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Sci Rep
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Scientific Reports
2045-2322
Nature Publishing Group UK London

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71928
10.1038/s41598-024-71928-9
Article
Comparative study of five machine learning algorithms on prediction of the height of the water-conducting fractured zone in undersea mining
Wu Zhengyu 1234
Chen Ying 5
Luo Dayou dyluo@iastate.edu

6
1 https://ror.org/01cyb5v38 grid.495258.7 School of Engineering, Fujian Jiangxia University, Fuzhou, 350108 Fujian China
2 Engineering Research Center of Phosphorus Resources Development and Utilization of Ministry of Education, Wuhan, 430000 Hubei China
3 https://ror.org/011xvna82 grid.411604.6 0000 0001 0130 6528 College of Civil Engineering, Fuzhou University, Fuzhou, 350016 Fujian China
4 Group Co., Ltd, Blooms Union, Wenzhou, 325024 Zhejiang China
5 https://ror.org/03mqfn238 grid.412017.1 0000 0001 0266 8918 School of Resources Environment and Safety Engineering, University of South China, Hengyang, 421000 Hunan China
6 https://ror.org/04rswrd78 grid.34421.30 0000 0004 1936 7312 Department of Civil, Construction and Environmental Engineering, Iowa State University, 813 Bissell Rd, Ames, IA 50011 USA
9 9 2024
9 9 2024
2024
14 2104719 3 2024
2 9 2024
© The Author(s) 2024
2024
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Prediction of water-conducting fractured zone (WCFZ) of mine overburden is the premise for reducing or eliminating water inrush hazards in undersea mining. To obtain a more robust and precise prediction of WCFZ in undersea mining, a WCFZ prediction dataset with 122 cases of fractured zones was constructed. Five machine learning algorithms (linear regression, XGBRegressor, RandomForestRegressor, LineareSVR, and KNeighborsRegressor) were employed to develop five corresponding predictive models, taking multiple factors into account.The optimal parameters for each model are obtained through ten-fold cross-validation (10CV). The model's predictive performance was validated and assessed using two metrics, namely the coefficient of determination (R2) and mean squared error (MSE). A comparison was made with the regression performance of commonly used empirical formulas. The results indicate that the constructed model outperforms reliance solely on theoretical criteria, showing a high R2 value of up to 0.925 and a low MSE value of 3.61. The proposed model was validated in a recently established mining area on Sanshan Island, China. It shows low absolute and relative errors of 0.71 m and 2.01%, respectively, between the predicted value from the model and observation result from the field, demonstrating a high level of consistency with on-site conditions. This paves a path to leveraging machine learning algorithms for predicting the height of WCFZ.

Keywords

Water-conductive fractured zone
Machine learning
Prediction model
Model comparison
Undersea mining
Subject terms

Civil engineering
Natural hazards
Engineering
National Natural Science Foundation of China52104122 Wu Zhengyu Open Project of Engineering Research Center of Phosphorus Resources Development and Utilization of Ministry of EducationLKF2021007 Wu Zhengyu Natural Fund project of Fujian Province Science and Technology Department2020J01943 Wu Zhengyu issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

As mineral resources continue to be depleted, easily accessible shallow resources are gradually exhausting. Deep-seated deposits, high-altitude deposits, and complex mining conditions such as underwater or seabed deposits have become important targets for extraction1,2. Underground mining disrupts the original balance of the stress field in the overlying rock, which easily leads to collapse, fracture, separation, and deformation of the overlying rock. The strata above the excavation area will settle at different displacements and rates, resulting in separation between the fracture surfaces in these strata3–5. The adjacent strata in the vertical direction will be separated due to differential displacement, forming cracks parallel to the stratum plane, which are called transverse cracks. In the horizontal direction, subsidence will break the formation into rock blocks. These rock blocks will rotate and separate, resulting in cracks that are either perpendicular to or intersect the formation plane, known as longitudinal cracks. As mining operations continue, cracks will continue to develop upwards6. If the mining area is located under a lake, river, or ocean, cracks will become channels that facilitate the flow of water7. Once the water extends to the bottom of the water-conducting fractured zone (WCFZ), it can trigger disasters8. Especially with the advancement of technology, the extraction of underwater minerals has gradually increased, making it prone to the formation of WCFZ, leading to water inflow and water inrush accidents9. The occurrence of water inrush accidents not only results in casualties and property losses but also disrupts the existing ecological environment10,11. According to statistics from the National Mine Safety Supervision Bureau investigation system, from 2003 to 2019, a total of 592 mine water inrush accidents occurred in China, resulting in 2,890 fatalities, as shown in Fig. 1. If the height of WCFZ is predicted before mining, and mining scale and methods are adjusted reasonably, it can prevent adverse interactions between the WCFZ and the overlying aquifer12. Therefore, accurately predicting the height of WCFZ in underwater mining, and achieving water-protected extraction, holds both theoretical and practical significance for safe mining and environmental protection.Fig. 1 Statistics on mine water inrush accidents in China from 2003 to 2019.

The estimation of WCFZ can be classified into two main categories: on-site measurement experiments and indoor prediction methods. In engineering practice, on-site measurements primarily include methods such as underground water injection leakage detection13, acoustic computed tomography (CT)14, borehole imaging technology15, resistivity scanning imaging technology16,17, and transient electromagnetic (TEM)18. On-site experiments can accurately determine the height of WCFZ. However, due to the complexity of underground or underwater mining environments, equipment operation, and cost constraints, On-site experiments are not widely used. Additionally, the data obtained from on-site measurements are real-time and can only be experimented with post-mining. Therefore it is challenging to accurately predict the height of WCFZ before extraction. Common indoor prediction methods include empirical formulas19,20, theoretical calculations21–23, numerical simulations24,25, physical models26,27, artificial intelligence11,28,29, etc. Normally summarized from on-site experiences, the use of empirical formulas is an easily operational method but only overly simplified factors are considered. Moreover, due to safety concerns, pillar thickness was normally exaggerated, which led to resource wastage. In theoretical calculations, mechanical theories simplify complex anisotropic rocks as ideal elastic–plastic bodies. However, influenced by assumptions and actual site conditions, these models often lack universality. It is a common challenge for numerical simulation methods to obtain precise geological condition parameters, which always require approximations or assumptions. Physical models demand high accuracy in material proportions and are unable to simulate specific complex geological conditions, in addition to being expensive and time-consuming.

In recent years, with the development of big data and machine learning, more and more researchers have been exploring the cross-integration of machine learning and various fields. For example, the Artificial neural network has been widely used to predict the height of a caving-fracturing zone30–32. Shahani et al.33 used four gradient-boosting machine learning algorithms to predict the uniaxial compressive strength of soft sedimentary rocks, and found that the XGBoost algorithm performed best in predicting the uniaxial compressive strength of soft sedimentary rocks. Kamran et al.34 developed a KNN-GWO model and successfully applied it to predict the stability of hard rock pillars. Kidega et al.35 and Kamran et al.36 applied machine learning to predict rockburst in underground engineering structures, which can further improve the prediction accuracy. A time-dependent model based on the energy balance was also proposed and validated to predict the height of the destressed zone in long-term condition37,38. Moreover, Razaei39 developed three methods, namely radial basis function neural network, fuzzy inference system, and statistical analysis models to predict the stress concentration coefficient around a mined panel, which showed high agreement with the real values.

At the same time, the prediction of the height of the WCFZ based on machine learning has developed rapidly. Hou et al.40 utilized a combination of genetic algorithms and a support vector machine to establish a predictive model for WFCZ height. Zhu et al.41 achieved favorable results in predicting the height of WCFZ by combining the Improved Cuckoo Search (ICS) algorithm with the Extreme Learning Machine (ELM). Guo et al.28 used a multi-population genetic algorithm (MPGA) to search for optimal SVR parameters, improving prediction accuracy and stability. Zhao et al.42 optimized the ELM model using the Grey Wolf Optimization Algorithm (GOA), Whale Optimization Algorithm (WOA), and Salp Optimization Algorithm (SOA). These prediction results were validated using measured data from a borehole television logging tool, showing good consistency in the predictions.

The aforementioned achievements in predicting the height of WCFZ are all of significant importance. However, due to the uncertainty and extreme complexity of accurately predicting WCFZ, developing an accurate and reliable model for predicting the WCFZ in overlying strata during mining remains a massive challenge. The accuracy and reliability of case-based methods for predicting WCFZ in overlying strata during mining mainly depend on the quantity and quality of cases involved in the analysis. Currently, most research is based on tens of cases, leading to less reliable and less generalizable predictive models. There is a need to further collect cases related to WCFZ in overlying strata during mining and establish a large dataset. On the other hand, existing methods have their specific applicability, lacking a universal solution. There is a shortage of predictive models with satisfying classification performance for WCFZ in overlying strata during mining. To address this challenge, a detailed analysis of the problem, dataset characteristics, and thorough performance evaluation of models are required to identify the optimal algorithm, improving the applicability and accuracy of predictive models.

To fill the current research gaps, this study established a large dataset containing 122 sets of engineering cases from literature related to WCFZ in overlying strata during mining. By introducing five common intelligent algorithms (LinearRegression, XGBRegressor, RandomForestRegressor, LinearSVR, and KNeighborsRegressor), five comprehensive predictive models for WCFZ in overlying strata during mining were constructed, considering multiple factors. Subsequently, the regression performance of the five models was comprehensively evaluated using the correlation coefficient R2 and Mean Squared Error (MSE). The predictive performance of these models was then compared with that of commonly used empirical formulas. Finally, based on the models developed in this study, an analysis of WCFZ in overlying strata during mining was conducted for the Xinli Mine Area on Sanshan Island, China, as depicted in Fig. 2.Fig. 2 Schematic diagram of the performance evaluation for WCFZ prediction based on the five models.

Data acquisition and analysis

Although the mechanism of WCFZ in overlying strata during mining is highly complex, involving a multitude of influencing factors, certain factors such as mining depth (H), hard rock proportion coefficient (c), mining thickness (d), and working face length (L)43 are generally considered worldwide. It should be noted that c is the ratio of the cumulative thickness of hard rock layers within the estimated height range (Hf) of the WCFZ to Hf itself. The formulas for calculating c and Hf are given by Eqs. (1) and (2), respectively.1 c=∑hHf

2 Hf=(15∼20)d

A total of 122 sets of non-duplicate and complete samples of WCFZ in overlying strata during mining were obtained from the available data, where 67 sets were sourced from Guo et al.28, 39 sets from Fan et al.44, and 16 sets from Chai et al.45, as shown in Table 1. The first 80% of the samples were designated as the training set, while the remaining 20% were allocated as the testing set.Table 1 Datasets.

No	H/m	c	d/m	L/m	Hf	No	H/m	c	d/m	L/m	Hf	
1	412.40	0.09	2.20	157.00	35.40	62	295.00	0.64	2.60	185.00	40.50	
2	489.00	0.47	4.50	160.00	54.79	63	453.60	0.16	4.00	195.00	44.96	
3	86.10	0.50	4.60	170.00	53.90	64	412.50	0.24	2.20	136.00	35.20	
4	472.50	0.53	4.50	132.00	57.45	65	320.00	0.60	1.23	90.00	31.98	
5	336.40	0.12	2.00	76.00	27.25	66	411.70	0.30	2.20	136.00	35.21	
6	89.00	0.95	2.03	69.00	45.86	67	475.00	0.37	6.10	170.00	64.60	
7	424.42	0.26	3.40	120.00	45.10	68	173.00	0.83	1.90	70.00	25.30	
8	590.00	0.51	9.00	220.00	76.37	69	282.00	0.74	4.00	71.00	33.00	
9	290.00	1.00	2.60	168.00	46.22	70	117.00	0.41	3.40	200.00	72.00	
10	290.00	0.18	2.60	168.00	39.14	71	350.00	0.36	2.50	135.00	20.00	
11	420.50	0.52	3.00	209.00	52.01	72	320.00	0.90	1.70	65.00	27.50	
12	357.00	0.38	7.53	170.00	61.90	73	150.00	0.30	2.00	174.00	58.40	
13	649.10	0.23	3.00	186.00	42.99	74	230.00	0.24	2.00	85.00	52.50	
14	475.20	0.28	3.90	209.00	49.05	75	101.00	0.45	2.20	158.00	63.00	
15	568.60	0.65	3.65	132.00	60.14	76	446.00	0.92	3.80	143.00	40.00	
16	557.25	0.45	5.80	186.00	65.25	77	173.00	0.78	1.90	70.00	26.70	
17	320.00	0.81	5.00	122.00	67.70	78	264.50	0.93	2.80	156.00	44.34	
18	412.55	0.08	2.20	157.00	35.20	79	475.00	0.37	6.10	170.00	64.60	
19	312.00	0.24	5.30	145.70	44.20	80	265.00	0.93	2.50	192.00	40.21	
20	679.00	0.46	2.10	180.00	44.54	81	264.50	0.26	2.80	148.50	40.35	
21	367.00	0.47	7.50	173.50	75.50	82	499.90	0.47	4.80	150.00	54.00	
22	403.20	0.10	1.80	120.00	22.61	83	450.00	0.89	4.30	55.00	42.50	
23	125.00	0.06	3.00	150.00	22.00	84	409.00	0.55	8.00	170.00	86.80	
24	665.00	0.19	7.50	222.00	53.70	85	269.00	0.52	8.13	193.00	72.90	
25	433.00	0.52	7.00	168.00	70.30	86	264.50	0.68	2.80	156.00	50.34	
26	434.10	0.35	3.00	145.00	47.55	87	265.00	0.93	2.80	156.00	44.34	
27	290.00	0.37	2.60	168.00	38.41	88	264.50	0.60	2.60	147.00	43.43	
28	485.00	0.36	4.80	175.00	62.50	89	290.00	0.26	2.80	148.50	40.35	
29	265.00	0.60	2.60	147.00	43.43	90	290.00	1.00	2.60	168.00	46.22	
30	269.00	0.68	2.80	156.00	50.34	91	290.00	0.37	2.60	168.00	38.41	
31	387.50	0.55	4.50	175.00	58.50	92	265.00	0.18	2.60	168.00	39.14	
32	441.97	0.36	3.40	120.00	48.90	93	265.00	0.93	2.50	192.00	40.21	
33	437.17	0.05	3.40	120.00	28.63	94	295.00	0.56	2.70	192.00	42.81	
34	463.00	0.62	7.60	116.00	86.40	95	433.00	0.64	2.60	185.00	40.50	
35	403.10	0.08	2.00	136.00	22.61	96	331.00	0.52	7.00	168.00	72.97	
36	476.40	0.63	3.65	132.00	57.49	97	312.00	0.55	7.40	160.00	64.25	
37	515.70	0.35	4.50	147.00	55.00	98	283.90	0.24	5.30	145.70	44.20	
38	450.00	0.72	8.00	170.00	86.80	99	665.00	0.63	5.70	177.90	51.40	
39	283.90	0.63	5.70	177.90	51.40	100	434.60	0.19	7.50	222.00	53.70	
40	499.90	0.47	4.80	150.00	54.79	101	418.60	0.62	8.70	153.00	71.00	
41	49.00	0.52	4.00	135.00	45.00	102	367.00	0.45	8.70	198.00	83.00	
42	420.06	0.14	3.00	145.00	30.29	103	357.00	0.47	7.50	173.50	75.50	
43	516.00	0.74	2.95	206.10	54.50	104	367.00	0.38	7.53	170.00	61.90	
44	367.00	0.41	7.52	190.00	61.77	105	520.00	0.41	7.52	190.00	61.77	
45	434.40	0.46	3.40	136.00	45.10	106	520.00	0.35	5.00	200.00	58.46	
46	445.40	0.07	4.00	195.00	38.81	107	570.00	0.33	5.00	180.00	67.86	
47	304.00	0.12	3.10	150.00	40.00	108	370.00	0.34	5.80	178.00	65.25	
48	362.80	0.33	2.00	138.00	31.62	109	370.00	0.45	4.50	135.00	57.47	
49	270.00	0.65	3.80	168.00	54.60	110	329.00	0.42	3.90	200.00	49.05	
50	331.00	0.55	7.40	160.00	64.25	111	475.00	0.45	8.10	134.00	83.90	
51	499.92	0.47	4.80	150.00	54.00	112	649.10	0.37	6.10	170.00	64.60	
52	351.30	0.53	2.00	105.00	36.99	113	272.00	0.23	3.00	186.00	42.99	
53	419.03	0.16	3.00	145.00	32.83	114	450.00	0.53	6.70	120.00	64.99	
54	357.70	0.33	2.00	128.00	33.96	115	490.00	0.65	9.50	123.00	78.00	
55	550.00	0.81	2.60	180.00	55.32	116	255.00	0.70	13.43	123.00	130.78	
56	265.00	0.56	2.70	192.00	42.81	117	270.00	0.50	5.10	78.00	51.30	
57	320.80	0.16	2.00	128.00	33.01	118	400.00	0.65	3.80	168.00	54.60	
58	316.80	0.14	2.00	128.00	31.61	119	485.00	0.81	5.77	154.00	70.70	
59	420.00	0.71	3.70	70.00	56.80	120	207.00	0.36	4.80	175.00	62.50	
60	478.30	0.54	3.85	209.00	52.15	121	368.00	0.51	7.69	240.00	62.31	
61	568.40	0.85	2.94	180.40	57.00	122	450.00	0.39	4.70	297.00	56.00	

At the same time, in order to more intuitively display the distribution of 122 sets of data, histograms are used to visualize the data. Figure 3 shows the histogram of input parameters. It can be seen that the distribution of mining depth data presents a double peak, centered around 300 and 500, respectively. This distribution is relatively dispersed and exhibits a large standard deviation. The P value is greater than 0.05, indicating that the data does not significantly deviate from the normal distribution. The data distribution of the hard rock proportion coefficient is close to the normal distribution, but there is a slight right skew, with a peak between 0.4 and 0.6. The P value is less than 0.05, indicating that the data deviates from the normal distribution. The mining thickness data distribution is biased to the right, showing a positive skewed distribution, with a peak between 2 and 4, after which the frequency gradually decreases, and the P value is very small, indicating that the data significantly deviates from the normal distribution. The data distribution of working face length is close to the normal distribution, but there is a right-skewed long tail, with a peak between 130 and 170. The P value is very small, indicating that the data significantly deviates from the normal distribution.Fig. 3 Histogram of input data.

Figure 4 shows the histogram of output parameters. The data of WCFZ roughly presents an unimodal distribution, with the peak appearing in the range of 40–60. The data gradually decreases after 60, with a long tail on the right side, indicating that there may be some large values in the data. From the fitted normal distribution curve, the data distribution has some deviation from the normal distribution.Fig. 4 Histogram of output parameters.

Each attribute has different units and values, so it is necessary to normalize the sample data, as shown in Eq. 3:3 Xij=xij-min(xij)max(xij)-min(xij)Yj=yj-min(yj)max(yj)-min(yj)

where, Xij represents the normalized value of the j-th input sample in the i-th attribute, and xij is the j-th input sample value in the i-th attribute before normalization. Similarly, Yj is the normalized value of the j-th output sample and yj is the j-th output sample value before normalization.

Prior to predicting the height of WCFZ in overlying strata during mining, it is necessary to analyze the factors influencing these fracture zones. This study employs the Pearson correlation coefficient to measure the influencing factors. The correlation coefficient is a real number ranging between [− 1, + 1]. When the correlation coefficient is between − 1 and 0, it indicates a negative correlation between variables; when the correlation coefficient is between 0 and 1, it indicates a positive correlation between variables; when the correlation coefficient is 0, there is no correlation between them. However, discussing the correlation between two variables requires consideration of the significance level. It is meaningless to only discuss the size of the correlation coefficient without mentioning the p-value; the correlation between the two variables may be due to chance factors. Therefore, it is necessary to assess the significance level of the correlation between two variables.

From Fig. 5 and Table 2, it can be observed that there is a weak positive correlation between d and L. However, the p-value in the table is 0.004 < 0.05, which indicates rejecting the null hypothesis. On the other hand, the weak negative correlation between d and H can be considered. However, the p-value is 0.017 < 0.05, indicating that the aforementioned statement needs further discussion. The correlation coefficient between the c and L is − 0.15 and the p-value is 0.11, indicating a weak negative correlation and a valid hypothesis in this case, respectively. Similarly, it is believed that there is a certain weak negative correlation between the c and H.Fig. 5 Correlation coefficients.

Table 2 Pearson correlation p-values.

Parameters	L	d	c	H	
L	0.000	0.004	0.110	0.613	
d	0.004	0.000	0.494	0.017	
c	0.110	0.494	0.000	0.078	
H	0.613	0.017	0.078	0.000	

Prediction models for WCFZ

Machine learning algorithms

LinearRegression

LinearRegression model is a commonly used regression algorithm to establish a linear relationship model between features and target variables. Its objective is to find the optimal model parameters by minimizing the difference between predicted values and actual values. This model is suitable for predicting continuous target variables with a simple and intuitive interpretability. It is widely applicable in many cases but requires additional attention when dealing with nonlinear problems and outliers46. Figure 6 shows the FLinearRegression flowchart.Fig. 6 Diagram of the LinearRegression process.

XGBRegressor

The XGBRegressor model is a regression model based on the Gradient Boosting Tree algorithm, which is widely used in modeling and predicting regression problems47. By integrating multiple weak learners and continuously optimizing the model's performance through iterative training. Its core involves optimizing the loss function through gradient descent in each iteration. However, when using the XGBRegressor model, it is important to set hyperparameters reasonably and handle the training time of large-scale datasets carefully. Figure 7 shows the structure diagram of the XGBRegressor model.Fig. 7 Schematic diagram of XGBRegressor structure.

RandomForestRegressor

The RandomForestRegressor model is a regression model based on the Random Forest algorithm. It constructs decision trees by randomly selecting features and samples, with each decision tree trained on different subsets of data and features48, as shown in Fig. 8. During prediction, the RandomForestRegressor model aggregates the predictions of all decision trees, obtaining the final regression prediction result through averaging or voting.Fig. 8 Schematic diagram of RandomForestRegressor structure.

LinearSVR

The LinearSVR model is a regression model based on the Support Vector Machine algorithm. It is a variant of the SVR algorithm used for solving regression problems. It works by finding an optimal hyperplane to divide the training data in the feature space into two parts, minimizing the difference between the predicted values of the target variable and the actual values. Unlike traditional SVR models, the Linear SVR model employs a linear kernel function, transforming nonlinear problems into linear ones49. Figure 9 is a structural diagram of the LinearSVR model.Fig. 9 Schematic diagram of LinearSVR structure.

KNeighborsRegressor

The KNeighborsRegressor model is a regression model based on the K-nearest neighbors’ algorithm. It works by finding the K nearest neighbors in the training data to a given test sample and making a regression prediction based on the target values of those neighbors50. This is a prediction based on similarity. When given a test sample unseen during training, the model calculates its distances to all samples in the training set and selects the K closest training samples. Then, it obtains the regression prediction for the test sample by averaging the target values of these K samples, weighted by their distances. Figure 10 provides a structural diagram of the KNeighborsRegressor model.Fig. 10 Schematic diagram of KNeighborsRegressor structure.

Algorithm optimization

During the model training process, ten-fold cross-validation (10CV) is employed to optimize the model parameters. Therefore, the optimal parameter combination within the given parameter space can be achieved, which enhances the performance and prediction accuracy of the regression model. In the grid search process, a series of prior candidate values for algorithm-related parameters are first provided. Through iterative traversal, all possible parameter value combinations are attempted to obtain the parameter value combination that yields the optimal algorithm performance, as depicted in Fig. 11.Fig. 11 Flowchart of 10CV.

Regression performance evaluation

First, the data is preprocessed. Then, the Pearson method is used to analyze the correlation between the height of the WCFZ and the influencing factors. The influencing factors are used as inputs for the prediction model. The influencing factors include mining depth, hard rock proportion coefficient, mining thickness, and working face length. Finally, the performance of each model is reflected through the prediction evaluation module, and variable contribution and importance are introduced to focus on the impact of important information related to the height of the WCFZ.

To assess the generalization performance of the five models constructed in this study, evaluation metrics that measure the models' generalization ability are needed. MSE and Coefficient of Determination (R2) are commonly used performance evaluation metrics in regression problems. The comparison between the predicted results of the models built using five different machine learning algorithms and the actual values is shown in Fig. 12 and Table 3.Fig. 12 Predicted results from (a) LinearRegression; (b) XGBRegressor; (c) RandomForestRegressor; (d) linear SVR; and (e) KNeighborsRegressor.

Table 3 Evaluation metrics for algorithms.

Evaluation metrics	LinearRegression	XGBRegressor	RandomForestRegressor	LinearSVR	KNeighborsRegressor	
R2	0.862	0.925	0.901	0.813	0.793	
MSE	10.15	3.61	7.81	25.76	32.47	

The results indicate that LinearRegression has a relatively high R2 value (0.862), explaining 86.2% of the variance in the target variable. It also has a low MSE of 10.15, indicating a small average deviation between predicted and actual values. Thus, the Linear Regression model performs well in prediction. XGBRegressor has the highest R2 value (0.925), explaining 92.5% of the variance in the target variable. It also has the lowest MSE (3.61), indicating the smallest average deviation between predicted and actual values. This is because XGBRegressor can handle nonlinear relationships well, exhibiting high predictive performance. Overall, the XGBRegressor performs the best in prediction. RandomForestRegressor has a relatively high R2 value (0.901), explaining 83.8% of the variance in the target variable. However, its MSE (7.81) is slightly higher than other models, indicating a larger average deviation between predicted and actual values. While performing well in prediction, it slightly lags behind the XGBoost regression model. LinearSVR has a relatively high R2 (0.813), explaining 81.3% of the variance in the target variable. However, its MSE (25.76) is also highe, indicating a larger average deviation between predicted and actual values. LinearSVR performs moderately in prediction due to its poor fit to nonlinear relationships and sensitivity to outliers. KNeighborsRegressor has a lower R2 value (0.793), indicating that the model explains 79.3% of the variance in the target variable. It also has a higher MSE (32.47), which means a larger average deviation between predicted and actual values. This model performs moderately in prediction, slightly inferior to other models.

Therefore, it can be concluded that the XGBRegressor performs the best in prediction, with the highest R2 value and the lowest MSE. Following that, LinearRegression and RandomForestRegression models perform well in prediction. LinearSVR and KNeighborsRegressor models exhibit moderate performance in prediction, slightly inferior to other models.

The residual plot is an important tool for assessing the fit and error structure of a regression model. In this paper, the established regression model is evaluated by analyzing the residual plot (Fig. 13). The residual plot displays the differences between predicted and actual values.Fig. 13 Residual plots of (a) LinearRegression; (b) XGBRegressor; (c) RandomForestRegressor; (d) Linear SVR; and (e) KNeighborsRegressor.

It can be found from Fig. 13a that the residual values vary within different ranges of predicted values. Although the MSE is slightly higher compared to some models, the LinearRegression model can also fit the data well overall. In contrast, the residual plot of the XGBRegressor model also exhibits characteristics of a random distribution, but compared to other models, its residual values are more concentrated around zero, indicating minimal deviation between predicted values and actual values. This further demonstrates the superiority of the XGBoost regression model in prediction. As for the RandomForestRegressor model, the residual plot presents a relatively random distribution, with residual values evenly distributed around zero, which suggests a good fitting can be obtained by this model. The residual plot of the LinearSVR model shows that most residual values are below zero, which might be due to systematic bias or failure to capture some important features in the data. However, additional feature engineering including feature transformation and selection, can be conducted to improve the predictive performance of the model. The residual plot of the KNeighborsRegressor model shows that the residual values decrease as the predicted values increase, and the residual values are relatively large, slightly inferior to other models.

It can be found from the residual plots that the XGBoost regression model performs the best in terms of prediction, followed by the LinearRegression and RandomForestRegressor models. In contrast, the predictive performance of the LinearSVR and KNeighborsRegressor models is relatively mediocre. The analysis of residual plots provides directions for improving model performance and further research to enhance predictive accuracy. For instance, since the residual plot of the KNeighborsRegressor model exhibits spatial autocorrelation, spatial regression models (such as SAR, SLM, SDM, etc.) can be considered to address the autocorrelation issue. For models with mediocre predictive performance (such as LinearSVR and KNeighborsRegressor), ensemble methods like Bagging and Boosting can be attempted, combining multiple models to improve overall predictive accuracy.

Meanwhile, this paper introduces variable contribution (Fig. 14) and importance (Fig. 15) to facilitate a quick understanding of the ranking of feature importance, which can achieve a more intuitive understanding of each feature’s contribution to a model’s prediction and their relative importance.Fig. 14 Contributions of (a) LinearRegression; (b) XGBRegressor; (c) RandomForestRegressor; (d) Linear SVR; and (e) KNeighborsRegressor.

Fig. 15 Importance plots of (a) LinearRegression; (b) XGBRegressor; (c) RandomForestRegressor; (d) Linear SVR; and (e) KNeighborsRegressor.

Shap (Shapley Additive Explanations) generates a prediction value for each sample with the model, and the Shap value is the numerical value assigned to each feature in that sample. Similar to the additive method of linear models, assuming the model's baseline score (often the mean of the target variable for all samples) is ybase, the i-th sample is xi, the j-th feature of the i-th sample is xi,j, and the Shap value of this feature is f(xi,j), then the model's prediction for sample xi is.4 yi=ybase+fxi,1+fxi,1+⋯+fxi,k

When f(xi,j) > 0, feature has a positive effect on the prediction of the target value; conversely, when f f(xi,j) < 0, the feature has a negative effect on the target prediction value. Therefore, Shap not only provides the magnitude of the feature's influence but also reflects the polarity of the influence of each feature in each sample.

In Fig. 14, the vertical axis ranks the features based on the sum of Shap values for all samples, while the horizontal axis represents the Shap values (the distribution of feature effects on the model output). Each point represents a sample, with the sample count stacked vertically, and the color indicates the feature value (red corresponds to high values, blue corresponds to low values). In Fig. 15, the absolute mean of Shap values for each feature is taken to obtain the distribution of feature importance, effectively blurring out the positive and negative influences seen in the previous figure.

From Figs. 14a and 15a, it can be observed that in the LinearRegression model, d is the most important feature. Points with lower d values have Shap values less than 0, indicating a negative impact on the prediction results, while higher values of d (red color) have a positive impact on the prediction results. The influence ranking of the other three features on the LinearRegression model is as follows: c > L > H. Both c and L have similar effects on d in the model, while H shows an opposite effect.

It is worth noting that most points of H are diffused around Shap = 0, indicating that it does not have a significant impact on most results but only affects a small portion of cases. From Figs. 14b and 15b, it can be seen that the influence of the first three features (d > c > L) on the XGBRegressor model is similar to that of the LinearRegression model. Higher values of H (red) have a negative impact on the prediction results. The importance ranking of the four features is the same. This may indicate that the features in the dataset have been adequately fitted to the target variable in both models, and the models have similar fitting effects. Therefore, it can be concluded that both models have similar abilities in explaining the variations in the dataset. Although the variable contribution rankings are the same, there are still differences in prediction performance and behavior between the models.

In the RandomForestRegressor model (Figs. 14c and 15c), d is the most important feature, with similar positive and negative impacts as described above. However, the importance of working face length, as indicated by the Shap values, is greater than that of the c. Both of them have points with low scores, where Shap values less than 0, indicating a negative impact on the prediction results. In the contrast, high scores (red) have a positive impact on the prediction results. For points with high values of d, the Shap values are less than 0, indicating a negative impact on the prediction results. For points with low values, the Shap values are greater than 0, indicating a positive effect. In the LinearSVR model (Figs. 14d and 15d), d has the most significant impact on the model, with effects similar to the three models mentioned above. However, the second most important feature is mining depth. Points with high scores have Shap values less than 0, indicating a negative impact on the prediction results, while low scores (red) have a positive impact on the prediction results. Following H in importance are L and c.

In the final KNeighborsRegressor model (Figs. 14e and 15e), it can be observed that H is the most important feature, but its Shap values are all on the right side of the vertical axis. This could indicate a nonlinear relationship between H and the prediction results, suggesting that the larger or smaller the value of the feature, the greater the impact on the prediction results. Following H in importance is L. It can be seen that points with low scores have Shap values less than 0, indicating a negative impact on the prediction results. Also, a positive effect can be indicated by thepoints with high scores and Shap values greater than 0. The d and c, thereafter, are diffused around Shap = 0, suggesting that they do not have a significant impact on most results but only affect a small portion of cases.

Case study

Background

By comparing with traditional methods, a comparative study was conducted in the Xinli Mine area in the southwest of the Sanshan Island gold mine in Shandong Province, China. The height of the fractured zone in the mining-induced overlying strata was predicted to further validate the effectiveness and engineering value of each model.

The Xinli Mine area is located at the confluence of the Bohai Bay and Wang River, with the Bohai Bay surrounding the west and north sides of the mining area, as shown in Fig. 16, with a total length of approximately 5000 km. The surface water of the mining area mainly comes from these two bodies of water. The ore body is mainly located below the Wang River and Bohai Bay, with an angle of approximately 60° with the coastline, and the dip angle of the ore is 46°. Based on the relationship between the bodies of water, it can be seen that the Xinli Mine area is largely influenced by seawater. The hard rock mainly consists of conglomerate and sandstone, and the aquifer is relatively abundant. The geological wells in the Xinli Mine area can illustrate the structure of the strata, as shown in Fig. 17.Fig. 16 The geographical location of Xinli Mine area in Sanshan Island, China. The map was generated with CNSKnowall Version 0151 and Gditu Version 202352.

Fig. 17 Geological column diagram of the Xinli Mine area.

There are many mining methods for undersea mining in the Sanshan Island Gold Mine, among which there are two main mining methods for mining close to the upper part, namely the point pillar upward layered filling mining method and the upward access mechanized filling mining method.

The point pillar upward horizontal layered filling mining method leaves point pillars to assist in supporting the roof, and the ore is mined in layers from bottom to top. After each layer of mining is completed, the layers are filled in a timely manner, and a working space of 2–3 m is always left between the filling body and the roof until the final layer of mining reaches the height of the mining stage. The interaction between the filling body and the point pillar forms a collaborative support system between the point pillar and the filling body, jointly maintaining the stability of the goaf and overlying rock layers.

Upward drift filling mining method refers to the filling mining method in which various layers are mined from bottom to top in the mining area, and the ore is mined using drift filling in the layers. Compared with the upward layered filling mining method, the characteristic of this method is that it uses a drift for backfilling, and during filling, the filling material is completely filled with the goaf, making it as close to the roof as possible. This mining method is suitable for mining inclined and steeply inclined ore bodies with unstable ore and surrounding rocks, high ore grade, and value.

In the process of mining undersea metal mines, there are many factors that affect the development height of the water-conducting fracture zone, mainly including the inclined length of the working face, the compressive strength of the roof, the mining depth, the mining height, the mining method, the mechanical properties and structural characteristics of the overburden rock, and the roof management method.

Underground mining may lead to the fracture of the upper rock mass, endangering the environment and causing death and property damage. As shown in Fig. 18, underground mining usually leads to ground movement, and the strata above the excavation area will break with different displacements and rates, resulting in separation between the fracture surfaces in these strata. Due to the difference in displacement, vertically adjacent strata will separate, so fractures parallel to the plane of the strata can be referred to as transverse fractures. In the horizontal direction, the settlement will cause the strata to break into rock blocks, which will rotate and separate, resulting in fractures perpendicular to or intersecting with the ground plane, known as longitudinal fractures. As mining operations continue, fractures will continue to develop upwards. If the mining area is located under a lake, river, or ocean, the fractures will become channels for water movement.Fig. 18 Formation mechanism of overburden mining fractures.

Due to the underwater mining of metal ore under the sea, there is a certain chance that the rock fractures in the fracture zone will connect to the water above it. It is for this reason that the fractures that form a hydraulic connection with the mined-out area during mining are called water-conducting fractures. Due to the effect of pressure, the part of the rock zone that forms longitudinal and transverse fractures is called overburden mining fractures53.

Field observations

To validate the accuracy of the prediction results, a panoramic borehole camera1 was used to measure the height of each fractured zone in the mining-induced overlying strata. With 360-degree borehole images and real-time videos, the condition of the borehole wall rocks can be clearly observed. Additionally, the device can record the characteristics of fractures above the caving zone to provide more detailed visual inspection information.

By increasing the depth of the borehole, it is possible to observe the connectivity of water apertures, the extent of fracture development, and even traces of water flow. Additionally, this device can determine the upper boundary of the fractured zone above the caving zone. In order to determine the height of the WCFZ at the top of the Xinli Mine area, four boreholes were drilled on the roadway, reaching a depth of − 200 m to measure the height of the fractured zone at a depth of − 240 m. Chen has already measured the height of the fractured zone at depths of − 200 m and − 165 m in references6,54.

In the first borehole, the fissure apertures are relatively large and connected above 33.64 m, and traces of water flow are also clearly visible, similar to the situation shown in1. However, in lower areas, the fissures are isolated and smaller in aperture size. In the second borehole, similar off-layers are located at distances of 34.18 m, 35.28 m, and 31.58 m from the bottom of the borehole. Based on this data, the height of the WCFZ at − 240 m depth can be determined. From these observations, it can be reasonably inferred that the height of the WFZ at − 240 m depth is similar. The conditions of different working faces in the Xinli Mine area are summarized in Fig. 19.Fig. 19 Data of different working faces in Xinli mining area.

Commonly used theoretical criteria

Under conventional mining conditions, the height of the WCFZ is predicted using empirical formulas based on extensive regression analysis of measured data. These formulas comprehensively consider factors such as d, overlying strata type, and coal seam dip angle, and are widely applied. According to the empirical formula method50 (see Table 4), the height of the WCFZ is predicted, where M represents the d.Table 4 Empirical formulas for the height of the WCFZ.

Rock type	Equations	
Hard	Hf′=100∑M1.2∑M+2.0±8.9	
Medium hard	Hf′=100∑M1.6∑M+3.6±5.6	
Weak	Hf′=100∑M3.1∑M+5.0±4.0	
Extremely weak	Hf′=100∑M5.0∑M+8.0±3.0	

In the Xinli Mine area, rock strata classification follows the "Three Downs" mining regulations and is divided into soft and weak categories. The classification is determined based on the coefficient of hard rock lithology, c, which quantifies two influencing factors: the uniaxial compressive strength of the rock layer and the overlying strata structure. The value of c refers to the ratio of the cumulative thickness of hard rock layers within the estimated height range of the WCFZ to the estimated height of the WCFZ itself55.5 c=∑hHf

where, ∑h represents the cumulative thickness of hard rock layers in the overlying strata, the hard rock layers mainly include sandstone (fine sandstone, medium sandstone, coarse sandstone), igneous rocks, etc.; Hf represents the estimated height of the WCFZ.

The on-site data from the Xinli Mine area in Sanshan Island is compared with the predictive results of five models (see Table 5). From Table 5, it can be observed that the empirical formula predicts the height of the WCFZ between 26.84 and 35.01 m, with absolute errors ranging from − 2.91 to 13.66 and relative errors ranging from 0.83 to 33.74. Since the empirical formula method only considers a single influencing factor, it exhibits the highest error.Table 5 Predicted heights of WCFZ by different methods.

Models	Field observation (m)	Predicted result (m)	Absolute error (m)	Relative error (%)	
Empirical equation	40.5	26.84–34.84	5.66 ~ 13.66	13.9–33.74	
32.1	27.01–35.01	− 2.91 to 5.09	9.06–15.86	
35.3	27.01–35.01	0.29–8.29	0.83–23.49	
Linear regression	40.5	43.26	− 2.76	6.81%	
32.1	30.92	1.18	3.68%	
35.3	37.74	− 2.44	6.91%	
XGBRegressor	40.5	39.31	1.19	2.94%	
32.1	33.63	− 1.53	4.77%	
35.3	34.59	0.71	2.01%	
Random forest regressor	40.5	43.17	− 2.67	6.59%	
32.1	33.89	− 1.79	5.58%	
35.3	37.48	− 2.18	6.18%	
LinearSVR	40.5	36.37	4.13	10.20%	
32.1	36.83	− 4.73	14.74%	
35.3	32.95	2.35	6.66%	
KNeighbors regressor	40.5	38.65	1.85	4.57%	
32.1	36.17	− 4.07	12.68%	
35.3	39.39	− 4.09	11.59%	

The predictive results of the five models are all superior to the traditional empirical formula. Among them, XGBRegressor performs the best. This is mainly because XGBRegressor effectively captures complex nonlinear relationships in the data through the ensemble of multiple weak classifiers, thereby improving the model's predictive accuracy. RandomForestRegressor exhibited a slightly worse performance, but still effectively captures complex nonlinear relationships in the data by utilizing an ensemble model of multiple decision trees. However, KNeighborsRegressor showed the worst prediction effectiveness. It might be due to the presence of outliers in the data, which leads to an inaccurate selection of nearest neighbors and further disruption of the model's predictive results.

Discussion

The sample data on the WCFZ dataset were normalized, and then predicted, compared, and validated by five models, namely LinearRegression, XGBRegressor, RandomForestRegressor, LinearSVR, and KNeighborsRegressor. The predictive results are compared with the true values, as shown in Fig. 2.

LinearRegression is a simple and intuitive model for linear relationships. Its advantages lie in its ease of understanding and interpretation, and it performs well on datasets with few features. However, it always involves complex nonlinear relationships in the prediction of the WCFZ. LinearRegression may be difficult in capturing the complexity of nonlinear features. Therefore, polynomial features or other nonlinear transformations may be considered to better fit the nonlinear relationships of complex geological conditions. Additionally, regularization methods such as Lasso and Ridge can be used to reduce the risk of overfitting. XGBRegressor performs well in this study, effectively capturing the complex nonlinear relationships in the overlying strata, demonstrating high flexibility. However, careful parameter tuning is required to avoid overfitting. Further research on parameter tuning and feature engineering methods can optimize the model's performance. RandomForestRegressor typically performs well in handling high-dimensional data and nonlinear relationships. Combining multiple decision trees provides good generalization performance and is relatively robust to outliers. As shown in Fig. 3, RandomForestRegressor is only slightly inferior to XGBRegressor. However, the interpretability of the RandomForestRegressor model is relatively poor, and parameter tuning is relatively complex. LinearSVR is suitable for high-dimensional data and nonlinear problems. However, it is found to perform poorly in predicting the WCFZ, which may be because LinearSVR is sensitive to large-scale datasets and noise, and the original dataset has not been processed for noise. Therefore, in future research, dimensionality reduction, data cleaning, and noise processing may be needed, or distributed computing and faster optimization algorithms may be considered, along with exploring new kernel functions and regularization strategies to improve the model's performance.

KNeighborsRegressor is suitable for modeling small-scale datasets and local relationships. As shown in Figs. 4 and 5, KNeighborsRegressor performs poorly in predicting the WCFZ, possibly due to limitations in performance when dealing with large-scale and high-dimensional data. In future research, dimensionality reduction techniques such as Principal Component Analysis (PCA) may be considered to reduce dimensions or attempt to improve performance using distance-weighted K-nearest neighbors.

Given the advantages and disadvantages of each model, the selection of sample data is crucial, and it needs to be representative and comprehensive. It is necessary to keep enriching sample data in practice and constantly improve and update models to make each model have better accuracy and generalization ability. At the same time, this study only studied the prediction performance of a single model in the height of the WCFZ and has not yet been optimized. Subsequent research should explore the impact of different optimization models on a single model to further improve the accuracy of machine learning in predicting the height of the water-conducting fracture zone.

The development of WCFZ in overburden strata due to mining is a complex process of movement and destruction in both time and space. Although it is difficult to convert qualitative factors into quantitative factors, it is still necessary to consider factors that have a significant impact on the high development of WCFZ, such as mining speed, time factors, and repeated mining. Considering more influencing factors and increasing the number of training samples can further improve the performance of the model.

Especially with the gradual depletion of shallow resources, underwater or seabed ore bodies with complex mining conditions have become important mining targets. If the highly developed WCFZ cannot be predicted in time, it is extremely easy to cause major personal and property damage accidents. Therefore, we should strengthen the research and prediction of the highly developed WCFZ, improve the accuracy and reliability of prediction, and provide more support and guarantee for sustainable development. At the same time, how to choose more objective and reasonable evaluation indicators for predicting the height of the WCFZ will become the focus and difficulty of future research.

Conclusion

As mineral resource exploitation extends into deeper sea areas, water influx caused by the formation of water-conducting fractured zones (WCFZ) has become a bottleneck problem restricting deep-sea safety production. In this study, we constructed a large dataset of WCFZ containing 122 engineering cases and established predictive models for WCFZ height based on five machine learning algorithms considering multiple factors. The main achievements and conclusions are as follows:Mining depth (H), hard rock proportion coefficient (c), mining thickness (d), and working face length (L) were considered as the main influencing factors for the height of WCFZ in overlying strata during mining. The Pearson correlation coefficient analysis shows that the correlation between d and L, d and H are both weakly positive with p-values of 0.004 and 0.017, respectively. On the contrary, the weak negative correlation between c and L can be indicated by a correlation coefficient of − 0.15 and a p-value of 0.11.

The more accurate prediction for the height of WCFZ than the traditional empirical formula was obtained from the machine learning algorithms. Compared with the traditional empirical formula, the average relative errors of LinearRegression, XGBRegressor, RandomForestRegressor, LinearSVR, and KNeighborsRegressor were decreased by 10.27%, 12.9%, 10.03%, 5.61%, and 6.53%, respectively. XGBRegressor exhibited the most accurate prediction among all the models, which might be due to its superior capacity to handle nonlinear relationships.

Consisting with the regression performance evaluation, XGBRegressor showed the best performance in predicting the height of WCFZ in the Xinli Mine area of Sanshan Island, showing absolute and relative errors of 0.71 m and 2.01%, respectively.,

The accuracy of the five predictive models used in this study for WCFZ height can meet the requirements of practical engineering application.

In light of the results from this study, future research is recommended to address the remaining knowledge gaps and limitations. It is important to consider additional influencing factors such as mining speed, time factors, and repeated mining. Furthermore, the impact of incorporating different optimization techniques within a single model should be examined to enhance the accuracy of machine learning predictions.

Fundings

This research is supported by financial grants from “the National Natural Science Foundation of China (52104122)”, “the Open Project of Engineering Research Center of Phosphorus Resources Development and Utilization of Ministry of Education (LKF2021007)”, and “the Natural Fund project of Fujian Province Science and Technology Department (2020J01943)”.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Author contributions

Concept and design: D.L. and Z.W.; data collection and analysis: Z.W. and Y.C.; drafting of the article: Z.W.; critical revision of the article for important intellectual content: D.L. and Y.C.; study supervision: D.L. Funding acquisition: Z.W. All authors reviewed the manuscript.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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