A method for predicting the strength of deep-sea surface sediments based on random forest algorithm

Abstract

The present invention provides a method for predicting the strength of deep-sea surface sediments based on a random forest algorithm, and uses computational fluid dynamics simulation to obtain the dimensionless penetration resistance coefficient acting on the T-Bar during the T-bar penetration into deep-sea surface sediments under different strengths, different rate effect parameters and different T-bar interface contact conditions. The dimensionless penetration resistance coefficient under the multi-parameter coupling effect is analyzed and trained by the random forest algorithm, and a multi-parameter evaluation method for predicting the dimensionless penetration resistance coefficient of deep-sea sediments is established.

Description

Technical Field

[0001] The present invention relates to the technical field of marine rock and soil parameter evaluation, and in particular to a method for predicting the strength of deep-sea surface sediments based on a random forest algorithm. Background Art

[0002] As the utilization of marine resources, geological disaster prediction and ecological environmental protection enter the deep sea, a large number of engineering facilities (such as marine foundations, pipelines, cables and in-situ long-term observation devices) are being built and put into service on the seabed (Ardelean and Minnebo, 2023; Liu et al., 2023). These submarine structures are located on the surface of the seabed, so the mechanical characteristics of shallow seabed sediments are receiving more and more attention (Dhakal and Gupta, 2023; Yu et al., 2023). Due to the complex deposition and transportation process and the influence of the hydrodynamic environment, seabed sediments have significant regional and spatial variability. The seabed surface in the deep sea is mostly muddy sediments, which can be called deep-sea surface sediments. Generally speaking, deep-sea surface sediments have low undrained shear strength, high compressibility, and strong fluidity. It is very difficult to sample such surface sediments, and it is difficult to conduct strength tests indoors (Zhang et al., 2021; Guo et al., 2023a and 2023b). Therefore, in the field of sediment surface strength testing and evaluation, the full-flow penetrometer in-situ testing technology has shown broad application prospects (Mohiuddin, et al., 2020; Guo et al., 2023b).

[0003] T-bar penetration is a full-flow static penetration technique that has received increasing attention in recent years and has been used for in-situ and indoor undrained shear strength tests of seabed sediment strength. Initial studies focused on the detection of sediment strength under full-flow conditions achieved by T-bar penetration in deep layers. Subsequently, the research on T-bar gradually expanded to shallow surface detection under non-full-flow conditions. However, these studies used the method of sediment buoyancy to simplify the consideration of the influence of upper environmental water. Furthermore, Guo et al (2023a and 2023b) used indoor normal gravity and hypergravity model tests and computational fluid dynamics (CFD) numerical simulation methods to explore the entire surface penetration process of the full-flow penetrometer under the influence of environmental water, and found that sediment density, strength, water environment, penetration depth, sediment type, etc. will have different degrees of influence on the penetration resistance coefficient, which is crucial for evaluating the strength of deep-sea surface sediments. At the same time, deep-sea surface sediments tend to exhibit non-Newtonian fluid properties with shear thinning characteristics, that is, the dynamic viscosity changes with the increase of shear rate (Zhang et al., 2021; Guo et al., 2023a and 2023b). At the same time, deep-sea surface sediments also show significant rate effect characteristics, that is, the undrained shear strength increases with the increase of shear rate. Under the coupling of so many parameters mentioned above, it also involves the continuous evolution of T-bar from full flow penetration to non-full flow penetration under different penetration depths. It is difficult to accurately predict the strength of deep-sea surface sediments only by the resistance obtained during T-bar penetration and the empirical penetration resistance coefficient (Torisu et al., 2012; Liu et al., 2017; Guo et al., 2020b and 2021b). Therefore, how to quickly and accurately predict the strength of deep-sea surface sediments through T-bar full flow penetration test results remains to be solved. Summary of the invention

[0004] In order to make up for the shortcomings of the prior art, the present invention provides a method for predicting the strength of deep-sea surface sediments based on a random forest algorithm. Computational fluid dynamics simulation is used to obtain the penetration resistance acting on the T-Bar during the T-bar penetration of deep-sea surface sediments under different strengths, different rate effect parameters and different T-bar interface contact conditions. Through the random forest algorithm, the penetration resistance under this multi-parameter coupling effect is analyzed and trained, and a multi-parameter evaluation method for predicting the dimensionless penetration resistance coefficient of deep-sea sediments is established.

[0005] The present invention is implemented by the following technical solution: a method for predicting the strength of deep-sea surface sediments based on a random forest algorithm, specifically comprising the following steps:

[0006] Step S1, using computational fluid dynamics to simulate the whole process of full-flow penetrometer penetrating deep-sea sediments under different strengths, different rate effect parameters and different T-Bar interface contact conditions under the influence of environmental water, obtaining dimensionless penetration resistance coefficient data N, and forming a machine learning data set with rate effect parameter γ, dimensionless penetration depth h / D and penetration resistance Q;

[0007] Step S2, performing data exploration and preprocessing on sample data of dimensionless penetration resistance coefficient obtained by numerical simulation, determining input and output data of machine learning, and dividing into training set and test set;

[0008] Step S3: Use the machine learning random forest algorithm to perform model training, standardize the input and output data of the training set, establish a random forest regression model, and perform hyperparameter optimization to determine the optimal model;

[0009] Step S4: Use the evaluation index of the machine learning regression model to evaluate the accuracy of the optimal model, and then use cross-validation and Monte Carlo simulation to evaluate the generalization ability and stability of the model.

[0010] As a preferred solution, step S1 specifically includes the following steps: deep sea surface sediments and environmental water are defined as two incompressible fluids, and a heterogeneous incompressible Euler-Euler two-phase flow model is used to simulate the flow process of the two fluids around the T-bar; the mathematical model includes a continuity equation and a momentum equation,

[0011] The continuity equation is expressed as:

[0012]

[0013] where r α ,ρ α and U α Volume fraction, density and velocity of ultrasoft sediments in the deep sea surface layer;

[0014] The momentum equation is expressed as:

[0015]

[0016] Where: P α is the pressure of deep sea surface sediments, μ α The dynamic viscosity of deep-sea surface sediments is expressed as: S Mα is the momentum source caused by external load; M α It is the interphase force of ultra-soft sediments in the deep sea surface under the influence of environmental water;

[0017] M α can be calculated by formula (3):

[0018]

[0019] in: is the contact drag A is the interphase resistance generated by the α phase (ambient water) on the β phase (deep sea surface sediment);

[0020]

[0021] Where: β and U β is the density and velocity of the surrounding water; C D is the drag coefficient, which is taken as 2.0 here; A α The contact area is calculated as:

[0022] As a preferred solution, step S2 specifically includes the following steps: performing preliminary statistical analysis on the data set, including correlation analysis and multicollinearity analysis, to perform feature selection; then, randomly dividing the data set into two parts according to a fixed ratio, namely a training set and a test set, for training and testing the model;

[0023] The model input parameters are the rate effect parameter γ, dimensionless penetration depth h / D and penetration resistance Q, and the model output parameter is the dimensionless penetration resistance coefficient N. The correlation coefficient is used to represent the correlation between two groups of variables. The most commonly used correlation coefficient indicator is the Pearson linear correlation coefficient R, and its calculation formula is shown in formula (5):

[0024]

[0025] Where n is the number of samples; x i and i are the i-th values ​​of the two sets of data respectively, Hewei Average value; S 2 is the sample variance; for the Pearson linear correlation coefficient, if R=0, it means there is no correlation between the two sets of data, R>0, positive correlation, R<0, negative correlation;

[0026] In multicollinearity analysis, the Pearson correlation coefficient between any two variables is first calculated, and then the penalty degree (TOL) and variance inflation factor (VIF) are calculated to further test the multicollinearity between the variables. The calculation formulas are shown in the following formulas (6) and (7):

[0027]

[0028]

[0029] The coefficient of determination is the probability that the explanatory variable j is regressed over all explanatory variables, and a penalty less than 0.2 or a variance inflation factor greater than 5 indicates the presence of multicollinearity problems.

[0030] As a preferred solution, in step S3, the random forest regression model adopts a binary decision regression tree, and the minimum mean square error principle is used for splitting to construct a new decision tree, and the subsequent branch nodes adopt the same criterion to form a complete random forest; the final output result of the random forest is the average value of all decision tree results;

[0031] In the process of constructing the binary decision regression tree of the random forest model, the exhaustive method is used to construct the training data set D = {(x1, y1), (x2, y2), …, (x N ,y N )} in the input space In the above example, n is the number of features (independent variables) and N is the number of samples. Recursively divide each region into two sub-regions R1 and R2, and determine the output value of each sub-region. Then traverse each feature and its value to find the most suitable node and split feature selection.

[0032] Furthermore, constructing a binary decision tree specifically includes the following steps:

[0033] Step S3-1, select the optimal segmentation variable j and segmentation point s according to the minimum mean square error principle, and solve:

[0034]

[0035] Step S3-2, traverse the variable j, scan the split point s for the fixed split variable j, and select the pair (j, s) that makes the formula (8) reach the minimum value;

[0036] Step S3-3: Divide the region using the selected pair (j, s) and determine the corresponding output value

[0037] R1(j,s)={x|x {j} ≤s},R2(j,s)={x|x {j} >s} (9)

[0038]

[0039] Step S3-4, continue to call steps S3-1 and S3-2 for the two sub-areas until the stop condition is met;

[0040] Step S3-5: Divide the input space into M regions R1, R2, ..., R M , generate a decision tree:

[0041]

[0042] Step S3-6, average the results of all decision trees:

[0043]

[0044] Step S3-7, forming a complete random forest model according to the maximum depth of the set model;

[0045] Where j = 1, 2, ..., n, s ∈ x i , I is the indicator function, I = sgn(x), (x∈R m ), f(x) is a single decision tree, is the combined random forest model, and k is the number of decision trees in the complete random forest.

[0046] As a preferred solution, the evaluation of model capability in step S4 is divided into three parts: accuracy, generalization ability and stability;

[0047] The accuracy of the model is evaluated using three validation statistical parameters, including the coefficient of determination R2, the mean absolute error MAE, and the mean absolute percentage error MAPE. The calculation formulas for the three evaluation indicators are:

[0048]

[0049] Where: y i represents the dimensionless drag coefficient (true value) obtained from numerical simulation; represents the dimensionless drag coefficient predicted by the random forest model (predicted value); represents the average value of the true value; M represents the number of data samples;

[0050] The generalization ability of the model is evaluated by cross-validation method, which is as follows: divide the data into k parts, use one of them as the test set, and use the other k-1 parts as the training set, calculate the accuracy of the model multiple times to evaluate the average accuracy of the model; the k value in the cross-validation of the model is usually selected as 5 or 10, and R2 is used as the evaluation indicator of model accuracy;

[0051] The stability of the model is evaluated by Monte Carlo simulation, specifically: n Monte Carlo simulations are performed. In each simulation, the training set and the test set are randomly divided according to a fixed ratio, and then the normalized convergence determinism coefficient R2, the normalized convergence root mean square error RMSE and the normalized convergence mean absolute error MAE of the training set and the test set are calculated. The calculation formula is:

[0052]

[0053] Where n is the number of Monte Carlo simulations; W kis the kth value of the random variable W; is the mean of the random variable W. Here, the random variable W can be R2, RMSE and MAE respectively. The calculation of R2 and MAE is given by formula (13) and formula (14) respectively. The calculation formula of RMSE is: The meanings of the variables in the formula are the same as those in formula (13).

[0054] The method for predicting the strength of deep-sea surface sediments based on computational fluid dynamics numerical simulation and random forest algorithm of the present invention can accurately evaluate the strength of deep-sea surface sediments through computational fluid dynamics multi-condition numerical simulation and machine learning algorithm. Due to the adoption of the above technical solution, the present invention has the following beneficial effects compared with the prior art:

[0055] (1) Compared with the segmented curve fitting of the traditional prediction method, the present invention integrates the dimensionless penetration resistance coefficient prediction into a mathematical model, covering the prediction of the penetration resistance coefficient at full depth and throughout the entire process;

[0056] (2) The deep-sea surface sediments in the present invention conform to the shear behavior of plastic fluids and can be described more accurately in the framework of fluid mechanics. The present invention uses computational fluid dynamics methods to well simulate the interaction between this plastic fluid with shear-thinning characteristics and the ocean structure, and accurately quantify the forces acting on the ocean structure;

[0057] (3) Compared with the existing numerical simulation and indoor physical test methods under the framework of soil mechanics, the present invention is economical, time-saving and labor-saving, and the calculation results are more reasonable and reliable, and has certain novelty;

[0058] (4) The present invention is simple to operate and easy to apply in practice. The trained random forest model overcomes the problem of low efficiency of numerical simulation calculations and provides a new method and idea for quickly and conveniently estimating deep-sea surface sediment parameters.

[0059] Additional aspects and advantages of the present invention will become apparent from the following description or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0061] Figure 1 The present invention is a flow chart of a method for evaluating the strength of deep-sea surface sediments based on a random forest algorithm;

[0062] Figure 2 Geometric model, boundary conditions and grid information for numerical simulation of T-bar penetration into deep-sea surface sediments;

[0063] Figure 3 is the dimensionless penetration resistance coefficient as a function of dimensionless depth under various rate effect parameters, undrained shear strength and T-Bar boundary conditions;

[0064] Figure 4 is the thermal diagram of the correlation coefficient between the condition factor and the dimensionless penetration resistance;

[0065] Figure 5 Flowchart for model training and hyperparameter optimization for random forests

[0066] Figure 6 R of the random forest model under different hyperparameters 2 ;

[0067] Figure 7 Comparison between the true value and predicted value of the random forest model;

[0068] Figure 8 The 10-fold cross validation results of the model on the training set and test set;

[0069] Fig. 9 The normalized convergence determinism coefficient R obtained for 200 Monte Carlo simulations 2 , normalized convergence root mean square error RMSE, normalized convergence mean absolute error MAE. DETAILED DESCRIPTION

[0070] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0071] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0072] Combine the following Figures 1 to 9 The deep sea surface sediment intensity prediction method based on random forest algorithm according to an embodiment of the present invention is specifically described.

[0073] The present invention proposes a method for predicting the strength of deep-sea surface sediments based on a random forest algorithm. The basic flow chart is as follows: Figure 1 As shown, the specific steps include:

[0074] Step S1, using computational fluid dynamics to simulate the whole process of full-flow penetrometer penetrating deep-sea sediments under different strengths, different rate effect parameters and different T-Bar interface contact conditions under the influence of environmental water, obtaining dimensionless penetration resistance coefficient data N, and forming a machine learning data set with rate effect parameter γ, dimensionless penetration depth h / D and penetration resistance Q;

[0075] The deep-sea surface sediments and environmental water are defined as two incompressible fluids. The heterogeneous incompressible Euler-Euler two-phase flow model is used to simulate the flow process of these two fluids around the T-bar. The mathematical model includes the continuity equation and the momentum equation.

[0076] The continuity equation is expressed as:

[0077]

[0078] where r α ,ρ α and U α Volume fraction, density and velocity of ultrasoft sediments in the deep sea surface layer;

[0079] The momentum equation is expressed as:

[0080]

[0081] Where: P α is the pressure of deep sea surface sediments, μ α The dynamic viscosity of deep-sea surface sediments is expressed as: S Mα is the momentum source caused by external load; M α It is the interphase force of ultra-soft sediments in the deep sea surface under the influence of environmental water;

[0082] M α can be calculated by formula (3):

[0083]

[0084] in: is the contact drag A is the interphase resistance generated by the α phase (ambient water) on the β phase (deep sea surface sediment);

[0085]

[0086] Where: β and U β is the density and velocity of the surrounding water; C D is the drag coefficient, which is taken as 2.0 here; A α The contact area is calculated as:

[0087] Here, the sediment and the ambient water are not mixed and have independent velocity fields, density fields, viscosity fields, etc., and only the pressure field is shared. The coupling of the two fluids is achieved through the interphase force M α accomplish.

[0088] According to the above coupling model, numerical simulations were carried out to study the interaction between deep-sea sediments and T-Bar. During the simulation, different undrained shear strengths, rate effect parameters and boundary conditions were set for the deep-sea surface sediments. T-Bar penetrated the deep-sea surface sediments at a constant speed. The simulation process can be performed using commercial software. After the simulation is completed, the sample data of the dimensionless penetration resistance coefficient N under different conditions are calculated, and the machine learning data set is formed together with the rate effect parameter γ, the dimensionless penetration depth h / D and the penetration resistance Q.

[0089] It should be noted that in the specific implementation process, the deep-sea surface sediments were set to different undrained shear strengths (0.5 kPa, 1.0 kPa, and 1.5 kPa) and various rate effect parameters (0, 0.1, 0.2, and 0.3), and T-Bar was simulated under no-slip and free-slip boundary conditions to represent the smooth and rough interface contact relationship. The geometric model and boundary conditions are as follows: Figure 2 (a) and (b) show that the T-Bar penetrates deep-sea surface sediments at a speed of 20 mm / s. Figure 2 (c) is the mesh after mesh sensitivity analysis. The simulation process was carried out using the commercial software ANSYS CFX. After the simulation was completed, the sample data of the dimensionless penetration resistance coefficient N under different conditions were calculated, and the machine learning data set was formed with the rate effect parameter γ, dimensionless penetration depth h / D and penetration resistance Q;

[0090] Step S2, performing data exploration and preprocessing on sample data of dimensionless penetration resistance coefficient obtained by numerical simulation, determining input and output data of machine learning, and dividing into training set and test set;

[0091] Perform preliminary statistical analysis on the data set, including correlation analysis and multicollinearity analysis, to select features; then, randomly divide the data set into two parts, training set and test set, in a fixed ratio, for model training and testing;

[0092] It should be noted that the model input parameters are the rate effect parameter γ, the dimensionless penetration depth h / D and the penetration resistance Q. The model output parameter is the dimensionless penetration resistance coefficient N. The total sample size of the data is 9589, including 4799 free slip T-bar samples and 4790 no-slip T-bar samples. The statistical characteristics of the machine learning sample data are calculated, and feature selection is performed, including correlation analysis and multicollinearity analysis.

[0093] Table 1 shows the statistical characteristics of machine learning sample data

[0094]

[0095] In order to perform feature selection more effectively, the input and output parameters are subjected to correlation analysis, and the correlation coefficient is used to indicate the degree of correlation between two groups of variables. The most commonly used correlation coefficient indicator is the Pearson linear correlation coefficient R, and its calculation formula is shown in formula (5):

[0096]

[0097] Where n is the number of samples; x i and i are the i-th values ​​of the two sets of data respectively, Hewei Average value; S 2 is the sample variance; for the Pearson linear correlation coefficient, if R=0, it means there is no correlation between the two sets of data, R>0, positive correlation, R<0, negative correlation;

[0098] Figure 4 The correlation heat map of input and output parameters is shown. It can be seen from the figure that γ, h / D and Q are all positively correlated with N. Among them, Q has the strongest linear correlation with N, with a correlation coefficient of 0.536, followed by γ with a correlation coefficient of 0.275, and finally h / D with a correlation coefficient of 0.149.

[0099] In the multicollinearity analysis, the Pearson correlation coefficient between any two variables is first calculated, and then the penalty (TOL) and variance inflation factor (VIF) are calculated to further test the multicollinearity between the variables. The calculation formulas are shown in the following formulas (6) and (7). Table 2 lists the penalty and variance inflation factor (Tolerance and VIF) of all feature variables used in the random forest regression model. The penalty of all variables is above 0.2, and the variance inflation factor is less than 5, which indicates that there is no multicollinearity problem in the feature data.

[0100]

[0101] The coefficient of determination is the probability that the explanatory variable j is regressed over all explanatory variables, and a penalty less than 0.2 or a variance inflation factor greater than 5 indicates the presence of multicollinearity problems.

[0102] Table 2 shows the variance inflation factors of the variables

[0103] feature Penalty Level (TOL) Variance Inflation Factor (VIF) Penetration strength (Q) 0.236 4.231 Dimensionless penetration depth (h / D) 0.294 3.406 Rate effect parameter (γ) 0.408 2.451

[0104] Based on the above correlation analysis and multicollinearity analysis, the data features in this embodiment are all positively correlated with the target parameter N, and there is no multicollinearity between the features. Therefore, all feature data can be used for random forest model training and testing. On this basis, the data set is divided into training set and test set in a ratio of 7:3.

[0105] Step S3: Use the machine learning random forest algorithm to perform model training, standardize the input and output data of the training set, establish a random forest regression model, and perform hyperparameter optimization to determine the optimal model; Figure 5 Flowchart built for the random forest prediction model;

[0106] The random forest regression model uses a binary decision regression tree. When splitting, it uses the minimum mean square error principle to split to build a new decision tree. Subsequent branch nodes use the same principle to form a complete random forest. The final output result of the random forest is the average of all decision tree results.

[0107] In the process of constructing the binary decision regression tree of the random forest model, the exhaustive method is used to construct the training data set D = {(x1, y1), (x2, y2), …, (x N ,y N )} in the input space In the above example, n is the number of features (independent variables) and N is the number of samples. Recursively divide each region into two sub-regions R1 and R2, and determine the output value of each sub-region. Then traverse each feature and its value to find the most suitable node and split feature selection.

[0108] Constructing a binary decision tree specifically includes the following steps:

[0109] Step S3-1, select the optimal segmentation variable j and segmentation point s according to the minimum mean square error principle, and solve:

[0110]

[0111] Step S3-2, traverse the variable j, scan the split point s for the fixed split variable j, and select the pair (j, s) that makes the formula (8) reach the minimum value;

[0112] Step S3-3: Divide the region using the selected pair (j, s) and determine the corresponding output value

[0113] R1(j,s)={x|x {j} ≤s},R2(j,s)={x|x {j} >s} (9)

[0114]

[0115] Step S3-4, continue to call steps S3-1 and S3-2 for the two sub-areas until the stop condition is met;

[0116] Step S3-5: Divide the input space into M regions R1, R2, ..., R M , generate a decision tree:

[0117]

[0118] Step S3-6, average the results of all decision trees:

[0119]

[0120] Step S3-7, forming a complete random forest model according to the maximum depth of the set model;

[0121] Where j = 1, 2, ..., n, s ∈ x i , I is the indicator function, I = sgn(x), (x∈R m ), f(x) is a single decision tree, is the combined random forest model, and k is the number of decision trees in the complete random forest.

[0122] After the initial training and testing of the model, the random forest is subjected to hyperparameter optimization to adjust the model parameters to improve performance. The hyperparameters include the number of decision trees, the maximum tree depth, the maximum number of features, the minimum number of samples required to split an internal node, and the minimum number of samples contained in a leaf node. Hyperparameter optimization is performed using k-fold cross validation on a fixed-ratio dataset, based on grid search.

[0123] It should be noted that in step S2, 70% of the training set is first standardized. The standardization is calculated based on the mean and standard deviation of the training set features. The training set is used to perform preliminary training on the random forest model to determine the performance of the basic model. After the preliminary training model, hyperparameter optimization is performed through grid search to adjust the model parameters to improve performance. Hyperparameter optimization uses 10-fold cross validation on 70% of the data set, based on Sklearn's grid search implementation. Model hyperparameters include the number of decision trees, the maximum tree depth, the maximum number of features, the minimum number of samples required to split internal nodes, and the minimum number of samples contained in leaf nodes.

[0124] Table 3 shows the optimal hyperparameter range, step size and value of the random forest model for hyperparameter optimization

[0125] Hyperparameters Hyperparameter Ranges Stepover Optimal value Number of estimators (n_estimators) 0～200 10 31 Maximum tree depth (max_depth) 3～20 1 16 Minimum number of samples required to split an internal node (min_samples_split) 1～20 1 2 The minimum number of samples contained in a leaf node (min_samples_leaf) 1～10 1 1 Maximum number of features (max_features) 1～3 1 3

[0126] Figure 6 Learning curves of random forest accuracy versus key hyperparameters are shown.

[0127] After training the random forest model using 70% of the training set (6712 samples), the prediction effect was tested on the 30% test set (2877 samples). The performance of the model on the training set and the test set is compared, as shown in Figure 2. Figure 7 As shown in Figure 2, it can be seen that the model performs well on the training set and the test set, and the predicted dimensionless penetration resistance coefficient is close to the actual value. Figure 7 The closeness between the predicted and actual values ​​of the dimensionless penetration resistance coefficient on the training set and the test set and the distribution of prediction errors are shown. On the training set, the absolute error is in the range of 0 to 0.830, and 99.42% of the error data fall within the 1% error line (0 to 0.176). On the test set, the absolute error is in the range of 0 to 2.215, and 98.31% of the error data fall within the 1% error line (0 to 0.176), with only a few data errors exceeding the 1% error line. It can be seen from the box plot that the mean absolute error of the training set and the test set is close to 0, and there are some outliers, indicating that the model has a small error on the training set and the test set and performs well. Therefore, the model can be used to predict the dimensionless penetration resistance coefficient.

[0128] Step S4: Use the evaluation index of the machine learning regression model to evaluate the accuracy of the optimal model, and then use cross-validation and Monte Carlo simulation to evaluate the generalization ability and stability of the model.

[0129] The evaluation of model capabilities is divided into three parts: accuracy, generalization ability and stability;

[0130] The accuracy of the model was evaluated using three validation statistical parameters, including the coefficient of determination R 2 , mean absolute error MAE and mean absolute percentage error MAPE. The calculation formulas for the three evaluation indicators are:

[0131]

[0132] Where: y i represents the dimensionless drag coefficient (true value) obtained from numerical simulation; represents the dimensionless drag coefficient predicted by the random forest model (predicted value); represents the average value of the true value; M represents the number of data samples;

[0133] The generalization ability of the model is evaluated by cross-validation method, which is as follows: divide the data into k parts, use one of them as the test set and the other k-1 parts as the training set, calculate the accuracy of the model multiple times to evaluate the average accuracy of the model; the k value in the cross-validation of the model is usually selected as 5 or 10, and the R 2 As an evaluation metric for model accuracy;

[0134] The stability of the model is evaluated by Monte Carlo simulation, which is as follows: n Monte Carlo simulations are performed, in each simulation, the training set and the test set are randomly divided according to a fixed ratio, and then the normalized convergence determinism coefficient R of the training set and the test set is calculated. 2 , normalized convergence root mean square error RMSE and normalized convergence mean absolute error MAE, the calculation formula is:

[0135]

[0136] Where n is the number of Monte Carlo simulations; W k is the kth value of the random variable W; is the mean of the random variable W, where the random variable W can be R 2 , RMSE and MAE, R 2 The calculation of and MAE are given by formula (13) and formula (14) respectively, and the calculation formula of RMSE is: The meanings of the variables in the formula are the same as those in formula (13).

[0137] It should be noted that in the specific implementation process, the optimal model obtained by hyperparameter optimization is used to predict the dimensionless penetration resistance coefficient of the training set, the test set and the entire data, and then the determination coefficient R of the training set, the test set and the entire data in this embodiment is calculated according to formula (13), formula (14) and formula (15). 2 , mean absolute error (MAE) and mean absolute percentage error (MAPE).

[0138] Table 4 shows the evaluation indicators of the prediction model on the training set, test set and all data

[0139]

[0140] As shown in Table 4, it can be seen that the prediction results of the dimensionless penetration resistance coefficient based on the random forest model are relatively ideal, and various evaluation indicators have been maintained at a high level. Therefore, the random forest model is suitable for predicting the penetration resistance coefficient.

[0141] In the cross-validation of the model, k is selected as 10, and R 2 As an evaluation indicator of model accuracy, 10-fold cross validation was performed on the training set and the test set. The cross validation results are as follows Figure 8 As shown in Figure 2, through 10-fold cross validation, we can see that the random forest model performs well. During the 10-fold cross validation process, R 2 The minimum value is 0.9970, the maximum value is 0.9993, and the average R 2 It is 0.9981. This shows that the model has strong generalization ability and can maintain high prediction accuracy on other new data.

[0142] 200 Monte Carlo simulations were performed to evaluate the generalization ability of the model. In each simulation, the training set and the test set were randomly divided into two groups according to a ratio of 7:3, and then the normalized convergence determinism coefficient R of the training set and the test set was calculated according to formula (16): 2 , root mean square error RMSE, mean absolute error MAE. In addition, the statistical characteristics of the three evaluation parameters of the training set and the test set in 200 simulations were evaluated by box plots, such as Fig. 9 The prediction model established above performs relatively stably on the training set and is basically not affected by the randomness of the data set division. However, it is slightly unstable on the test set, but the normalized R 2 , RMSE and MAE all converge to 1 after 100 simulation runs, and the overall performance of the model is relatively stable. Overall, it can be seen from the box plot that the training set R 2 , RMSE and MAE are better than the test set, but the test set error is still small ( - represents the mean), indicating that the model performs well.

[0143] In the description of this specification, the description of the terms "one embodiment", "some embodiments", "specific embodiments", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0144] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the strength of deep-sea surface sediments based on random forest algorithm, characterized in that , specifically including the following steps: Step S1, using computational fluid dynamics to simulate the whole process of full-flow penetrometer penetrating deep-sea sediments under different strengths, different rate effect parameters and different T-Bar interface contact conditions under the influence of environmental water, obtaining dimensionless penetration resistance coefficient data N, and forming a machine learning data set with rate effect parameter γ, dimensionless penetration depth h / D and penetration resistance Q; The deep-sea surface sediments and environmental water are defined as two incompressible fluids. The heterogeneous incompressible Euler-Euler two-phase flow model is used to simulate the flow process of these two fluids around the T-bar. The mathematical model includes the continuity equation and the momentum equation. The continuity equation is expressed as: where r α ,ρ α and U α Volume fraction, density and velocity of ultrasoft sediments in the deep sea surface layer; The momentum equation is expressed as: Where: P α is the pressure of deep sea surface sediments, μ α The dynamic viscosity of deep-sea surface sediments is expressed as: S Mα is the momentum source caused by external load; M α It is the interphase force of ultra-soft sediments in the deep sea surface under the influence of environmental water; M α can be calculated by formula (3): in: is the contact drag force A is the interphase resistance exerted by the α-phase environmental water on the β-phase deep-sea surface sediments; Where: β and U β is the density and velocity of the surrounding water; C D is the drag coefficient, which is taken as 2.0 here; A α The contact area is calculated as: A α =|▽r α ; Step S2, performing data exploration and preprocessing on sample data of dimensionless penetration resistance coefficient obtained by numerical simulation, determining input and output data of machine learning, and dividing into training set and test set; Step S3: Use the machine learning random forest algorithm to perform model training, standardize the input and output data of the training set, establish a random forest regression model, and perform hyperparameter optimization to determine the optimal model; The random forest regression model uses a binary decision regression tree. When splitting, it uses the minimum mean square error principle to split to build a new decision tree. Subsequent branch nodes use the same principle to form a complete random forest. The final output result of the random forest is the average of all decision tree results. In the process of constructing the binary decision regression tree of the random forest model, the exhaustive method is used to construct the training data set D = {(x1, y1), (x2, y2), …, (x N ,y N )} in the input space In the formula, n is the number of features and N is the number of samples. Recursively divide each region into two sub-regions R1 and R2, and determine the output value of each sub-region. Traverse each feature and its value to find the most suitable node and split feature selection. Constructing a binary decision tree specifically includes the following steps: Step S3-1, select the optimal segmentation variable j and segmentation point s according to the minimum mean square error principle, and solve: Step S3-2, traverse the variable j, scan the split point s for the fixed split variable j, and select the pair (j, s) that makes the formula (8) reach the minimum value; Step S3-3: Divide the region using the selected pair (j, s) and determine the corresponding output value R1(j,s)={x|x {j} ≤s},R2(j,s)={x|x {j} >s} (9) Step S3-4, continue to call steps S3-1 and S3-2 for the two sub-areas until the stop condition is met; Step S3-5: Divide the input space into M regions R1, R2, ..., R M , generate a decision tree: Step S3-6, average the results of all decision trees: Step S3-7, forming a complete random forest model according to the maximum depth of the set model; Where j = 1, 2, ..., n, s ∈ x i , I is the indicator function, I = sgn(x), (x∈R m ), f(x) is a single decision tree, is the combined random forest model, k is the number of decision trees in the complete random forest. Step S4: Use the evaluation indicators of the machine learning regression model to evaluate the accuracy of the optimal model, and then use cross-validation and Monte Carlo simulation to evaluate the generalization ability and stability of the model.

2. A method for predicting the strength of deep sea surface sediments based on a random forest algorithm according to claim 1, characterized in that ,The step S2 specifically includes the following steps: ,perform preliminary statistical analysis on the data set, including correlation ,analysis and multicollinearity analysis to perform feature selection; ,then, the data set is randomly divided into two parts in a fixed ,ratio, respectively as a training set and a test set, for training and testing of the ,model; The model input parameters are the rate effect parameter γ, dimensionless penetration depth h / D and penetration resistance Q, and the model output parameter is the dimensionless penetration resistance coefficient N. The correlation coefficient is used to represent the correlation between two groups of variables. The most commonly used correlation coefficient indicator is the Pearson linear correlation coefficient R, and its calculation formula is shown in formula (5): Where n is the number of samples; x i and i are the i-th values ​​of the two sets of data respectively, Hewei Average value; S 2 is the sample variance; for the Pearson linear correlation coefficient, if R=0, it means there is no correlation between the two sets of data, R>0, positive correlation, R<0, negative correlation; In multicollinearity analysis, the Pearson correlation coefficient between any two variables is first calculated, and then the penalty degree (TOL) and variance inflation factor (VIF) are calculated to further test the multicollinearity between the variables. The calculation formulas are shown in the following formulas (6) and (7): The coefficient of determination is the probability that the explanatory variable j is regressed over all explanatory variables, and a penalty less than 0.2 or a variance inflation factor greater than 5 indicates the presence of multicollinearity problems.

3. The method for predicting the strength of deep sea surface sediments based on random forest algorithm according to claim 1 is characterized in that ,The evaluation of the model capability in the step S4 is divided into three parts: accuracy, ,generalization ability and stability; The accuracy of the model was evaluated using three validation statistical parameters, including the coefficient of determination R 2 , mean absolute error MAE and mean absolute percentage error MAPE. The calculation formulas for the three evaluation indicators are: Where: y i represents the dimensionless drag coefficient obtained from numerical simulation; represents the dimensionless drag coefficient predicted by the random forest model; represents the average value of the true value; m represents the number of data samples; The generalization ability of the model is evaluated by cross-validation method, which is as follows: the data is divided into k parts, one of which is used as the test set, and the other k-1 parts are used as the training set. The accuracy of the model is calculated multiple times to evaluate the average accuracy of the model. The k value in the cross-validation of the model is 5 or 10, and the R 2 As an evaluation metric for model accuracy; The stability of the model is evaluated by Monte Carlo simulation, which is as follows: n Monte Carlo simulations are performed, in each simulation, the training set and the test set are randomly divided according to a fixed ratio, and then the normalized convergence determinism coefficient R of the training set and the test set is calculated. 2 , normalized convergence root mean square error RMSE and normalized convergence mean absolute error MAE, the calculation formula is: Where n is the number of Monte Carlo simulations; W k is the kth value of the random variable W; is the mean of the random variable W, where the random variable W can be R 2 , RMSE and MAE, R 2 The calculation of and MAE are given by formula (13) and formula (14) respectively, and the calculation formula of RMSE is: The meanings of the variables in the formula are the same as those in formula (13).

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