture content and dry density, and can quickly output the predicted thermal conductivity result, which greatly reduces the test cost and time cycle. It can support rapid calculation in engineering scenarios such as ground source heat pump design and roadbed thermal stability analysis.

[0021] Based on machine learning predictions, the theoretical relationship of thermal conductivity of red soil is introduced for qualitative verification. Relying on the physical law that "the thermal conductivity generally increases when the saturation increases and the thermal conductivity generally decreases when the porosity increases", the rationality of the trend of the prediction results is verified. This can effectively avoid abnormal outputs of machine learning and further improve the reliability of engineering applications. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is an overall flowchart of the method for predicting the thermal conductivity of red soil based on data augmentation and machine learning in this invention. Figure 2 This is a comparison chart of the t-SNE dimensionality reduction distributions of the original data and the enhanced data of this invention; Figure 3 The images show scatter plots and error distribution plots of the predicted and actual values ​​of different candidate machine learning models of the present invention, including (a) random forest model, (b) artificial neural network model, (c) long short-term memory network model, and (d) support vector machine model. Detailed Implementation

[0023] In an embodiment of this application, a method for predicting the thermal conductivity of red soil based on data augmentation and machine learning is provided, such as... Figure 1As shown, this embodiment includes five steps: acquiring original sample data, determining predictive input features, constructing an enhanced sample dataset, establishing a target prediction model, and predicting the thermal conductivity of red soil.

[0024] S1. Obtaining raw sample data: We obtained 42 sets of red soil sample data and constructed the original sample dataset A.

[0025] Each set of sample data is represented as follows: ; In the formula, Saturation; Porosity; Moisture content; Dry density; is the thermal conductivity.

[0026] The statistical ranges of each variable in the original sample data are shown in Table 1.

[0027] Table 1 shows the statistical range of the original sample data:

[0028] The raw sample data is used for correlation analysis, data augmentation, and machine learning model building.

[0029] S2. Predicting Input Feature Determination: The Pearson correlation coefficient was used to analyze the correlation between saturation, porosity, water content, dry density, and thermal conductivity. The formula for calculating the Pearson correlation coefficient r is: ; In the formula, and These represent the i-th observation values ​​of the two variables, and These represent the means of the two variables, respectively.

[0030] The correlation coefficients between various physical parameters and thermal conductivity are shown in Table 2.

[0031] Table 2 shows the correlation coefficients between various physical parameters and thermal conductivity:

[0032] Table 2 shows that saturation and moisture content are positively correlated with thermal conductivity, porosity is negatively correlated with thermal conductivity, and dry density is positively correlated with thermal conductivity. As saturation increases, air in the pores is gradually replaced by water, improving the overall heat transfer capacity of the soil. Increased porosity reduces the continuity of contact between particles, increases the proportion of low-thermal-conductivity air in the pores, and reduces the soil's thermal conductivity. Increased moisture content helps reduce the thermal contact resistance between particles. Increased dry density makes the soil particles more compact, which is beneficial for heat transfer.

[0033] Therefore, saturation Porosity n, water content and dry density The thermal conductivity k is determined as the predicted output variable and is used as the predicted input feature of the machine learning model.

[0034] The mapping relationship between predicted input features and thermal conductivity is expressed as follows: ; In the formula, k represents the thermal conductivity of the red soil; This represents the nonlinear mapping relationship established by the machine learning prediction model; Indicates saturation; n represents porosity; Indicates moisture content; Indicates dry density.

[0035] S3. Enhanced Sample Dataset Construction: To improve the coverage of the data space by the 42 original samples, this embodiment adopts a data augmentation method that combines cubic spline interpolation and Gaussian noise injection, and enhances data quality through feature bias verification, sample supplementation and distribution comparison control.

[0036] 3.1 Establishing equidistant interpolation coordinates: Establish equidistant sample coordinates according to the arrangement order of the 42 original samples.

[0037] Saturation Porosity n, water content Dry density The same set of interpolation coordinates is used for the thermal conductivity k, so that the same interpolation coordinates correspond to a complete set of predicted input features and thermal conductivity.

[0038] 3.2 Cubic spline interpolation: Cubic spline interpolation was used to expand the 42 original samples into 100 interpolated samples.

[0039] The cubic spline function in the i-th interpolation interval is: ; In the formula, This represents the cubic spline interpolation result at the interpolation coordinate x; x represents the coordinate to be interpolated. Represents the coordinates of the left endpoint of the i-th interpolation interval; This represents the coordinates of the right endpoint of the i-th interpolation interval; i represents the interpolation interval index. , , and Let represent the cubic spline coefficients in the i-th interpolation interval; This represents the coordinate difference between the coordinates to be interpolated and the left endpoint of the interpolation interval.

[0040] Using the same target interpolation coordinates, interpolation results for saturation, porosity, water content, dry density, and thermal conductivity were obtained, forming 100 sets of interpolation samples with corresponding relationships.

[0041] 3.3 Gaussian noise injection: The first 50 samples out of 100 interpolation samples were selected, and Gaussian noise was added to the saturation, porosity, water content, dry density and thermal conductivity of each sample to generate 50 noisy samples.

[0042] Gaussian noise injection uses: ; In the formula, x represents the interpolated sample variable value before noise is added; This represents the variable value after noise has been added; represents a Gaussian random perturbation; N represents a normal distribution; 0 represents that the mean of the Gaussian random perturbation is 0; This represents the variance of the Gaussian random perturbation.

[0043] The Gaussian noise intensity was set to 5% of the corresponding variable value range in the original samples. By limiting the noise intensity, the noisy samples were made to exhibit a moderate variation within the vicinity of the original data.

[0044] 3.4 Sample merging and feature bias verification: The 100 interpolated samples and 50 noisy samples were merged to form 150 temporary enhanced samples.

[0045] The minimum and maximum values ​​of each variable in the original sample are used as the original value ranges for the corresponding variables. For generated values ​​that exceed the original value range, the proportion of their deviation from the nearest interval boundary relative to the original value range of the variable is calculated. When the proportion of any variable in a generated sample exceeds 15%, that sample is removed.

[0046] By using a whole-group elimination method, the four predicted input features in the same enhanced sample maintain a complete correspondence with the thermal conductivity.

[0047] 3.5 Sample Supplementation: After removing abnormal samples, if the number of valid samples is less than 150, samples are randomly drawn from the 42 original samples to supplement them until the number of enhanced samples reaches 150.

[0048] This results in the enhanced sample dataset B.

[0049] 3.6 Enhanced Sample Distribution Comparison: The t-SNE method is used to map the original sample dataset A and the augmented sample dataset B to a two-dimensional space, and the sample distributions of the two are compared.

[0050] like Figure 2 As shown, the main distribution areas of the original samples and the enhanced samples overlap. The enhanced samples are mainly distributed in the vicinity of the original samples and do not form independent clusters that are significantly different from the distribution of the original samples, indicating that the enhanced samples maintain the main distribution characteristics of the original samples.

[0051] S4: Establishing the target prediction model: 4.1 Data Standardization: The Z-score method was used to standardize saturation, porosity, water content, and dry density. ; in, The data is standardized, and x represents the original data. The mean of the original data. This represents the standard deviation of the original data.

[0052] 4.2 Dataset Partitioning: The 150 augmented samples were divided into a training set and a test set in a 7:3 ratio, with the training set consisting of 105 samples and the test set consisting of 45 samples.

[0053] The training set is used to train the candidate machine learning model, and the test set is used to evaluate the predictive performance of the candidate machine learning model.

[0054] 4.3 Candidate Machine Learning Models: Establish the following four candidate machine learning models: (1) Random forest model, using the Bagging ensemble strategy, with 100 decision trees; (2) Support vector machine model, using radial basis kernel function, with penalty coefficient C of 1; (3) Artificial neural network model, with a single hidden layer structure and 10 hidden layer neurons, trained using Bayesian regularized backpropagation algorithm; (4) Long Short-Term Memory Network Model, with 20 hidden units, a Dropout rate of 0.2, trained using the Adam optimizer, and a maximum number of iterations of 300.

[0055] 4.4 Model Evaluation: The mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination were used. Evaluate the predictive performance of candidate machine learning models.

[0056] The mean absolute error (MAE) is: ; The root mean square error (RMSE) is: ; Coefficient of determination for: ; In the formula, This is the actual value. For predicted values, is the mean of the actual values, and N is the sample size.

[0057] With the coefficient of determination The root mean square error (RMSE) is used as the primary evaluation index, while the mean absolute error (MAE) is used as a secondary evaluation index.

[0058] To evaluate the impact of data augmentation on model prediction performance, the same candidate models and parameters were used for training and evaluation on both the original sample dataset A and the augmented sample dataset B. The performance comparisons of each model are shown in Table 3.

[0059] Table 3 shows the performance comparison of each model on the original dataset and the augmented dataset:

[0060] As shown in Table 3, the RMSE of all four candidate machine learning models decreased after using the augmented sample dataset. The improvement in both values ​​indicates that data augmentation improved the predictive performance of the candidate models.

[0061] The support vector machine model has a MAE of 0.096 W / (m·K) on the augmented sample dataset, but its RMSE is 0.153 W / (m·K). The RMSE is 0.750. The random forest model has the lowest RMSE on the augmented sample dataset. The highest score was achieved, therefore, the random forest model was selected as the target prediction model based on the main evaluation indicators.

[0062] The random forest model's MAE, RMSE, and The values ​​were 0.151 W / (m·K), 0.223 W / (m·K), and 0.622, respectively; after using the augmented sample dataset, the corresponding values ​​were 0.100 W / (m·K), 0.142 W / (m·K), and 0.782, respectively.

[0063] like Figure 3 As shown, the random forest model's predicted values ​​generally fit the actual values ​​well, and its predicted points are relatively concentrated near the diagonal where the predicted and actual values ​​are equal, which is consistent with the evaluation results in Table 3.

[0064] S5: Prediction of thermal conductivity of red soil: 5.1 Obtaining the parameters to be predicted: Obtain the saturation of the red soil to be predicted Porosity n, water content and dry density The prediction input vector is constructed in the following order: ; In the formula, x is the input vector of the red soil to be predicted; Indicates saturation; n represents porosity; Indicates moisture content; Indicates dry density.

[0065] 5.2 Input Data Processing: The Z-score method in S4 was used to standardize the saturation, porosity, water content and dry density of the red soil to be predicted, and the input data of the target prediction model were obtained.

[0066] 5.3 Thermal conductivity output: The standardized input data is fed into the random forest model determined by S4. Through the regression processing of the random forest model, the thermal conductivity k of the red soil to be predicted is obtained.

[0067] 5.4 Physical relationship between saturation and porosity: The relationship between saturation and water content, soil particle specific gravity, and porosity is as follows: ; The relationship between porosity and dry density, soil particle specific gravity, and water density is as follows: ; In the formula, Indicates saturation; Indicates moisture content; Indicates the specific gravity of soil particles; n represents porosity; Indicates dry density; This indicates the density of water.

[0068] The above relationships are used to explain the physical connections between saturation, porosity, moisture content, and dry density.

[0069] 5.5 Theoretical relationship between thermal conductivity of red soil: The theoretical relationship for the thermal conductivity of red soil is: ; The thermal conductivity of soil under saturated conditions is: ; The thermal conductivity of soil in a dry state is: ; Kersten's coefficient is: ; The thermal conductivity of soil particles is: ; The thermal conductivity of water is: ; In the formula, k represents the thermal conductivity of the red soil; This represents the thermal conductivity of soil under saturated conditions. This represents the thermal conductivity of soil in a dry state. Represents the dimensionless Kersten coefficient; Indicates the thermal conductivity of soil particles; This represents the thermal conductivity of water; This indicates parameters related to soil type; T represents temperature, in °C. At a temperature T of 20℃, the thermal conductivity of soil particles Take 2.5 W / (m·K) and the thermal conductivity of water Take 0.596 W / (m·K), parameters When the value is 3.0, the theoretical relationship for the thermal conductivity of red soil is expressed as follows: ; In the formula, k represents the thermal conductivity of the red soil; n represents the porosity. Indicates saturation.

[0070] As can be seen from the above formula, when other conditions are generally similar, the increase in saturation increases the Kersten coefficient, and the overall thermal conductivity of red soil increases; the increase in porosity decreases the thermal conductivity in the dry state, and affects the heat transfer ratio between the solid and liquid phases in the saturated state, thus reducing the overall thermal conductivity of red soil.

[0071] 5.6 Qualitative verification of prediction results: For a group of red soil samples with similar physical properties to be predicted, the overall trend of the thermal conductivity output by the random forest model is compared.

[0072] When the prediction results show that the thermal conductivity of samples with higher saturation is generally higher and the thermal conductivity of samples with higher porosity is generally lower, the prediction results are consistent with the theoretical relationship of thermal conductivity of red soil.

[0073] The theoretical relationship is used to qualitatively describe the overall direction of change in the machine learning prediction results, and the thermal conductivity output by the random forest model is used as the prediction result of this method.

[0074] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for predicting the thermal conductivity of red soil based on data augmentation and machine learning, characterized in that, Includes the following steps: S1. Obtain red soil sample data and construct the original sample dataset; S2. Perform feature correlation analysis on the original sample dataset to determine the input features that affect the thermal conductivity k of red soil. S3. A two-stage data augmentation strategy is adopted to expand the original sample dataset and generate an augmented dataset. S4. Enhance the normalization of the dataset, construct multiple candidate machine learning prediction models, use the enhanced dataset for model training and validation, and select the final prediction model. S5. Obtain the saturation of the red soil to be predicted. Porosity n, water content and dry density After standardization, the thermal conductivity k of the red soil to be predicted is obtained by inputting it into the target prediction model.

2. The method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 1, characterized in that: In S2, the feature correlation analysis uses the Pearson correlation coefficient to assess the strength of the linear correlation between each input feature and the thermal conductivity. The formula for calculating the Pearson correlation coefficient r is: ； in, and These represent the i-th observation values ​​of the two variables, and These represent the means of the two variables, respectively. Based on the Pearson correlation coefficient analysis results, the parameters with the most significant correlation with thermal conductivity were selected as the input features of the prediction model.

3. The method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 2, characterized in that: In S2, the key input features selected include saturation. Porosity n, water content and dry density .

4. The method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 1, characterized in that: S3 includes: Phase 1: Establish equidistant interpolation coordinates along the sample dimensions, and use the same interpolation coordinates to perform cubic spline interpolation on the input features and corresponding thermal conductivity, expanding the 42 sets of samples into 100 sets of interpolation samples. Second stage: Select the first 50 samples from the 100 interpolated samples, add Gaussian noise with an intensity of 5% of the corresponding variable range of the original sample, and generate 50 noisy samples. The interpolated samples are merged with the noisy samples, and the merged samples are subjected to feature bias verification. Samples with a bias of more than 15% for any variable are removed. When the number of valid samples is less than 150, samples are drawn from the original sample dataset to supplement it, forming an augmented sample dataset with 150 samples.

5. The method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 4, characterized in that: Cubic spline interpolation uses the following formula: ； In the formula, This represents the cubic spline interpolation result at the interpolation coordinate x; x represents the coordinate to be interpolated. Represents the coordinates of the left endpoint of the i-th interpolation interval; This represents the coordinates of the right endpoint of the i-th interpolation interval; i represents the interpolation interval index. , , and Let represent the cubic spline coefficients in the i-th interpolation interval; This represents the coordinate difference between the coordinates to be interpolated and the left endpoint of the interpolation interval; Gaussian noise injection is performed using the following formula: ； In the formula, x represents the interpolated sample variable value before noise is added; This represents the variable value after noise has been added; represents a Gaussian random perturbation; N represents a normal distribution; 0 represents that the mean of the Gaussian random perturbation is 0; This represents the variance of the Gaussian random perturbation.

6. The method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 4, characterized in that: The t-SNE method is used to map the original sample dataset and the augmented sample dataset to a two-dimensional space, and the sample distributions of the two are compared. The enhanced samples were used to determine that they maintained the main distribution characteristics of the original samples.

7. The method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 1, characterized in that: In S4, the machine learning prediction models constructed include four types: support vector machine, random forest, artificial neural network, and long short-term memory network; mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination are used. Evaluate the predictive performance of candidate machine learning models.

8. The method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 1, characterized in that: In S5, based on saturation The theoretical relationship between porosity n and thermal conductivity k of red soil was used to qualitatively verify the overall variation law of the predicted thermal conductivity.

9. A method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 8, characterized in that: The theoretical relationships used in the qualitative verification include: ； ； ； ； ； ； ； ； In the formula, k represents the thermal conductivity of the red soil; This represents the thermal conductivity of soil under saturated conditions. This represents the thermal conductivity of soil in a dry state. Represents the dimensionless Kersten coefficient; Indicates the thermal conductivity of soil particles; This represents the thermal conductivity of water; Indicates parameters related to soil type; T represents temperature, in °C; Indicates saturation; Indicates moisture content; Indicates the specific gravity of soil particles; n represents porosity; Indicates dry density; This indicates the density of water.

10. A method for predicting the thermal conductivity of red soil based on data augmentation and machine learning according to claim 9, characterized in that: The theoretical relationship is used to characterize the overall increase in thermal conductivity as saturation increases and the overall decrease in thermal conductivity as porosity increases.

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