Reef limestone strength prediction method based on pore characteristics machine learning

Abstract

The present invention discloses a method for predicting the strength of reef limestone based on pore characteristics and machine learning, belonging to the cross - technical field of geotechnical engineering and artificial intelligence, including: obtaining three - dimensional digital cores of reef limestone, extracting pore characteristics after pre - processing; establishing a multi - source pore - physical coupling feature data fusion framework based on pore characteristics; integrating random forest and gradient boosting tree, dynamically weighting the parameters in pore characteristics, designing a composite loss function, training in layers and embedding physical constraints to construct a machine learning model for predicting the strength of reef limestone; adopting stratified K - fold cross - validation to test the robustness of the machine learning model for predicting the strength of reef limestone and verify its interpretability. The present invention deeply explores the relationship between pore characteristics and the strength of reef limestone by processing data, constructing and optimizing the machine learning model for predicting the strength of reef limestone, improves the prediction accuracy, reliability and interpretability of the model, and provides an effective solution for predicting the strength of reef limestone.

Description

Technical Field

[0001] The present invention belongs to the cross - technical field of geotechnical engineering and artificial intelligence, and specifically relates to a method for predicting the strength of reef limestone based on pore characteristics and machine learning. Background Technique

[0002] In the field of geotechnical engineering and the strength assessment of geological materials, the traditional detection of the mechanical properties of reef limestone mainly relies on physical and mechanical experimental methods, such as uniaxial / triaxial compression tests, point load tests, etc. Although these methods can directly obtain the rock strength parameters, their inherent defects significantly restrict the engineering application efficiency: First, the experimental process requires destructive loading of samples, resulting in the inability to reuse precious geological samples; Second, it usually takes 2 - 4 weeks from sample collection, preparation to the completion of strength testing, which is difficult to meet the rapid decision - making needs of large - scale projects; Third, the cost of a single experiment is as high as several thousand yuan, posing a heavy economic burden on reef stability assessment projects that require a large number of tests.

[0003] Although existing theoretical models attempt to predict the strength of reef limestone through a single parameter such as porosity, their prediction accuracy (usually the coefficient of determination R² < 0.7) far fails to meet the engineering design requirements. The root cause is that the pore structure of reef limestone is controlled by the coral biological skeleton, showing a biogenic spatial distribution law that is completely different from sedimentary rocks - the pore network forms a gradient density distribution along the coral growth direction in three - dimensional space, and there are significant topological connectivity differences between pore clusters. Such complex spatial characteristics have a strong non - linear correlation with mechanical properties, while traditional empirical formulas only rely on the macroscopic statistical parameter of porosity and completely ignore key micro - structural information such as pore geometry, spatial arrangement directionality, and connectivity, resulting in a deviation of 30% - 50% between the model prediction results and the measured values.

[0004] In view of the above - mentioned technical bottlenecks, there is an urgent need to develop a non - destructive, high - efficiency, and high - precision method for predicting the strength of reef limestone. Summary of the Invention

[0005] Aiming at the deficiencies in the background technique, the purpose of the present invention is to propose a method for predicting the strength of reef limestone based on pore characteristics and machine learning. By integrating three - dimensional digital core technology and machine learning algorithms, it breakthroughly realizes the quantitative characterization of pore space distribution characteristics and the accurate mapping of non - linear mechanical responses, providing an innovative solution for the strength assessment of complex biogenic rocks.

[0006] The technical solution adopted by the present invention:

[0007] A method for predicting the strength of reef limestone based on pore characteristics and machine learning, comprising the following steps:

[0008] Step S1) Obtain three - dimensional digital core data and pre - process it, and extract pore characteristics at multiple scales;

[0009] Step S2) Establish a multi-source pore-physical coupling feature data fusion framework based on pore characteristics;

[0010] Step S3) Integrate random forest and gradient boosting tree, dynamically weight the parameters in pore characteristics, design a composite loss function, train in layers and embed physical constraints to construct a machine learning model for predicting the strength of reef limestone;

[0011] Step S4) Based on hierarchical K-fold cross-validation, optimize physical constraints, jointly optimize hyperparameters, test the robustness of the machine learning model for predicting the strength of reef limestone and verify its interpretability.

[0012] Preferably, in the step S1), the specific process of obtaining and preprocessing three-dimensional digital core data is as follows:

[0013] First, use a micron-level high-resolution CT scanning system to obtain three-dimensional digital core data of reef limestone samples; eliminate noise through the Otsu adaptive threshold segmentation algorithm combined with morphological closing operation, and accurately segment the rock matrix and pore structure;

[0014] In the step S1), the specific process of multi-scale extraction of pore characteristics is as follows:

[0015] Use a three-dimensional image analysis framework to extract pore characteristics hierarchically and multi-scale:

[0016] ① Quantify geometric pore characteristics

[0017] Based on the pore skeletonization algorithm, calculate the equivalent pore size distribution histogram, use the triangular mesh surface fitting technology to quantify the pore curvature, and calculate the shortest connected path and tortuosity in the pore network through the Dijkstra algorithm to generate the pore connectivity index;

[0018] ② Analyze spatial distribution pore characteristics

[0019] Establish a three-dimensional space coordinate system along the original growth direction of the coral, use the Voronoi diagram to divide the reef limestone sample into sub-units of 5×5×5 mm³, count the proportion of pore volume in each unit and calculate the density gradient vector; at the same time, extract the main extension direction of the pore cluster through principal component analysis, and calculate the cosine value of the angle between it and the coral growth axis as the direction correlation coefficient;

[0020] ③ Model topological pore characteristics

[0021] Based on the three-dimensional pore network model, count the number of adjacent pores connected to each pore node to generate a coordination number distribution matrix, and use the breadth-first search algorithm to identify the largest connected pore cluster and calculate the proportion of its volume in the total pore volume;

[0022] All pore characteristic parameters are standardized by Z-score and stored in the structured feature database to provide input vectors.

[0023] Preferably, in the step S2), the specific steps for establishing the pore-physical coupling feature data fusion framework are as follows:

[0024] Sb1) Calibrate physical properties

[0025] Measure the geometric dimensions of the reef limestone sample to calculate the volume V, obtain the mass M, and determine the dry density ρ_d;

[0026] Sb2) Align feature dimensions

[0027] Use the Box-Cox transformation to eliminate the order-of-magnitude differences between pore features and physical properties, perform dimensional unification processing on pore features and physical properties, and then align the feature dimensions;

[0028] Sb3) Establish a spatio-temporal correlation model

[0029] Bind the spatially distributed pore features and physical properties to three-dimensional spatial coordinates through a spatial registration algorithm to ensure that the spatial positions of each dimension in the feature matrix X = [x1,...,x 12 ,V,M,ρ_d] can be traced, thereby establishing a spatio-temporal correlation model;

[0030] Sb4) Enhance pore-physical coupling feature interaction

[0031] Based on the spatio-temporal correlation model, introduce pore-physical coupling feature terms, use the mutual information method to screen the feature subset with a correlation with strength > 0.3, and fuse the pore-physical coupling feature matrix to enhance the pore-physical coupling feature interaction;

[0032] Sb5) Optimize the robustness of pore-physical coupling feature data

[0033] Fill in missing values and correct outliers for the fused pore-physical coupling feature matrix, and finally generate a standardized feature matrix X ∈ R^(n×15), whose condition number κ(X^TX) < 10^3 to ensure the stability of the feature matrix input.

[0034] Preferably, in the step S3), the specific steps for constructing the reef limestone strength prediction machine learning model are as follows:

[0035] Sc1) Integrate heterogeneous models

[0036] Construct a dual-channel learning framework of random forest and gradient boosting tree to integrate heterogeneous models, where RF sets 200 decision trees to capture the discretized association rules of pore topology features, and GBDT configures 500 rounds of iteration to model the continuous gradient effect of spatially distributed pore features;

[0037] Sc2) Dynamic feature weighting

[0038] Quantify the contribution of each pore feature to strength prediction based on SHAP value analysis, apply a weight coefficient of 1.2 - 2.0 times to the parameters in the pore features, and update the weight matrix every 10 rounds of training through a sliding window mechanism, dynamically adjusting the weight matrix during the training process;

[0039] Sc3) Design a composite loss function

[0040] Define a hybrid loss function of L = 0.7MAE + 0.3Huber_loss, where MAE is used to constrain the overall prediction deviation, and Huber_loss (δ = 1.5MPa) is used to suppress the interference of outliers. The hyperparameters α = 0.7 and β = 0.3 are determined by Bayesian optimization;

[0041] Sc4) Hierarchical training strategy

[0042] First, freeze the GBDT layer and train the RF branch alone until the MAE on the validation set < 2.5MPa, that is, reach the convergence state, and then unfreeze the entire network for joint fine-tuning; use the AdamW optimizer with Nesterov momentum acceleration, and the initial learning rate of 3e-4 is reduced to 1e-5 by cosine annealing;

[0043] Sc5) Embed physical constraints

[0044] Introduce a porosity-strength monotonicity penalty term in the output layer. When the predicted value rises with the increase of porosity, apply a gradient correction with an L1 regularization strength coefficient of λ = 0.1;

[0045] Construct a machine learning model for predicting the strength of reef limestone by integrating heterogeneous models, dynamic feature weighting, designing a composite loss function, hierarchical training strategy, and embedding physical constraints.

[0046] Preferably, in the step S4), the specific steps for testing the robustness of the machine learning model for predicting the strength of reef limestone and verifying its interpretability are as follows:

[0047] Sd1) Hierarchical K-fold cross-validation

[0048] Stratify the machine learning model for predicting the strength of reef limestone by porosity intervals and perform 5-fold cross-validation. During the training of each fold, synchronously monitor the MAE curves of the training set and the validation set. When the MAE of the validation set rises continuously for 3 rounds by more than 0.5MPa, trigger the early stopping mechanism and stop the training of the current fold to prevent overfitting;

[0049] Sd2) Optimize the embedding of physical constraints

[0050] Introduce a porosity-strength monotonicity correction module into the output layer of the machine learning model for predicting the strength of reef limestone, which is a physical constraint. Real-time detect the trend of the predicted value changing with the porosity. If the porosity increases while the predicted strength does not decrease, then use the linear interpolation method to force the predicted value onto the theoretical monotonic decreasing curve, so that the corrected predicted value 100% satisfies the physical law;

[0051] Sd3) Joint optimization of hyperparameters

[0052] Adopt a hybrid strategy of grid search and Bayesian optimization to perform two-stage parameter tuning within the preset space: first use grid search for rough tuning to determine the optimal region, and then use Bayesian optimization for fine search. Use the weighted sum of RMSE and MAE of the validation set as the objective function to find the global optimal hyperparameter combination;

[0053] Sd4) Test the robustness of the machine learning model for predicting the strength of reef limestone

[0054] Construct a noisy dataset and a dataset with missing features, respectively test the performance decay rate of the machine learning model for predicting the strength of reef limestone, and use adversarial sample training to enhance the stability of the decision boundary;

[0055] Sd5) Interpretability verification

[0056] Quantify the contribution degree of each feature through global analysis of SHAP values, ensure that the SHAP values of the parameters in the pore features rank among the top 5, and the consistency with the rock mechanics theory is >90%.

[0057] Compared with the prior art, the present invention proposes a method for predicting the strength of reef limestone based on pore features of machine learning. The advantages of this method are:

[0058] (1) Non-destructive and efficient detection, breaking through the limitations of traditional methods. The present invention uses CT scanning and digital core analysis technology to completely replace traditional destructive mechanical experiments, realizing non-destructive evaluation of the strength of reef limestone. The samples can be reused 100%, solving the problem of scarcity of geological samples; the detection cycle is shortened from 2-4 weeks of traditional methods to 2-4 hours (including scanning and model prediction), the single cost is reduced, and the efficiency is improved; the prediction accuracy is high, and the error is significantly reduced compared with the traditional porosity model, meeting the requirements of high-precision engineering design;

[0059] (2) Multi-dimensional feature fusion, revealing the mechanical mechanism of biological pores, breaking through the limitations of a single porosity parameter. For the first time, fuse 12-dimensional features of three major categories of pore geometry (equivalent pore size, curvature), space (density gradient, direction correlation) and topology (coordination number, proportion of pore clusters), and combine physical properties to construct a 15-dimensional composite feature space to comprehensively characterize the characteristics of biogenic pores; use SHAP to reveal the non-linear correlation law between the pore network and strength, filling the theoretical gap in the mechanical mechanism of biological rock masses;

[0060] (3) Machine learning guided by physical constraints ensures engineering reliability. A porosity-strength monotonicity correction module is embedded in the model to force the prediction results to conform to the laws of rock mechanics. The prediction error in extreme porosity areas is reduced. Through adversarial training such as noise injection and feature masking, the performance attenuation rate of the model under complex working conditions is less than 15%, which is significantly better than traditional models.

[0061] (4) The environmental and cost benefits are significant. It can avoid the destructive consumption of tens of thousands of tons of reef limestone samples each year and reduce the impact of ecological exploration. The system has low overall energy consumption and is more energy-efficient than traditional experimental equipment, saving project costs. The technology can be extended to projects such as island development and undersea tunnels. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The present invention is a flow chart of the reef limestone strength prediction method based on pore characteristic machine learning. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present application to further clearly and completely describe the technical solutions in the embodiments of the present application. It should be noted that the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of this application.

[0064] In order to make the invention objectives, technical solutions and advantages of the present application clearer, the embodiments of the present application are further described in detail in conjunction with the drawings in the specification: In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the advantages of the present invention will be further illustrated by comparing the embodiments in conjunction with the drawings and specific implementation methods.

[0065] The present invention proposes a reef limestone strength prediction method based on pore feature machine learning, and the steps of the method are described in detail:

[0066] Step S1) acquiring and preprocessing three-dimensional digital core data, and extracting pore characteristics at multiple scales;

[0067] Specifically, in step S1), the specific process of obtaining and preprocessing the three-dimensional digital core data is as follows:

[0068] First, a micron-scale high-resolution CT scanning system (scanning accuracy ≤ 5μm) is used to obtain the three-dimensional digital core data of the reef limestone samples. Since there are noise points in the original three-dimensional digital core data, the noise points are eliminated by using the Otsu adaptive threshold segmentation algorithm combined with morphological closing operation. Through the operations of dilation first and then erosion, the small cavities within the pore structure region are filled, adjacent pore structures are connected, and the boundaries of the pore structures are made smoother and more accurate, thus precisely segmenting the rock matrix and the pore structure.

[0069] Specifically, in the step S1), the specific process of multi-scale extraction of pore characteristics is as follows:

[0070] Using a three-dimensional image analysis framework, pore characteristics are extracted hierarchically and multi-scale:

[0071] ① Quantify geometric pore characteristics

[0072] Based on the pore skeletonization algorithm, calculate the equivalent pore size distribution histogram (statistically divided into 10 levels in the diameter range of 0.1 - 2.0mm). Through the equivalent pore size distribution histogram, the distribution proportion of pore structures of different sizes in the data can be intuitively understood. The surface of the pore structure is discretized into multiple triangular meshes by using the triangular mesh surface fitting technology. By calculating the curvature of each triangular mesh, the pore curvature (curvature radius 0.05 - 1.5mm) is quantified. Among them, the pore curvature reflects the degree of bending of the pore structure surface, which is of great significance for studying properties such as the flow resistance of fluids in the pore structure. And calculate the shortest connected path in the pore network through the Dijkstra algorithm, and at the same time obtain the tortuosity (i.e., the ratio of the actual path length to the shortest connected path). The larger the tortuosity, the more complex the flow path of the fluid in the pore structure. Further generate the pore connectivity index (taking continuous values from 0 to 1). The closer the pore connectivity index is to 1, the better the connectivity of the pore structure; otherwise, the connectivity is worse.

[0073] ② Analyze the spatial distribution pore characteristics

[0074] Establish a three-dimensional space coordinate system along the original growth direction of the coral. Use the Voronoi diagram to divide the sample into sub-units of 5×5×5mm³, and statistically calculate the volume ratio of the pore structure in each sub-unit (i.e., the ratio of the pore structure volume in the sub-unit to the total volume of the sub-unit), and calculate the density gradient vector (gradient modulus 0 - 0.8mm⁻¹). At the same time, extract the main extension direction of the pore clusters (a set of multiple pores that are interconnected and aggregated) through principal component analysis (PCA), and calculate the cosine value of the angle between it and the coral growth axis as the direction correlation coefficient (in the range of 0 - 1). The closer the direction correlation coefficient is to 1, the stronger the correlation between the main extension direction of the pore cluster and the coral growth axis; otherwise, the correlation is weaker.

[0075] ③ Model topological pore characteristics

[0076] Based on a three-dimensional pore network model, the coordination number distribution matrix is generated by counting the number of adjacent pores connected to each pore node (with the peak between 2 and 4). The coordination number distribution matrix records the quantity distribution of pore nodes with different coordination numbers in the entire pore network. Through analysis, the complexity and uniformity of the connections in the pore network can be understood; and the breadth-first search (BFS) algorithm is used to identify the largest connected pore cluster (a set with the largest number of pores and the largest volume), and calculate the proportion of its volume in the total pore volume (the dynamic range is 10% - 95%);

[0077] All pore characteristics are standardized by Z-score and stored in a structured feature database. After the standardization process, all pore characteristics are on the same measurement scale, providing an input vector.

[0078] Step S2) Establish a multi-source pore-physical coupling feature data fusion framework based on pore characteristics;

[0079] Specifically, in the said step S2), the specific process of establishing the pore-physical coupling feature data fusion framework is as follows:

[0080] Sb1) Calibrate physical properties

[0081] Use a laser rangefinder to measure the geometric dimensions of the reef limestone sample to calculate the volume V. Through the relevant dimension data, the volume V of the reef limestone sample is calculated according to the corresponding geometric volume calculation formula; an electronic balance is used to obtain the mass M; and the dry density ρ_d is measured by the oven drying method, that is, the reef limestone sample is placed in an oven, and under certain temperature and time conditions, the moisture in the reef limestone sample is completely evaporated, and then according to the mass of the dried reef limestone sample and the volume of the original reef limestone sample, the dry density ρ_d is calculated; the volume, mass, and dry density are physical properties;

[0082] Sb2) Align feature dimensions

[0083] Pore characteristics (such as pore curvature, tortuosity, etc.) and the obtained physical properties (volume, mass, dry density) may have different dimensions. The Box-Cox transformation is used to eliminate the differences between pore characteristics and physical properties, and to achieve the dimensional unification of pore characteristics and physical properties; after dimensional unification and difference elimination, each feature has the same weight and comparability in subsequent data analysis and modeling, and then the feature dimensions are aligned;

[0084] Sb3) Establish a spatio-temporal correlation model

[0085] Bind the spatially distributed pore features and physical properties in three-dimensional space coordinates through a spatial registration algorithm, bind the spatially distributed pore features and physical properties in three-dimensional space coordinates. In the constructed feature matrix X = [x1,..., x 12 , V, M, ρ_d] (where x1 to x 12 represent the parameters in the pore features), the features of each dimension correspond to specific three-dimensional spatial positions, enabling the tracing of the spatial positions of each dimension in the feature matrix X = [x1,..., x 12 , V, M, ρ_d], thereby establishing a spatio-temporal correlation model; by binding the physical properties with the spatially distributed pore features, the physical properties can be related to the spatial structure;

[0086] Sb4) Enhance the pore-physical coupling feature interaction

[0087] Based on the spatio-temporal correlation model, introduce pore-physical coupling feature terms, including derivative parameters such as pore volume fraction (V_pores / V) and pore curvature per unit mass (∑ curvature / M). Use the mutual information method to screen the feature subset with a correlation with strength > 0.3, and fuse the pore-physical coupling feature matrix to enhance the pore-physical coupling feature interaction;

[0088] Sb5) Optimize the data robustness of the pore-physical coupling features

[0089] Perform missing value filling and outlier correction on the fused 15-dimensional pore-physical coupling feature matrix. Through missing value filling and outlier correction, improve the quality and integrity of the pore-physical coupling feature matrix; after processing, finally generate a standardized feature matrix X ∈ R^(n×15), whose condition number κ(X^TX) < 10^3 ensures the stability of the standardized feature matrix input.

[0090] Step S3) Integrate the random forest and gradient boosting tree, dynamically weight the parameters in the pore features, design a composite loss function, and perform hierarchical training and embed physical constraints to construct a machine learning model for predicting the strength of reef limestone;

[0091] Specifically, in the said step S3), the specific process of constructing the machine learning model for predicting the strength of reef limestone is as follows:

[0092] Sc1) Integrate heterogeneous models

[0093] Construct a dual-channel learning framework of Random Forest (RF) and Gradient Boosting Decision Tree (GBDT), integrating heterogeneous models. Among them, RF is set with 200 decision trees (maximum depth 15) to capture the discretized correlation law of topological pore features; GBDT is configured with 500 rounds of iteration (learning rate 0.05). Through iterative training and gradual correction of errors, the continuous gradient effect of spatial distribution pore features is modeled. By integrating heterogeneous models, the relationship between pore features and reef limestone strength can be learned more comprehensively.

[0094] Sc2) Dynamic feature weighting

[0095] Based on the analysis of SHAP value (Shapley Additive exPlanation), quantify the contribution degree of each pore feature to strength prediction, apply a weight coefficient of 1.2 - 2.0 times to the parameters in the pore features (including pore curvature, direction correlation coefficient, etc.), and update the weight matrix every 10 rounds of training through a sliding window mechanism, dynamically adjusting the weight matrix during the training process. Different pore features have different importance for reef limestone strength prediction. Through SHAP value analysis, the contribution degree of each pore feature can be accurately evaluated, and dynamically updating the weight matrix can adapt to data changes and the model learning process.

[0096] Sc3) Design a composite loss function

[0097] Define a hybrid loss function of L = 0.7MAE + 0.3Huber_loss, where MAE is used to constrain the overall prediction deviation, and Huber_loss (δ = 1.5MPa) is used to suppress the interference of outliers. The hyperparameters α = 0.7 and β = 0.3 are determined by Bayesian optimization. MAE can intuitively reflect the deviation degree of overall prediction but is sensitive to outliers; Huber_loss can effectively reduce the impact of outliers on the model. By combining them and using Bayesian optimization to determine the optimal weights, the robustness can be enhanced.

[0098] Sc4) Hierarchical training strategy

[0099] First, freeze the GBDT layer and train the RF branch alone until the MAE on the validation set < 2.5MPa, that is, reach the convergence state, and then unfreeze the entire network for joint fine-tuning. Use the AdamW optimizer with Nesterov momentum acceleration (γ = 0.9), and the initial learning rate of 3e-4 is reduced to 1e-5 by cosine annealing.

[0100] Sc5) Embed physical constraints

[0101] Introduce a porosity-strength monotonicity penalty term in the output layer. When the predicted value rises as the porosity increases, apply a gradient correction with an L1 regularization intensity coefficient λ = 0.1. Ensure that the predicted value monotonically increases as the porosity increases through the penalty term, which conforms to the actual physical law. Suppress excessive complexity and prevent overfitting through gradient correction.

[0102] Construct a machine learning model for predicting the strength of reef limestone by integrating heterogeneous models, dynamic feature weighting, designing a composite loss function, a hierarchical training strategy, and embedding physical constraints.

[0103] Step S4) Based on hierarchical K-fold cross-validation, optimize the physical constraints, jointly optimize the hyperparameters, test the robustness of the machine learning model for predicting the strength of reef limestone, and verify its interpretability.

[0104] Specifically, in the step S4), the specific process of testing the robustness of the machine learning model for predicting the strength of reef limestone and verifying its interpretability is as follows:

[0105] Sd1) Hierarchical K-fold cross-validation

[0106] Divide the machine learning model for predicting the strength of reef limestone into multiple sub-intervals according to the porosity interval (6% - 32%, step size 5%). Perform 5-fold cross-validation (training:validation = 8:2). During each fold of training, synchronously monitor the MAE curves of the training set and the validation set. When the MAE of the validation set rises continuously for 3 rounds by more than 0.5 MPa, trigger the early stopping mechanism and stop the training of the current fold to prevent overfitting. This method can not only effectively evaluate the performance but also reduce unnecessary computational effort through the early stopping mechanism and improve the optimization efficiency.

[0107] Sd2) Optimize the embedding of physical constraints

[0108] Introduce a porosity-strength monotonicity correction module in the output layer of the machine learning model for predicting the strength of reef limestone, which is the physical constraint. Real-time detect the trend of the predicted value changing with the porosity. If the porosity increases while the predicted strength does not decrease, then use the linear interpolation method to force the predicted value onto the theoretical monotonic decreasing curve (the interpolation reference point is taken from the quantiles of the training set), so that the corrected predicted value 100% satisfies the physical law, that is, the strength must decrease when the porosity increases, thereby improving the credibility and scientificity of the model.

[0109] Sd3) Jointly optimize the hyperparameters

[0110] Adopt a hybrid strategy of Grid Search and Bayesian Optimization to perform two-stage parameter tuning within a preset space (RF tree depth 8 - 20, GBDT learning rate 0.01 - 0.1, loss weight α = 0.5 - 0.8): first, use grid search for rough tuning to determine the optimal region, and then use Bayesian optimization for fine search. Take the weighted sum of RMSE and MAE of the validation set (weight ratio 6:4) as the objective function to find the global optimal hyperparameter combination. The combination of grid search and Bayesian optimization balances search efficiency and accuracy well;

[0111] Sd4) Test the robustness of the machine learning model for predicting reef limestone strength

[0112] Construct noisy datasets (add ±5% Gaussian noise) and feature-missing datasets (randomly mask 30% of the feature values) to simulate the situations of errors and incomplete data acquisition respectively. Test the performance decay rate of the machine learning model for predicting reef limestone strength respectively (RMSE increase < 15% is judged as qualified), and use adversarial sample training to enhance the stability of the decision boundary and improve the robustness; these tests aim to evaluate the robustness of the machine learning model for predicting reef limestone strength under different scenarios and ensure that it can still maintain a high performance level when facing noise, missing data or adversarial attacks;

[0113] Sd5) Interpretability verification

[0114] Quantify the contribution degree of each feature through global SHAP value analysis to ensure that the SHAP values of the parameters in the pore characteristics (such as pore connectivity index, direction correlation coefficient, etc.) rank among the top 5, and the consistency with rock mechanics theory > 90%; verify the interpretability of the machine learning model for predicting reef limestone strength to ensure that the importance of the parameters in the pore characteristics is consistent with the theoretical expectation. Through SHAP value analysis, it is possible to clearly understand which features have the greatest impact on the prediction results of the machine learning model for predicting reef limestone strength, thereby enhancing the transparency and credibility of the machine learning model for predicting reef limestone strength.

[0115] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0116] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application is also intended to include these modifications and variations.

Claims

1. A method for predicting the strength of reef limestone based on pore characteristics and machine learning, characterized in that Including: Step S1) Obtain three-dimensional digital core data and preprocess it, and extract pore features at multiple scales; Use a micron-level high-resolution CT scanning system to obtain three-dimensional digital core data of a reef limestone sample; eliminate the noise of the three-dimensional digital core data through the Otsu adaptive threshold segmentation algorithm combined with morphological closing operation, and accurately segment the rock matrix and pore structure; Utilize a three-dimensional image analysis framework to extract pore features hierarchically and at multiple scales: ①Quantify geometric pore features Based on the pore skeletonization algorithm, calculate the equivalent pore size distribution histogram, use the triangular mesh surface fitting technology to quantify the pore curvature, and calculate the shortest connected path and tortuosity in the pore network through the Dijkstra algorithm to generate a pore connectivity index; ②Analyze the spatial distribution of pore features Establish a three-dimensional space coordinate system along the original growth direction of the coral, use the Voronoi diagram to divide the reef limestone sample into sub-units of 5×5×5 mm³, count the volume proportion of the pore structure in each unit and calculate the density gradient vector; at the same time, extract the main extension direction of the pore clusters through principal component analysis, and calculate the cosine value of the angle between it and the coral growth axis as the direction correlation coefficient; ③Model topological pore features Based on the three-dimensional pore network model, count the number of adjacent pores connected to each pore node to generate a coordination number distribution matrix, and use the breadth-first search algorithm to identify the largest connected pore cluster and calculate its proportion in the total pore volume; All pore features are standardized by Z-score and stored in a structured feature database to provide an input vector; Step S2) Establish a multi-source pore-physical coupling feature data fusion framework based on pore features; Step S3) Integrate random forest and gradient boosting tree, dynamically weight the parameters in the pore features, design a composite loss function, train hierarchically and embed physical constraints to construct a machine learning model for predicting the strength of reef limestone; Step S4) Based on hierarchical K-fold cross-validation, optimize the physical constraints, jointly optimize the hyperparameters, test the robustness of the machine learning model for predicting the strength of reef limestone and verify its interpretability.

2. The method for predicting the strength of reef limestone based on pore characteristics and machine learning according to claim 1, wherein In the said step S2), the specific steps for establishing the pore-physical coupling feature data fusion framework are as follows: Sb1) Calibrate physical properties Measure the geometric dimensions of the reef limestone sample to calculate the volume V, obtain the mass M, and determine the dry density ρ_d; Sb2) Align feature dimensions Use the Box-Cox transformation to eliminate the order-of-magnitude difference between pore features and physical properties, perform dimensional unification processing on pore features and physical properties, and then align the feature dimensions; Sb3) Establish a spatio-temporal correlation model Bind the spatially distributed pore characteristics and physical properties to the three-dimensional space coordinates through a spatial registration algorithm to ensure tracing back to the spatial positions of each dimension in the feature matrix X = [x1,..., x 12 , V, M, ρ_d], where x1,..., x 12 represent the parameters in the pore characteristics, thereby establishing a spatio-temporal correlation model; Sb4) Enhance the interaction of pore-physical coupling features Based on the spatio-temporal correlation model, introduce pore-physical coupling feature terms, use the mutual information method to screen the feature subset with a correlation with strength > 0.3, and fuse out the pore-physical coupling feature matrix to enhance the interaction of pore-physical coupling features; Sb5) Optimize the robustness of pore-physical coupling feature data Missing value filling and outlier correction are performed on the fused pore-physical coupling feature matrix, and finally a standardized feature matrix \(X\in R^{n\times15}\) is generated. The condition number \(\kappa(X^TX)<10^3\) ensures the stability of the input of the standardized feature matrix. Here, \(X\) represents the standardized feature matrix, that is, the standardized pore-physical coupling feature matrix, \(R\) represents the real number space, \(n\) represents the number of rows of matrix \(X\), that is, the number of samples, \(\kappa(\cdot)\) represents the condition number of the matrix, and \(X^T\) is , which represents the transpose matrix of matrix \(X\), and \(T\) represents the transpose operation. Then \(X^TX\) represents the product of the transpose matrix and the original matrix.

3. A method for predicting the strength of reef limestone based on pore characteristics and machine learning according to claim 1, characterized in that, In the said step S3), the specific steps for constructing the machine learning model for predicting the strength of reef limestone are as follows: Sc1) Integrate heterogeneous models Construct a dual-channel learning framework of Random Forest (RF) and Gradient Boosting Decision Tree (GBDT), integrating heterogeneous models. Among them, RF sets 200 decision trees to capture the discretized association law of topological pore features, and GBDT configures 500 rounds of iteration to model the continuous gradient effect of spatial distribution pore features; Sc2) Dynamic feature weighting Quantify the contribution of each pore feature to strength prediction based on SHAP value analysis, apply a weight coefficient of 1.2 - 2.0 times to the parameters in the pore features, and update the weight matrix every 10 rounds of training through a sliding window mechanism, dynamically adjusting the weight matrix during the training process; Sc3) Design a composite loss function Define a hybrid loss function of L = 0.7MAE + 0.3Huber_loss, where MAE is used to constrain the overall prediction deviation, and Huber_loss (δ = 1.5 MPa) is used to suppress the interference of outliers. The hyperparameters α = 0.7 and β = 0.3 are determined by Bayesian optimization; Sc4) Hierarchical training strategy First freeze the GBDT layer and train the RF branch alone until the MAE on the validation set < 2.5 MPa, that is, reach the convergence state, and then unfreeze the entire network for joint fine-tuning; use the AdamW optimizer with Nesterov momentum acceleration, and the initial learning rate of 3e-4 is decreased to 1e-5 by cosine annealing; Sc5) Embed physical constraints Introduce a porosity-strength monotonicity penalty term in the output layer. When the predicted value rises with the increase of porosity, apply a gradient correction with an L1 regularization strength coefficient λ = 0.1; Construct a machine learning model for predicting the strength of reef limestone by integrating heterogeneous models, dynamic feature weighting, designing a composite loss function, hierarchical training strategy, and embedding physical constraint methods.

4. A method for predicting the strength of reef limestone based on pore characteristics and machine learning according to claim 1, characterized in that In the step S4), the specific steps for testing the robustness of the machine learning model for predicting the strength of reef limestone and verifying its interpretability are as follows: Sd1) Hierarchical K-fold cross-validation Stratify the machine learning model for predicting the strength of reef limestone according to the porosity interval, perform 5-fold cross-validation, and synchronously monitor the MAE curves of the training set and the validation set during each fold of training. When the MAE of the validation set rises continuously for 3 rounds by more than 0.5 MPa, trigger the early stopping mechanism and stop the training of the current fold to prevent overfitting; Sd2) Optimize the embedding of physical constraints Introduce a porosity-strength monotonicity correction module in the output layer of the machine learning model for predicting the strength of reef limestone, which is the physical constraint. Real-time detect the trend of the predicted value changing with the porosity. If the porosity increases while the predicted strength does not decrease, then force the predicted value to be adjusted to the theoretical monotonically decreasing curve by linear interpolation method, so that the corrected predicted value 100% satisfies the physical law; Sd3) Joint hyperparameter optimization Adopt a hybrid strategy of grid search and Bayesian optimization to perform two-stage parameter tuning within the preset space: first use grid search for rough tuning to determine the optimal region, and then use Bayesian optimization for fine search. Use the weighted sum of RMSE and MAE of the validation set as the objective function to find the global optimal hyperparameter combination; Sd4) Test the robustness of the machine learning model for predicting the strength of reef limestone Construct a noisy dataset and a dataset with missing features, respectively test the performance decay rate of the machine learning model for predicting the strength of reef limestone, and use adversarial sample training to enhance the stability of the decision boundary; Sd5) Interpretability verification Quantify the contribution degree of each feature through global SHAP value analysis, ensure that the SHAP values of the parameters in the pore features rank among the top 5, and the consistency with the rock mechanics theory is >90%.

Images