An Evaluation of the Mine Water Inrush based on the Data expansion and Deep learning

An Evaluation of the Mine Water Inrush based on the Data expansion and Deep learning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An Evaluation of the Mine Water Inrush based on the Data expansion and Deep learning Shoufeng Tang, Ye Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4385835/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 3 You are reading this latest preprint version Abstract The accuracy of coal mine water inrush prediction models is affected mainly by the small number of samples and difficulty in feature extraction. In this paper, a new data augmentation water inrush prediction method is proposed. This method uses a natural neighbors theory and mutual information dropout sparse autoencoder -improved SMOTE to augment and predict the risk of water inrush in coal mines. By learning water intrusion features through the autoencoder, we can achieve better separation between classes and weaken the influence of data overlap between classes in the original sample. Then, the natural neighbors search algorithm is used to determine the intrinsic neighbor relationships between samples, remove outliers and noise samples, and use different oversampling methods for borderline samples and center samples in the minority class. Synthetic samples are generated in the feature space, mapped back to the original space and merged with the original samples to form an expanded water inrush dataset. Finally, the effectiveness of the proposed method is confirmed by comparing the measured water inrush data and prediction model results in typical mining areas in North China. The results from this study can be used to more accurately analyze the characteristics of water inrush accidents, improve the accuracy of water inrush accident prediction, and promote the application of machine learning in water inrush prediction. Mine water inrush Feature extraction Natural neighbors theory Improved SMOTE Mutual information dropout Sparse autoencoder Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Highlight The main contributions of this article are as follows: (1) A new oversampling data preprocessing method is proposed. Natural neighbors theory is introduced to remove outliers and noise points existing in water inrush datasets. (2) A new oversampling data augmentation algorithm is proposed. This algorithms divides minority class samples into center samples and borderline samples according to natural neighbors theory. The center samples are oversampled via spatial interpolation to increase the diversity of synthetic samples. The natural neighbors interpolation method is used for borderline samples to reduce the probability of synthetic noise and retain the distribution pattern of the original data. (3) Mutual information dropout is introduced into the SAE to retain neurons that are conducive to the expression of water inrush features through the mutual information mask matrix, extract highly relevant water inrush accident features, and improve the accuracy of the prediction model. (4) The causes and water inrush channels of the coal seam floor are analyzed and studied. The main geological and hydrological factors affecting the occurrence of floor water inrush accidents are determined. Introduction The mining environment in North China coalfields is complex. As coal mines continue to be mined deeper, the pressure on the coal seam floor has also increased. Under the combined influence of various unfavorable factors, such as high pressure, high water content, and confining layer thinning, the risk of water inrush increases significantly. Through studies on the water inrush mechanism, many scholars have applied data analysis algorithms, such as regression analysis (Shi and Han. 2004; Du et al. 2014 ; Weitao et al. 2015 ; Liu et al. 2009 ), classification ( Liu et al. 2011 ), support vector machine(Shi et al. 2017 ; Cao and hao 2011; Zhigang et al. 2008 ; Qiao 2010 ), neural network (Zhao and Hu 2014 ; Zhao et al. 2013 ; Shi 2012 ), and random forest algorithms (Zhao et al. 2018 ), to the prediction of water inrush in coal mines. Due to the small amount of water inrush data in coal mines, the data features required for the prediction model cannot be provided, which reduces the accuracy of the prediction model. This paper presents a new oversampling method. Different from the traditional SMOTE (N.V.Chawla. et al.2002) method of randomly selecting sampling points and linear interpolation, this paper introduces the natural neighbors theory (J.Li. et al2021, Leng Q. et al 2023 , Li J, Zhu Q, Wu Q. et al 2021 ) to determine the neighbor relationships between samples. The outliers and noise values existing in the water inrush dataset are removed to reduce the risk of overfitting of the prediction model, and the water inrush data samples are divided into center minority class samples and borderline minority class samples (Z. Xu. et al 2022, G.Douzas, F.Bacao. 2019, S.Susan, A.Kumar. 2019). Since the nearest neighbor of a borderline minority sample contains majority class samples, it is easier to generate new noise samples as sampling points. To address this problem, this paper presents a natural neighbors interpolation method to expand the amount of data. At the same time, for center minority samples, a spatial interpolation method is proposed to generate new synthetic water inrush samples. This paper presents an improved SMOTE ( ISMOTE ) algorithm based on natural neighbors and spatial interpolation to expand a water inrush sample set and uses the mutual information dropout sparse autoencoder ( MISAE ) to extract the characteristics of coal mine water inrush data and evaluate the risk of coal mine water inrush. At present, few studies have focused on water inrush prediction methods based on data augmentation deep learning. Water accident assessment model The occurrence of water inrush accidents in coal mines is the result of a variety of influencing factors. There is an interaction between the influencing factors of the accident, which makes the water inrush accident and its influencing factors form a nonlinear system. The Ministry of Coal proposed the water inrush coefficient method (Hao and Jingming 2015 ). The “lower three belts” theory (Zhang and Liu 1990), the “two-zone” model (Shi and Han 2005; Duan 2012), the “lower four belts” theory (Minggao et al. 1995), the “Strong Permeability Channel” theory (Li 2014), the “KS” (Key Strata) theory (Shi et al. 2015), etc. were all born out of this. The analysis reveals that the five first-level indicators of aquifer conditions, aquifer conditions, coal seam conditions, structural conditions, and mining conditions, as well as the corresponding twelve secondary indicators, are the primary factors affecting the water inrush from the coal floor. This conclusion is based on the summary of prior studies. Table 1 shows the influencing factors of coal seam water inrush. Table 1 Main influencing factors of coal seam water inrush First-level indicators Secondary-level indicators Aquifer conditions Aquifer thickness Aquifer water pressure Working surface distance Water barrier conditions Muddy rock thickness Sandy rock thickness Limestone section thickness Coal seam conditions Coal seam thickness Coal seam dip Construction conditions Fault drop Mining conditions Mining area Strike length Mining height Method theory Natural neighbors theory The idea of natural neighbors theory is inspired by real-world friend relationships. If sample x i has sample x j as a nearest neighbor and x j also has x i as a nearest neighbor, then samples x i and x j are true neighbors of each other. The natural neighbors theory is a detection algorithm without parameter settings. This algorithm continuously searches for the r -nearest neighbors of each sample in the dataset during operation until each sample has r -nearest neighbors of each other, thus forming a stable data structure. At this time, the eigenvalue λ is equal to r . $$\left( {\forall {x_i}} \right)\left( {\exists {x_j}} \right)\left( {r \in n} \right) \wedge \left( {{x_i} \ne {x_j}} \right) \to \left( {x_{i}^{{}} \in N{N_r}\left( {{x_j}} \right)} \right) \wedge \left( {{x_j} \in N{N_r}\left( {{x_i}} \right)} \right)$$ 1 In the formula, x i and x j represent two different samples in the dataset, and NN r ( x i ) and NN r ( x j ) represent the sets of r nearest neighbors of xi and x j , respectively. In a stable data structure, there is a different sample x j for any x i , making them the r nearest neighbors to each other. If x i belongs to the λ nearest neighbor of x j , and at the same time, sample x j also belongs to the λ nearest neighbor of sample x i , then the two samples are natural neighbors of each other, as shown in Eq. 2 $${x_i} \in NaN\left( {{x_j}} \right) \Leftrightarrow {x_i} \in N{N_r}\left( {{x_j}} \right) \wedge {x_j} \in N{N_r}\left( {{x_i}} \right)$$ 2 In the formula, NN r ( x j ) represents the natural neighbors set of x j . If there is an outlier in the dataset, then if and only if all samples except this point have reached the natural stable structure. Outliers have no natural neighbors, that is, NaN ( x i ) = = 0. Based on the definition of outliers, when the natural neighbors search algorithm is running, the algorithm stops if the number of inverse neighbor samples in two adjacent iterations remains unchanged. At this time, samples without inverse nearest neighbors are outliers, and the search pseudocode is shown in Algorithm 1. Algorithm-1 Search for NaN ( NaN-Search ) Input: Water inrush data set X Output: natural neighbors feature λ , natural neighbors NaN, number of inverse neighbors of the sample nb 1: Initialize the search round number r = 1, num = 0 (the number of x i with nb = 0), NN r ( x i )= ∅ , RNN ( xi )= ∅ ( xi ’s inverse nearest neighbor), NaN ( x i )= ⊘ ; 2: Establish a k-dimensional tree on the water inrush data set X 3: For each x i ∈ X , find its r -th neighbor x j by using k-d tree. Update nb ( x j ) = nb ( x j ) + 1, NNr ( x i ) = NNr ( x i )∪{ x j }, RNN ( x j ) = RNN ( x j )∪{ x i }; 4: Compute the number num of xi with nb ( x i ) = 0; 5: If num does not change λ = r ; 6: For each x i ∈ X , NaN ( x i ) = RNN ( x i )∩ NN r ( x i ); 7: Otherwise r = r + 1 , go to step 3; 8: Return: λ , NaN , nb Coal mine water inrush prediction model based on data augmentation The data-expanded surge prediction algorithm presented in this paper consists of three basic sub-structures: the decoder network (for mapping high-dimensional surge data overlapping into characteristic space), the oversampling model (using natural neighbors theory to remove outlier and noise sample, generate high-quality new samples using the proposed spatial insert method) and the decoder network (to map the synthetic sample back into the original space). In particular: 1. The mutual information dropout autoencoder is trained using ( x , y ) from the original data set. 2. Use the trained encoder network to map X into a feature space with better inter-class separability( z = Encoder ( x )). 3. Using the natural neighbors theory, remove noisy points and outliers from the data sets and determine center and borderline samples. In order to produce high-quality synthetic data z new , samples are oversampled using the two spatial oversampling techniques presented in this article. 4. Map z new back to the original space using the trained decoder network, then combine it with the original data x to create an expanded data set. After obtaining the expanded data set, an autoencoder is used to predict water inrush accidents (Dan Liu, 2023, P.Soltanzadeh, M.Hashemzadeh, 2021). Natural neighbors based spatial interpolation SMOTE This paper introduces the natural neighbors theory into the SMOTE algorithm. First, the natural neighbors search algorithm in Algorithm 1 is used to search the dataset to remove noise and outliers. Then, the minority class samples are divided into center samples and borderline samples based on natural neighbors theory, and two different spatial interpolation methods are used to generate new water inrush samples. Finally, adds the synthesized water inrush samples to the original dataset to expand the water inrush dataset (A. Wahid, C.S.R. Annavarapu. 2021, D.Elreedy, A.F.Atiya. 2019). The Fig. 1 shows the main structure of the algorithm proposed in this article. The model performs three steps in the oversampling stage, including removing outliers and noise points, distinguishing borderline samples and center samples, and synthesizing new instances. A binary classification dataset X consists of majority class samples S maj and minority class samples S min . Label ( x i ) represents the class label of sample x i ∈ X . Based on the natural neighbors theory, noise samples and outlier samples are defined as follows: Definition 1 If sample x i satisfies ∀ x j ∈ NaN ( x i ) and Label ( x j ) ≠ Label ( x i ), then x i is a noise point. That is, if x i belongs to the minority class sample but its natural neighbors are all majority class samples, then x i is defined as a noise point. Definition 2 If sample x i satisfies ∣ NaN ( x i )∣==0, ∣ NaN ( x i )∣ represents the number of natural neighbors of x i . Then, x i is defined as an outlier. Noise and outliers in the dataset will affect the normal data distribution of the sample, making it difficult for the classifier to fit the offset points and thus resulting in a decrease in the generalizability of the prediction model. Therefore, in the coal mine water inrush prediction model, noise and outliers must first be removed from the original dataset. After removing noise and outliers from the preprocessed water inrush dataset, it becomes a regularly distributed dataset, and better prediction accuracy can be achieved. Definition 3 If sample x i ∈ S min and xi is not noise or an outlier, if ∃ x j ∈ NaN ( x j ) makes Label ( x j ) ≠ Label ( x i ), then x i is defined as a borderline minority class sample. There are majority class samples in the natural neighbors sample of the borderline samples, but when their natural neighbors are all majority class samples, x i is a noise point. The Fig. 2 shows the noise points and outliers in the data set. According to the natural neighbors search algorithm, borderline minority class samples existing in the dataset can be identified through traversal, and the Danger dataset is used to store these borderline samples. Since there are majority class samples among the natural neighbors of the borderline samples, it is easier to synthesize incorrect class samples during oversampling. Therefore, in this paper, two different spatial oversampling methods are used to oversample center minority samples and borderline minority class samples, thereby generating new samples of the required categories and reducing noise and damage to the distribution of the original dataset (Pan,T et al. 2020). For the borderline sample S i ∈ Danger , two minority class natural neighbors sample S i1 and S i2 of x i are randomly selected. The algorithm first uses the natural neighbors sample S i1 and S i2 to synthesize the midpoint according to Formula 3,4 and then connects x i and the midpoint and performs interpolation to synthesize a new sample. $${S_{{\text{mid}}}}={S_{i1}}+{\delta _1}({S_{i2}} - {S_{i1}})$$ 3 $$S_{i}^{{new}}={S_i}+{\delta _2}({S_{mid}} - {S_i})$$ 4 δ1 and δ2 in the formula are two random numbers between 0 and 1. This step is repeated until borderline sample oversampling is complete. The Fig. 3 shows the Borderline sample oversampling method. For the center minority sample x i ∈ Safe in the dataset, sample S 1 is selected, and the sample point S new with the largest Euclidean distance d between the selected sample and the Safe dataset is calculated to form a sampling space, as shown in the Fig. 4 .Assume that S 1 = ( x 1 , y 1 ) and the farthest Euclidean distance sample point in the minority class sample set is S d = ( x 2 , y 2 ). A data point is randomly sampled in the adoption space as a synthetic sample point S new =( x new , y new ), where x new = random ( x 2 , x 1 ) and y new = random ( y 2 , y 1 ). Different from the SMOTE , the new synthetic sample point is located in the sampling space formed by the selected sample and its farthest sample in the minority class rather than on the line connecting the two points. The farthest distance sample point is selected to form a sampling space to randomly form synthetic samples. Compared with linear sampling, the proposed sampling approach can form a more diverse synthetic sample set, and there will be no situation where sample-dense areas become denser and sparse areas become sparser and effectively addresses the drawbacks of the SMOTE algorithm, which alters the data distribution pattern with ease. The spatial interpolation method enhances the sample set's mathematical features' comprehensiveness and diversifies the characteristics of the minority class data. The results of NaN-ISMOTE algorithm under complex data distribution conditions is shown in Fig. 5 . MISAE In this paper, an encoder-decoder is used to learn a separable feature space so that samples of different categories are far apart. In this case, the synthetic samples are also far from the majority class samples, thus reducing the risk of falling into the danger zone. The encoder network aims to map raw data into a separable feature space and consists of multiple encoder layers. The encoder is represented as: $$z=f(Wx+b)$$ 5 In the formula, f represents the activation function of the neuron, W is defined as the weight matrix, and b is the bias vector of the hidden layer. The function of the encoder is to transform the output from the hidden layer to the reconstructed data output vector. $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{x} =h(W'z+b)$$ 6 In the formula, h is the activation function of the hidden layer of the autoencoder, W is the weight matrix between model layers, and b is the bias vector output by the output layer. The objective function of the autoencoder can be defined as: $$J=\frac{1}{N}\sum\limits_{{m=1}}^{M} {(\frac{1}{2}\left\| {{y_m} - {x_m}} \right\|_{2}^{2})}$$ 7 In the formula, the error between the original sample set input data x and the reconstructed data y decoded by the decoder is expressed as J . By minimizing the error J , each parameter of the autoencoder is optimized to obtain the optimal data representation of the input data. Since the influencing factors of water inrush accidents have different contributions to accidents, MI-Dropout is introduced into the encoder layer. By establishing a binary mask moment of mutual information sorting, the weight of feature neurons with a small correlation is set to 0, and the neurons that are beneficial to the expression of water intrusion features are retained. The mutual information is expressed as: $$I(X,Y)=H(x)+H(y) - H(x,y)$$ 8 $$H(X)= - \int\limits_{x} {p(x)\log p(x)dx}$$ 9 p ( x,y ) represents the joint probability density, and p ( x ) and p ( y ) are the marginal probability density functions. H ( x ) is defined as the entropy of parameter x. The water inrush label dataset defines the output matrix of the l-th hidden layer of the model as h i l . Then, the mutual information between the target expression and the output of the hidden layer neuron is calculated: $$I(h_{i}^{l},Y)=H(h_{i}^{l})+H(y) - H(h_{i}^{l},y)$$ 10 The mutual information is sorted to obtain the vector S in descending order, and a new mask matrix is constructed: $$\varepsilon _{i}^{l}=\left( {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 1&{S_{i}^{l} \geqslant k\cdot \mu } \end{array}} \\ {\begin{array}{*{20}{c}} 0&{S_{i}^{l}<k\cdot \mu } \end{array}} \end{array}} \right.$$ 11 In the formula, S i l is the position of the i-th neuron in the l-th hidden layer in the vector. Μ is the loss rate in the random deactivation strategy. The larger the value is, the more neurons in the hidden layer are activated. The forward propagation process of the model is expressed as: $$\tilde {h}_{i}^{l}=\varepsilon _{i}^{l} * h_{i}^{l}$$ 12 $$z_{i}^{{l+1}}=w_{i}^{{l+1}}\tilde {h}_{i}^{l}+b_{i}^{{l+1}}$$ 13 $$h_{i}^{{l+1}}=f(z_{i}^{{l+1}})=f(w_{i}^{{l+1}}\tilde {h}_{i}^{l}+b_{i}^{{l+1}})$$ 14 MISAE includes three basic modules: (1) Feature extraction layer. An autoencoder is used as the feature extraction layer structure, which is defined as g ( x ; w ; b ), where x is the input function of the model and w and b are the interlayer weights and bias sizes, respectively, that need to be learned in the SAE model. G () is the feature extractor function constructed by the SAE, which is used to extract hidden features in water inrush data; (2) The MI-Dropout layer. In this layer, the neurons in the hidden layer are sorted through mutual information, and a binary mask matrix is constructed to randomly deactivate the neurons in the hidden layer. The output vector of the mutual information drop layer is used as the input of the next feature extraction layer or combined with the softmax layer for model prediction; (3) The softmax classification layer is defined as \(y=soft\hbox{max} (\tilde {h}_{i}^{l};w;b)\) . The structure is shown in Fig. 6 . The oversampling algorithm is shown in Algorithm 2. Case Analysis In this section, we evaluate the performance of the coal mine water inrush prediction algorithm proposed in this paper and test it on water inrush data extracted from actual working faces in typical mining areas in North China. Comparison algorithms include IWOA-SVM, PCA-OPF, PCA-Fisher and other recent water inrush prediction algorithms (Lian C, Mei Y, et al 2021 , Jiang Zehua, et al 2021, Qiu Xingguo, LiJing 2022), as well as the oversampling algorithms SMOTE and Borderline-SMOTE . The SMOTE parameters are set to k1 = 5 , and the BL-SMOTE parameters are set to k1 = 5 and k2 = 5 . Classification algorithms generally use Accuracy as the main result analysis indicator. Recall and the F-measure are also used for performance evaluation. $$\begin{gathered} Accuracy=\frac{{TP+TN}}{{TP+TN+FP+FN}} \hfill \\ Recall=\frac{{TP}}{{TP+FN}} \hfill \\ F - measure=\frac{{{{(1+\beta )}^2}*recall*precision}}{{{\beta ^2}*recall*precision}} \hfill \\ \end{gathered}$$ 15 The accuracy is calculated as the ratio of the number of correct classifications of the algorithm to the total number of samples. The higher the Accuracy is, the better the performance of the prediction algorithm. F1 is the harmonic mean of precision and recall, mainly focusing on the minority class. The Recall indicates the number of positive samples correctly predicted by the algorithm among the original samples present in the dataset samples. Water inrush dataset experiment All water inrush data used in the experiments in this section are collected from the Internet of Things Research Center of the China University of Mining and Technology, who measured water inrush data on working faces in typical mining areas in North China. A total of 80 sets of collected data is used in the experiments. After the data collection is completed, all water inrush instance data is standardized. The standardization formula is as follows: $${x_{norm}}=\frac{{x - {x_{\hbox{min} }}}}{{{x_{\hbox{max} }} - {x_{\hbox{min} }}}}$$ 16 NaN-ISMOTE-MISAE algorithm ablation experiment The NaN-ISMOTE-MISAE algorithm proposed in this article first uses natural neighbors to remove noise points and outliers and then uses different interpolation methods for data expansion according to the different areas where the minority class samples are located. Second, the prediction model uses the MISAE algorithm to extract highly relevant water inrush features. Therefore, two SMOTE prediction models without natural neighbors data preprocessing and refined sampling methods are used to verify the effectiveness of the proposed oversampling method. The prediction results of the SAE and MISAE are compared using the same dataset to verify the effectiveness of the proposed water inrush feature extraction method. Figure 7 and Table 2 shows the prediction curves of the different models. Table 2 Ablation experiment results NaN-ISMOTE-MISAE NaN-ISMOTE-SAE BLSMOTE-MISAE SMOTE-MISAE Accuracy 0.9375 0.9125 0.9 0.8750 Recall 0.9524 0.9259 0.9245 0.9057 F1 Score 0.9362 0.9346 0.9245 0.9057 The prediction value obtained based on the prediction model proposed in this article is more consistent with the actual water inrush sample label. Under the same operating environment and dataset, the ability of the proposed method to predict mine floor water inrush is stronger. The data augmentation algorithm can effectively increase the number of water inrush samples in the dataset, increase the diversity of the synthetic dataset, and provide sufficient water inrush occurrence characteristics. A comparison of the prediction results of the NaN-ISMOTE-MISAE and NaN-ISMOTE-SAE shows that in the traditional SAE model, the noise information of irrelevant variables in water inrush samples will propagate to high-dimensional features, causing the model to extract irrelevant variable information and affecting the feature extraction performance of the water inrush prediction model. The MISAE resets the weight of feature neurons with a smaller correlation to 0 , retains neurons that are beneficial to the expression of water inrush features, improves feature extraction capabilities, and obtains better prediction accuracy. Comparing the results of the NaN-ISMOTE-MISAE , SMOTE-MISAE and BLSMOTE-MISAE oversampling algorithms, the model results proposed in this article are better. This is due to the introduction of natural neighbors theory to preprocess the dataset. Using natural neighbors theory to eliminate noise and outliers and create a normally distributed data set. This enhanced the prediction model's capacity for generalization. In the borderline sample and center sample regions, the NaN-ISMOTE algorithm simultaneously employs two sampling techniques. Among these, the risk of noise produced when borderline samples are oversampled is efficiently decreased by random interpolation of natural nearest neighbor intermediate points. The use of spatial random interpolation method in the center sample can improve the diversity of the synthetic data set. Therefore, the NaN-ISMOTE algorithm improves the accuracy of subsequent prediction algorithms. Comparison between the NaN-ISMOTE-MISAE algorithm and water inrush prediction algorithms in recent years The comparison results between the prediction algorithm proposed in this paper and the coal mine floor water inrush prediction algorithm proposed in recent years are shown in Fig. 8 and Table 3 . The NaN-ISMOTE expanded water inrush dataset is used. Compared with traditional algorithms such as PCA , the MISAE algorithm causes less damage to the secondary features in the water inrush data and can more completely preserve the feature vector of the sample. Compared with the IWOA-SVM , the shallow network has difficulty mining the complex mapping relationship between water inrush characteristics and accident occurrence. Therefore, the MISAE is needed to extract hidden features from water inrush data and reduce the impact of irrelevant feature information on model expression. Moreover, compared with other classification algorithms such as the Fisher and OPF algorithms, the MISAE has greater advantages in the field of water inrush prediction and is highly suitable for analyzing and predicting nonlinear and complex floor water inrush data. Table 3 The simulation results NaN-ISMOTE-MISAE IWOA-SVM PCA-OPF PCA-Fisher Accuracy 0.9375 0.9000 0.8625 0.8625 Recall 0.9444 0.9412 0.9200 0.9375 F1 Score 0.9533 0.9231 0.8932 0.8911 Conclusion To solve the problems of small numbers of floor water inrush data samples and difficulty in extracting water inrush features, the NaN-ISMOTE and MISAE methods were introduced to improve the prediction model. The NaN-ISMOTE algorithm is used to expand the water burst dataset, and at the same time, it addresses the shortcomings of being unable to distinguish noise data and easily changing the distribution pattern of the dataset. This paper introduces the natural neighbors theory to reduce the risk of overfitting of the prediction model by removing outliers and noise samples ​​from the water inrush dataset. The water inrush data samples are divided into center minority class samples and borderline minority class samples, and two targeted oversampling methods are proposed for oversampling. These two methods improve the diversity of the synthetic data and enhances the coverage of the minority class data area by synthetic samples while retaining the distribution pattern of the original data and reducing the impact of borderline samples on oversampling. The MISAE is used to extract water inrush accident features, and mutual information is used to evaluate the importance of neurons in the hidden layer of the model for predicting the target. Suppressing the interference of factors that are less relevant to the occurrence of water inrush accidents in the model improves the feature extraction performance of the classifier and increases the model prediction accuracy. The experimental results show that the model proposed in this paper can more accurately analyze the characteristics of water inrush accidents, improve the accuracy of water inrush accident prediction, and promote the application of deep learning and data expansion in coal mine water inrush prediction. Declarations Funding The funding was provided by Key Technologies Research and Development Program (Grant No.2017YFF0205500). Consent to Publish All authors: (1) This material has not been published in whole elsewhere; (2) The manuscript is not currently being considered for publication in another journal; (3) All authors have been personally and actively involved in substantive work leading to the manuscript, and will hold themselves jointly and individually responsible for its content. Authors Contributions All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Shoufeng Tang and Ye Zhang. The manuscript was written by Ye Zhang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Competing Interests No potential conflict of interest was reported by the authors. References A. Wahid, C.S.R. Annavarapu, (2021) NaNOD: A natural neighbourbased outlier detection algorithm, Neural Comput.Appl 33(6) 2107–2123. Cao QK, Zhao F (2011) Prediction of water inrush from coal floor based on genetic-support vector regression. J Coal 36(12):2097–2101 Du CL, Zhang XY, Fenglian Li (2014) Application of improved CART algorithm in prediction of water inrush from coal seam floor. Ind Mine Autom 40(12):52–56. https://doi.org/10.13272/j.issn.1671- 251x.2014.12.014 Dan Liu, Shisheng Zhong, Lin Lin, Minghang Zhao, Xuyun Fu, Xueyun Liu, (2023) Deep attention SMOTE: Data augmentation with a learnable interpolation factor for imbalanced anomaly detection of gas turbines, Computers in Industry, 151, https://doi.org/10.1016/j.compind.2023.103972. D.Elreedy, A.F.Atiya (2019) A comprehensive analysis of synthetic minority oversampling technique(SMOTE)for handling class imbalance, Inform.Sci.50532–64. G.Douzas, F.Bacao, (2019) Geometric smote a geometrically enhanced drop-in replacement for smote, Information Sciences 501:118–135. Hao H, Jingming W (2015) Research on water inrush from the blind fault of coal floor by physical experiment. J North China Inst Sci Technol (nat Sci) 12(1):11–16 J.Li, Q.Zhu, Q.Wu, et al. (2021) SMOTE-NaN-DE: Addressing the noisy and borderline examples problem in imbalanced classification by natural neighbors and differential evolution, Knowl.-Based Syst.223107056. Jiang Zehua, et al (2021) Prediction of Coal Seam Floor Water Inrush Based on PCA-OPF Model, 36(1):6 Liu Z, Jin D, Liu Q (2009) Prediction of water inrush from seam floor based on binomial logistic regression model and CART tree. Coal Geol Explor 37(1):56–61 Liu Z, Jin D, Liu Q (2011) Prediction of water inrush through coal floors based on data mining classification technique. Procedia Earth Planet Sci 3:166–174. https://doi.org/10.1016/j.proeps.2011.09.079 Leng, Q, Guo, J , Jiao, E. , Meng, X , Wang, C (2023) Nanbdos: adaptive and parameter-free borderline oversampling via natural neighbor search for class-imbalance learning. Knowledge-based systems. Li J, Zhu Q, Wu Q,et al (2021) A novel oversampling technique for class-imbalanced learning based on SMOTE and natural neighbors. Information Sciences 565:438-455. Lian C, Mei Y, et al (2021) Application of Pca-Fisher Discriminant Model in Prediction of Water Inrush From Coal Seam Floor Journal of Mathematics in Practice and Theory, 51(6):9. N.V.Chawla, K.W.Bowyer, L.O.Hall, et al. (2002) SMOTE: Synthetic minorityover-sampling technique, J. Artificial Intelligence Res.16321–357 Pan, T., Zhao, J., Wu, W., Yang, J (2020) Learning imbalanced datasets based on SMOTE and Gaussian distribution. Information Sciences, 512, 1214-1233. P.Soltanzadeh, M.Hashemzadeh, (2021) Rcsmote: range-controlled synthetic minority over-sampling technique for handling the class imbalance problem, Information Sciences: 542:92–111. Qiao Y (2010) Application research of genetic algorithm and artificial neural networks in the prediction of mine water gushing-out. Xi’an University of Architecture and Technology, Xi’an (in Chinese) Qiu Xingguo, Li Jing (2022) Prediction model of water inrush in coal mine based on IWOA-SVM, 48(1):7 Shi LQ, Han J (2004) Floor water inrush mechanism and prediction. China University of Mining and Technology Press, Xuzhou Shi L, Gao W, Han J et al (2017) A nonlinear risk evaluation method for water inrush through the seam floor. Mine Water Environ 34(4):1–9. https://doi.org/10.1007/s10230-017-0449-1 Shi L (2012) Analysis of water inrush coefficient and its applicability. J Shandong Univ Sci Technol 31(6):6–9. https://doi.org/10.16452/j.cnki.sdkjzk.2012.06.002 S.Susan, A.Kumar, (2019) Ssomaj-smote-ssomin:Three-step intelligent pruning of majority and minority samples for learning from imbalanced datasets, Applied Soft Computing 78:141–149. Weitao L, Shanghui L, Shiliang L et al (2015) Principal component logistic regression analysis in application of water outbursts from coal seam floor. J Liaoning Tech Univ 34(8):905–909 Zhigang Y, Haibo B, Hairong Z (2008) A novel SVM model for the analysis and prediction of water inrush from coal mine. J Chin Secur Sci 18(7):166–170. https://doi.org/10.1016/S1005-8885(08)60096-5 Zhao Z, Hu M (2014) Multi-level forecasting model of coal mine water inrush based on self-adaptive evolutionary extreme learning machine. Appl Math Inf Sci Lett 2(3):103–110. https://doi.org/10.12785/amisl/020305 Zhao Z, Li P, Xu X (2013) Forecasting model of coal mine water inrush based on extreme learning machine. Appl Math Inf Sci 7(3):1243–1250. https://doi.org/10.12785/amis/070349 Zhao D, Wu Q, Cui F, Xu H, Zeng Y, Cao Y, Du Y (2018) Using random forest for the risk assessment of coal-floor water inrush in Panjiayao Coal Mine, northern China. Hydrogeol J 26(7):2327–2340. https://doi.org/10.1007/s10040-018-1767-5 Z. Xu, D. Shen, Y. Kou, et al (2022) A synthetic minority oversampling technique based on Gaussian mixture model filtering for imbalanced data classification, IEEE Trans. Neural Netw.Learn.Syst. 1–14, http://dx.doi.org/10.1109/TNNLS.2022.3197156. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editor assigned by journal 10 May, 2024 Submission checks completed at journal 09 May, 2024 First submitted to journal 07 May, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4385835","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":301127727,"identity":"0db89504-4905-4ccc-ad06-e7df2f995347","order_by":0,"name":"Shoufeng Tang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYDACZiDmOcDAz8DeABU5QKQWyR4ekNIEYrQwwLRIJBCpRb6d+eCDN2fqJOwlHz+TuvmDQY7vRgLj5wI8WgwOsyUbzrlxWIJHOs1MOieBwVjyRgKz9Ax8Wph5zKR5Phyo45HOYQNpSdxwI4GNmQefw5r5v//m+VAnwSN5BqylnqAWhsM8QAU3mCV4JHjAWhIMCGkB+sVYcs4ZoF/OpBlb56RJGM4887BZGq/D+g8//PDmWJ0Ee/vhh7dzbGzk+Y4nH/yM12FoQAKIGRtI0DAKRsEoGAWjABsAANK0Ri2hjdOdAAAAAElFTkSuQmCC","orcid":"","institution":"China University of Mining and Technology","correspondingAuthor":true,"prefix":"","firstName":"Shoufeng","middleName":"","lastName":"Tang","suffix":""},{"id":301127728,"identity":"01c64f1c-d96f-4ac9-be6e-8c33430e541a","order_by":1,"name":"Ye Zhang","email":"","orcid":"","institution":"China University of Mining and Technology","correspondingAuthor":false,"prefix":"","firstName":"Ye","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-05-08 01:54:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4385835/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4385835/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":56877096,"identity":"8d7713af-eefb-4303-8c29-88adc749f760","added_by":"auto","created_at":"2024-05-21 15:20:36","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":231119,"visible":true,"origin":"","legend":"\u003cp\u003eThe overview of the proposed model\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/bad2914b5419980940722949.png"},{"id":56876670,"identity":"98250593-c07e-4c2d-957d-e053f051dd13","added_by":"auto","created_at":"2024-05-21 15:12:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":6262,"visible":true,"origin":"","legend":"\u003cp\u003eNoise points and outliers in the data set\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/24be55c0c552fbe574916b5f.png"},{"id":56877095,"identity":"cb30413a-0540-4002-89bd-9f3afa9473a2","added_by":"auto","created_at":"2024-05-21 15:20:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":26075,"visible":true,"origin":"","legend":"\u003cp\u003eBorderline sample oversampling method\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/447d66b6e118319b38c06865.png"},{"id":56877094,"identity":"bc7b9111-9808-42ce-a90f-41c2de768ddb","added_by":"auto","created_at":"2024-05-21 15:20:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":9096,"visible":true,"origin":"","legend":"\u003cp\u003eCenter sample space oversampling method\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/fd23a5a7fdfe49a03151304a.png"},{"id":56876671,"identity":"06a803a7-62ac-4e80-a10f-a31debe2000e","added_by":"auto","created_at":"2024-05-21 15:12:35","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":14996,"visible":true,"origin":"","legend":"\u003cp\u003eResults of ISMOTE algorithm under complex data distribution conditions\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/052b8e01caf80e9074553418.png"},{"id":56876673,"identity":"8b5b4dca-7397-4faf-be1c-fed6337f695a","added_by":"auto","created_at":"2024-05-21 15:12:36","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":51828,"visible":true,"origin":"","legend":"\u003cp\u003eSparse autoencoder structure based on mutual information\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/e43370ee078a3fb5cc98d7d3.png"},{"id":56876675,"identity":"e8f32887-22fd-4c00-acd6-5e92e020287b","added_by":"auto","created_at":"2024-05-21 15:12:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":789379,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/7ccd1131b1695229aeb05652.png"},{"id":56876676,"identity":"6cfb5859-b740-49ce-8ae3-b1790f9cc137","added_by":"auto","created_at":"2024-05-21 15:12:36","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":605909,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/4420068c38327698e9c096e9.png"},{"id":56877619,"identity":"71027f7c-9e06-46bc-99ed-c688cfb4548d","added_by":"auto","created_at":"2024-05-21 15:28:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2471517,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4385835/v1/92f33600-d6c4-46b9-b65f-5ec07648cce0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Evaluation of the Mine Water Inrush based on the Data expansion and Deep learning","fulltext":[{"header":"Highlight","content":"\u003cp\u003eThe main contributions of this article are as follows:\u003c/p\u003e\u003cp\u003e(1) A new oversampling data preprocessing method is proposed. Natural neighbors theory is introduced to remove outliers and noise points existing in water inrush datasets.\u003c/p\u003e\u003cp\u003e(2) A new oversampling data augmentation algorithm is proposed. This algorithms divides minority class samples into center samples and borderline samples according to natural neighbors theory. The center samples are oversampled via spatial interpolation to increase the diversity of synthetic samples. The natural neighbors interpolation method is used for borderline samples to reduce the probability of synthetic noise and retain the distribution pattern of the original data.\u003c/p\u003e\u003cp\u003e(3) Mutual information dropout is introduced into the SAE to retain neurons that are conducive to the expression of water inrush features through the mutual information mask matrix, extract highly relevant water inrush accident features, and improve the accuracy of the prediction model.\u003c/p\u003e\u003cp\u003e(4) The causes and water inrush channels of the coal seam floor are analyzed and studied. The main geological and hydrological factors affecting the occurrence of floor water inrush accidents are determined.\u003c/p\u003e"},{"header":"Introduction","content":"\u003cp\u003eThe mining environment in North China coalfields is complex. As coal mines continue to be mined deeper, the pressure on the coal seam floor has also increased. Under the combined influence of various unfavorable factors, such as high pressure, high water content, and confining layer thinning, the risk of water inrush increases significantly. Through studies on the water inrush mechanism, many scholars have applied data analysis algorithms, such as regression analysis (Shi and Han. 2004; Du et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Weitao et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), classification ( Liu et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), support vector machine(Shi et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Cao and hao 2011; Zhigang et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Qiao \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), neural network (Zhao and Hu \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Zhao et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Shi \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), and random forest algorithms (Zhao et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), to the prediction of water inrush in coal mines.\u003c/p\u003e \u003cp\u003eDue to the small amount of water inrush data in coal mines, the data features required for the prediction model cannot be provided, which reduces the accuracy of the prediction model. This paper presents a new oversampling method. Different from the traditional \u003cem\u003eSMOTE\u003c/em\u003e (N.V.Chawla. et al.2002) method of randomly selecting sampling points and linear interpolation, this paper introduces the natural neighbors theory (J.Li. et al2021, Leng Q. et al \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e, Li J, Zhu Q, Wu Q. et al \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) to determine the neighbor relationships between samples. The outliers and noise values existing in the water inrush dataset are removed to reduce the risk of overfitting of the prediction model, and the water inrush data samples are divided into center minority class samples and borderline minority class samples (Z. Xu. et al 2022, G.Douzas, F.Bacao. 2019, S.Susan, A.Kumar. 2019). Since the nearest neighbor of a borderline minority sample contains majority class samples, it is easier to generate new noise samples as sampling points. To address this problem, this paper presents a natural neighbors interpolation method to expand the amount of data. At the same time, for center minority samples, a spatial interpolation method is proposed to generate new synthetic water inrush samples.\u003c/p\u003e \u003cp\u003eThis paper presents an improved \u003cem\u003eSMOTE\u003c/em\u003e (\u003cem\u003eISMOTE\u003c/em\u003e) algorithm based on natural neighbors and spatial interpolation to expand a water inrush sample set and uses the mutual information dropout sparse autoencoder (\u003cem\u003eMISAE\u003c/em\u003e) to extract the characteristics of coal mine water inrush data and evaluate the risk of coal mine water inrush. At present, few studies have focused on water inrush prediction methods based on data augmentation deep learning.\u003c/p\u003e "},{"header":"Water accident assessment model","content":"\u003cp\u003eThe occurrence of water inrush accidents in coal mines is the result of a variety of influencing factors. There is an interaction between the influencing factors of the accident, which makes the water inrush accident and its influencing factors form a nonlinear system. The Ministry of Coal proposed the water inrush coefficient method (Hao and Jingming \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The \u0026ldquo;lower three belts\u0026rdquo; theory (Zhang and Liu 1990), the \u0026ldquo;two-zone\u0026rdquo; model (Shi and Han 2005; Duan 2012), the \u0026ldquo;lower four belts\u0026rdquo; theory (Minggao et al. 1995), the \u0026ldquo;Strong Permeability Channel\u0026rdquo; theory (Li 2014), the \u0026ldquo;KS\u0026rdquo; (Key Strata) theory (Shi et al. 2015), etc. were all born out of this. The analysis reveals that the five first-level indicators of aquifer conditions, aquifer conditions, coal seam conditions, structural conditions, and mining conditions, as well as the corresponding twelve secondary indicators, are the primary factors affecting the water inrush from the coal floor. This conclusion is based on the summary of prior studies. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the influencing factors of coal seam water inrush.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMain influencing factors of coal seam water inrush\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFirst-level indicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSecondary-level indicators\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eAquifer conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAquifer thickness\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAquifer water pressure\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWorking surface distance\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eWater barrier conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMuddy rock thickness\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSandy rock thickness\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLimestone section thickness\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCoal seam conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCoal seam thickness\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCoal seam dip\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstruction conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFault drop\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eMining conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMining area\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStrike length\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMining height\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Method theory","content":"\u003cdiv id=\"Sec4\"\u003e\n \u003ch2\u003eNatural neighbors theory\u003c/h2\u003e\n \u003cp\u003eThe idea of natural neighbors theory is inspired by real-world friend relationships. If sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e has sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e as a nearest neighbor and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e also has \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e as a nearest neighbor, then samples \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e are true neighbors of each other. The natural neighbors theory is a detection algorithm without parameter settings. This algorithm continuously searches for the \u003cem\u003er\u003c/em\u003e-nearest neighbors of each sample in the dataset during operation until each sample has \u003cem\u003er\u003c/em\u003e-nearest neighbors of each other, thus forming a stable data structure. At this time, the eigenvalue \u003cem\u003e\u0026lambda;\u003c/em\u003e is equal to \u003cem\u003er\u003c/em\u003e.\u003c/p\u003e\n \u003cdiv id=\"Equ1\"\u003e\n \u003cdiv id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$$\\left( {\\forall {x_i}} \\right)\\left( {\\exists {x_j}} \\right)\\left( {r \\in n} \\right) \\wedge \\left( {{x_i} \\ne {x_j}} \\right) \\to \\left( {x_{i}^{{}} \\in N{N_r}\\left( {{x_j}} \\right)} \\right) \\wedge \\left( {{x_j} \\in N{N_r}\\left( {{x_i}} \\right)} \\right)$$\u003c/div\u003e\n \u003cdiv\u003e1\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn the formula, \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e represent two different samples in the dataset, and \u003cem\u003eNN\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) and \u003cem\u003eNN\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e) represent the sets of \u003cem\u003er\u003c/em\u003e nearest neighbors of \u003cem\u003exi\u003c/em\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e, respectively. In a stable data structure, there is a different sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e for any \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, making them the \u003cem\u003er\u003c/em\u003e nearest neighbors to each other.\u003c/p\u003e\n \u003cp\u003eIf \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e belongs to the \u003cem\u003e\u0026lambda;\u003c/em\u003e nearest neighbor of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e, and at the same time, sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e also belongs to the \u003cem\u003e\u0026lambda;\u003c/em\u003e nearest neighbor of sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, then the two samples are natural neighbors of each other, as shown in Eq.\u0026nbsp;\u003cspan\u003e2\u003c/span\u003e\u003c/p\u003e\n \u003cdiv id=\"Equ2\"\u003e\n \u003cdiv id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$${x_i} \\in NaN\\left( {{x_j}} \\right) \\Leftrightarrow {x_i} \\in N{N_r}\\left( {{x_j}} \\right) \\wedge {x_j} \\in N{N_r}\\left( {{x_i}} \\right)$$\u003c/div\u003e\n \u003cdiv\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn the formula, \u003cem\u003eNN\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e) represents the natural neighbors set of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e\n \u003cp\u003eIf there is an outlier in the dataset, then if and only if all samples except this point have reached the natural stable structure. Outliers have no natural neighbors, that is, \u003cem\u003eNaN\u003c/em\u003e (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;=\u0026thinsp;0.\u003c/p\u003e\n \u003cp\u003eBased on the definition of outliers, when the natural neighbors search algorithm is running, the algorithm stops if the number of inverse neighbor samples in two adjacent iterations remains unchanged. At this time, samples without inverse nearest neighbors are outliers, and the search pseudocode is shown in Algorithm 1.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Taba\" border=\"1\"\u003e\n \u003ccolgroup cols=\"1\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAlgorithm-1 Search for \u003cem\u003eNaN\u003c/em\u003e (\u003cem\u003eNaN-Search\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInput: Water inrush data set \u003cem\u003eX\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOutput: natural neighbors feature \u003cem\u003e\u0026lambda;\u003c/em\u003e, natural neighbors NaN, number of inverse neighbors of the sample \u003cem\u003enb\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1: Initialize the search round number \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, \u003cem\u003enum\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0 (the number of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e with \u003cem\u003enb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0), \u003cem\u003eNN\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)=\u003cem\u003e\u0026empty;\u003c/em\u003e, \u003cem\u003eRNN\u003c/em\u003e(\u003cem\u003exi\u003c/em\u003e)=\u003cem\u003e\u0026empty;\u003c/em\u003e (\u003cem\u003exi\u003c/em\u003e\u0026rsquo;s inverse nearest neighbor), \u003cem\u003eNaN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)=\u003cem\u003e⊘\u003c/em\u003e;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2: Establish a \u003cem\u003ek-dimensional\u003c/em\u003e tree on the water inrush data set \u003cem\u003eX\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3: For each \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eX\u003c/em\u003e, find its \u003cem\u003er\u003c/em\u003e-th neighbor \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e by using \u003cem\u003ek-d\u003c/em\u003e tree. Update \u003cem\u003enb\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003enb\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;+\u0026thinsp;1, \u003cem\u003eNNr\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003eNNr\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)\u0026cup;{\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e}, \u003cem\u003eRNN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003eRNN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e)\u0026cup;{\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e};\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4: Compute the number num of xi with \u003cem\u003enb\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;0;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5: If num does not change \u003cem\u003e\u0026lambda;\u0026thinsp;=\u0026thinsp;r\u003c/em\u003e;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6: For each \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eX\u003c/em\u003e, \u003cem\u003eNaN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003eRNN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)\u0026cap;\u003cem\u003eNN\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e);\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7: Otherwise \u003cem\u003er\u0026thinsp;=\u0026thinsp;r\u0026thinsp;+\u0026thinsp;1\u003c/em\u003e, go to step 3;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8: Return: \u003cem\u003e\u0026lambda;\u003c/em\u003e, \u003cem\u003eNaN\u003c/em\u003e, \u003cem\u003enb\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\"\u003e\n \u003ch2\u003eCoal mine water inrush prediction model based on data augmentation\u003c/h2\u003e\n \u003cp\u003eThe data-expanded surge prediction algorithm presented in this paper consists of three basic sub-structures: the decoder network (for mapping high-dimensional surge data overlapping into characteristic space), the oversampling model (using natural neighbors theory to remove outlier and noise sample, generate high-quality new samples using the proposed spatial insert method) and the decoder network (to map the synthetic sample back into the original space). In particular: 1. The mutual information dropout autoencoder is trained using (\u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e) from the original data set. 2. Use the trained encoder network to map \u003cem\u003eX\u003c/em\u003e into a feature space with better inter-class separability(\u003cem\u003ez\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eEncoder\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)). 3. Using the natural neighbors theory, remove noisy points and outliers from the data sets and determine center and borderline samples. In order to produce high-quality synthetic data \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e, samples are oversampled using the two spatial oversampling techniques presented in this article. 4. Map \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e back to the original space using the trained decoder network, then combine it with the original data \u003cem\u003ex\u003c/em\u003e to create an expanded data set. After obtaining the expanded data set, an autoencoder is used to predict water inrush accidents (Dan Liu, 2023, P.Soltanzadeh, M.Hashemzadeh, 2021).\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eNatural neighbors based spatial interpolation\u003c/strong\u003e \u003cstrong\u003eSMOTE\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eThis paper introduces the natural neighbors theory into the \u003cem\u003eSMOTE\u003c/em\u003e algorithm. First, the natural neighbors search algorithm in Algorithm 1 is used to search the dataset to remove noise and outliers. Then, the minority class samples are divided into center samples and borderline samples based on natural neighbors theory, and two different spatial interpolation methods are used to generate new water inrush samples. Finally, adds the synthesized water inrush samples to the original dataset to expand the water inrush dataset (A. Wahid, C.S.R. Annavarapu. 2021, D.Elreedy, A.F.Atiya. 2019). The Fig.\u0026nbsp;\u003cspan\u003e1\u003c/span\u003e shows the main structure of the algorithm proposed in this article.\u003c/p\u003e\n \u003cp\u003eThe model performs three steps in the oversampling stage, including removing outliers and noise points, distinguishing borderline samples and center samples, and synthesizing new instances.\u003c/p\u003e\n \u003cp\u003eA binary classification dataset \u003cem\u003eX\u003c/em\u003e consists of majority class samples \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emaj\u003c/em\u003e\u003c/sub\u003e and minority class samples \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e. \u003cem\u003eLabel\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) represents the class label of sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eX\u003c/em\u003e. Based on the natural neighbors theory, noise samples and outlier samples are defined as follows:\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eDefinition 1\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eIf sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e satisfies \u0026forall;\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eNaN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) and \u003cem\u003eLabel\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;\u0026ne;\u0026thinsp;\u003cem\u003eLabel\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e), then \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is a noise point. That is, if \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e belongs to the minority class sample but its natural neighbors are all majority class samples, then \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is defined as a noise point.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eDefinition 2\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eIf sample x\u003csub\u003ei\u003c/sub\u003e satisfies ∣\u003cem\u003eNaN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)∣==0, ∣\u003cem\u003eNaN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)∣ represents the number of natural neighbors of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e. Then, \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is defined as an outlier.\u003c/p\u003e\n \u003cp\u003eNoise and outliers in the dataset will affect the normal data distribution of the sample, making it difficult for the classifier to fit the offset points and thus resulting in a decrease in the generalizability of the prediction model. Therefore, in the coal mine water inrush prediction model, noise and outliers must first be removed from the original dataset. After removing noise and outliers from the preprocessed water inrush dataset, it becomes a regularly distributed dataset, and better prediction accuracy can be achieved.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eDefinition 3\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eIf sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e and xi is not noise or an outlier, if \u0026exist;\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eNaN\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e) makes \u003cem\u003eLabel\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;\u0026ne;\u0026thinsp;\u003cem\u003eLabel\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e), then x\u003csub\u003ei\u003c/sub\u003e is defined as a borderline minority class sample.\u003c/p\u003e\n \u003cp\u003eThere are majority class samples in the natural neighbors sample of the borderline samples, but when their natural neighbors are all majority class samples, \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is a noise point. The Fig.\u0026nbsp;\u003cspan\u003e2\u003c/span\u003e shows the noise points and outliers in the data set.\u003c/p\u003e\n \u003cp\u003eAccording to the natural neighbors search algorithm, borderline minority class samples existing in the dataset can be identified through traversal, and the Danger dataset is used to store these borderline samples. Since there are majority class samples among the natural neighbors of the borderline samples, it is easier to synthesize incorrect class samples during oversampling. Therefore, in this paper, two different spatial oversampling methods are used to oversample center minority samples and borderline minority class samples, thereby generating new samples of the required categories and reducing noise and damage to the distribution of the original dataset (Pan,T et al. 2020).\u003c/p\u003e\n \u003cp\u003eFor the borderline sample \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eDanger\u003c/em\u003e, two minority class natural neighbors sample \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei2\u003c/em\u003e\u003c/sub\u003e of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e are randomly selected. The algorithm first uses the natural neighbors sample \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei2\u003c/em\u003e\u003c/sub\u003e to synthesize the midpoint according to Formula 3,4 and then connects \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e and the \u003cem\u003emidpoint\u003c/em\u003e and performs interpolation to synthesize a new sample.\u003c/p\u003e\n \u003cdiv id=\"Equ3\"\u003e\n \u003cdiv id=\"FileID_Equ3\" name=\"EquationSource\"\u003e$${S_{{\\text{mid}}}}={S_{i1}}+{\\delta _1}({S_{i2}} - {S_{i1}})$$\u003c/div\u003e\n \u003cdiv\u003e3\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ4\"\u003e\n \u003cdiv id=\"FileID_Equ4\" name=\"EquationSource\"\u003e$$S_{i}^{{new}}={S_i}+{\\delta _2}({S_{mid}} - {S_i})$$\u003c/div\u003e\n \u003cdiv\u003e4\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cem\u003e\u0026delta;1\u003c/em\u003e and \u003cem\u003e\u0026delta;2\u003c/em\u003e in the formula are two random numbers between 0 and 1. This step is repeated until borderline sample oversampling is complete. The Fig.\u0026nbsp;\u003cspan\u003e3\u003c/span\u003e shows the Borderline sample oversampling method.\u003c/p\u003e\n \u003cp\u003eFor the center minority sample \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u0026isin;\u003cem\u003eSafe\u003c/em\u003e in the dataset, sample \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e is selected, and the sample point \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e with the largest Euclidean distance \u003cem\u003ed\u003c/em\u003e between the selected sample and the \u003cem\u003eSafe\u003c/em\u003e dataset is calculated to form a sampling space, as shown in the Fig.\u0026nbsp;\u003cspan\u003e4\u003c/span\u003e.Assume that \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e=\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e,\u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e) and the farthest Euclidean distance sample point in the minority class sample set is \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e=\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e,\u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e). A data point is randomly sampled in the adoption space as a synthetic sample point \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e=(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e,\u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e), where \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e=\u003cem\u003erandom\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e,\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e) and \u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e=\u003cem\u003erandom\u003c/em\u003e(\u003cem\u003ey\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e,\u003cem\u003ey\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e). Different from the \u003cem\u003eSMOTE\u003c/em\u003e, the new synthetic sample point is located in the sampling space formed by the selected sample and its farthest sample in the minority class rather than on the line connecting the two points.\u003c/p\u003e\n \u003cp\u003eThe farthest distance sample point is selected to form a sampling space to randomly form synthetic samples. Compared with linear sampling, the proposed sampling approach can form a more diverse synthetic sample set, and there will be no situation where sample-dense areas become denser and sparse areas become sparser and effectively addresses the drawbacks of the \u003cem\u003eSMOTE\u003c/em\u003e algorithm, which alters the data distribution pattern with ease. The spatial interpolation method enhances the sample set\u0026apos;s mathematical features\u0026apos; comprehensiveness and diversifies the characteristics of the minority class data. The results of \u003cem\u003eNaN-ISMOTE\u003c/em\u003e algorithm under complex data distribution conditions is shown in Fig.\u0026nbsp;\u003cspan\u003e5\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\"\u003e\n \u003ch2\u003eMISAE\u003c/h2\u003e\n \u003cp\u003eIn this paper, an encoder-decoder is used to learn a separable feature space so that samples of different categories are far apart. In this case, the synthetic samples are also far from the majority class samples, thus reducing the risk of falling into the danger zone.\u003c/p\u003e\n \u003cp\u003eThe encoder network aims to map raw data into a separable feature space and consists of multiple encoder layers. The encoder is represented as:\u003c/p\u003e\n \u003cdiv id=\"Equ5\"\u003e\n \u003cdiv id=\"FileID_Equ5\" name=\"EquationSource\"\u003e$$z=f(Wx+b)$$\u003c/div\u003e\n \u003cdiv\u003e5\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn the formula, \u003cem\u003ef\u003c/em\u003e represents the activation function of the neuron, \u003cem\u003eW\u003c/em\u003e is defined as the weight matrix, and \u003cem\u003eb\u003c/em\u003e is the bias vector of the hidden layer.\u003c/p\u003e\n \u003cp\u003eThe function of the encoder is to transform the output from the hidden layer to the reconstructed data output vector.\u003c/p\u003e\n \u003cdiv id=\"Equ6\"\u003e\n \u003cdiv id=\"FileID_Equ6\" name=\"EquationSource\"\u003e$$\\overset{\\lower0.5em\\hbox{$\\smash{\\scriptscriptstyle\\frown}$}}{x} =h(W\u0026apos;z+b)$$\u003c/div\u003e\n \u003cdiv\u003e6\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn the formula, \u003cem\u003eh\u003c/em\u003e is the activation function of the hidden layer of the autoencoder, \u003cem\u003eW\u003c/em\u003e is the weight matrix between model layers, and \u003cem\u003eb\u003c/em\u003e is the bias vector output by the output layer. The objective function of the autoencoder can be defined as:\u003c/p\u003e\n \u003cdiv id=\"Equ7\"\u003e\n \u003cdiv id=\"FileID_Equ7\" name=\"EquationSource\"\u003e$$J=\\frac{1}{N}\\sum\\limits_{{m=1}}^{M} {(\\frac{1}{2}\\left\\| {{y_m} - {x_m}} \\right\\|_{2}^{2})}$$\u003c/div\u003e\n \u003cdiv\u003e7\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn the formula, the error between the original sample set input data \u003cem\u003ex\u003c/em\u003e and the reconstructed data \u003cem\u003ey\u003c/em\u003e decoded by the decoder is expressed as \u003cem\u003eJ\u003c/em\u003e. By minimizing the error \u003cem\u003eJ\u003c/em\u003e, each parameter of the autoencoder is optimized to obtain the optimal data representation of the input data.\u003c/p\u003e\n \u003cp\u003eSince the influencing factors of water inrush accidents have different contributions to accidents, \u003cem\u003eMI-Dropout\u003c/em\u003e is introduced into the encoder layer. By establishing a binary mask moment of mutual information sorting, the weight of feature neurons with a small correlation is set to 0, and the neurons that are beneficial to the expression of water intrusion features are retained. The mutual information is expressed as:\u003c/p\u003e\n \u003cdiv id=\"Equ8\"\u003e\n \u003cdiv id=\"FileID_Equ8\" name=\"EquationSource\"\u003e$$I(X,Y)=H(x)+H(y) - H(x,y)$$\u003c/div\u003e\n \u003cdiv\u003e8\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ9\"\u003e\n \u003cdiv id=\"FileID_Equ9\" name=\"EquationSource\"\u003e$$H(X)= - \\int\\limits_{x} {p(x)\\log p(x)dx}$$\u003c/div\u003e\n \u003cdiv\u003e9\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cem\u003ep\u003c/em\u003e(\u003cem\u003ex,y\u003c/em\u003e) represents the joint probability density, and \u003cem\u003ep\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) and \u003cem\u003ep\u003c/em\u003e(\u003cem\u003ey\u003c/em\u003e) are the marginal probability density functions. \u003cem\u003eH\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) is defined as the entropy of parameter x. The water inrush label dataset defines the output matrix of the l-th hidden layer of the model as \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003el\u003c/em\u003e\u003c/sup\u003e. Then, the mutual information between the target expression and the output of the hidden layer neuron is calculated:\u003c/p\u003e\n \u003cdiv id=\"Equ10\"\u003e\n \u003cdiv id=\"FileID_Equ10\" name=\"EquationSource\"\u003e$$I(h_{i}^{l},Y)=H(h_{i}^{l})+H(y) - H(h_{i}^{l},y)$$\u003c/div\u003e\n \u003cdiv\u003e10\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe mutual information is sorted to obtain the vector \u003cem\u003eS\u003c/em\u003e in descending order, and a new mask matrix is constructed:\u003c/p\u003e\n \u003cdiv id=\"Equ11\"\u003e\n \u003cdiv id=\"FileID_Equ11\" name=\"EquationSource\"\u003e$$\\varepsilon _{i}^{l}=\\left( {\\begin{array}{*{20}{c}} {\\begin{array}{*{20}{c}} 1\u0026amp;{S_{i}^{l} \\geqslant k\\cdot \\mu } \\end{array}} \\\\ {\\begin{array}{*{20}{c}} 0\u0026amp;{S_{i}^{l}\u0026lt;k\\cdot \\mu } \\end{array}} \\end{array}} \\right.$$\u003c/div\u003e\n \u003cdiv\u003e11\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn the formula, \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003el\u003c/em\u003e\u003c/sup\u003e is the position of the \u003cem\u003ei-th\u003c/em\u003e neuron in the \u003cem\u003el-th\u003c/em\u003e hidden layer in the vector. \u003cem\u003e\u0026Mu;\u003c/em\u003e is the loss rate in the random deactivation strategy. The larger the value is, the more neurons in the hidden layer are activated. The forward propagation process of the model is expressed as:\u003c/p\u003e\n \u003cdiv id=\"Equ12\"\u003e\n \u003cdiv id=\"FileID_Equ12\" name=\"EquationSource\"\u003e$$\\tilde {h}_{i}^{l}=\\varepsilon _{i}^{l} * h_{i}^{l}$$\u003c/div\u003e\n \u003cdiv\u003e12\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ13\"\u003e\n \u003cdiv id=\"FileID_Equ13\" name=\"EquationSource\"\u003e$$z_{i}^{{l+1}}=w_{i}^{{l+1}}\\tilde {h}_{i}^{l}+b_{i}^{{l+1}}$$\u003c/div\u003e\n \u003cdiv\u003e13\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ14\"\u003e\n \u003cdiv id=\"FileID_Equ14\" name=\"EquationSource\"\u003e$$h_{i}^{{l+1}}=f(z_{i}^{{l+1}})=f(w_{i}^{{l+1}}\\tilde {h}_{i}^{l}+b_{i}^{{l+1}})$$\u003c/div\u003e\n \u003cdiv\u003e14\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eMISAE includes three basic modules:\u003c/p\u003e\n \u003cp\u003e(1) Feature extraction layer. An autoencoder is used as the feature extraction layer structure, which is defined as \u003cem\u003eg\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e;\u003cem\u003ew\u003c/em\u003e;\u003cem\u003eb\u003c/em\u003e), where x is the input function of the model and w and b are the interlayer weights and bias sizes, respectively, that need to be learned in the SAE model. \u003cem\u003eG\u003c/em\u003e() is the feature extractor function constructed by the SAE, which is used to extract hidden features in water inrush data;\u003c/p\u003e\n \u003cp\u003e(2) The \u003cem\u003eMI-Dropout\u003c/em\u003e layer. In this layer, the neurons in the hidden layer are sorted through mutual information, and a binary mask matrix is constructed to randomly deactivate the neurons in the hidden layer. The output vector of the mutual information drop layer is used as the input of the next feature extraction layer or combined with the softmax layer for model prediction;\u003c/p\u003e\n \u003cp\u003e(3) The \u003cem\u003esoftmax\u003c/em\u003e classification layer is defined as \u003cspan\u003e\u003cspan\u003e\\(y=soft\\hbox{max} (\\tilde {h}_{i}^{l};w;b)\\)\u003c/span\u003e\u003c/span\u003e. The structure is shown in Fig.\u0026nbsp;\u003cspan\u003e6\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eThe oversampling algorithm is shown in Algorithm 2.\u003c/p\u003e\n \u003cdiv\u003e\n \u003cdiv align=\"left\"\u003e\u003cimg src=\"https://myfiles.space/user_files/122228_c8a1650c59388082/122228_custom_files/img1716303690.png\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\"\u003e\n \u003ch2\u003eCase Analysis\u003c/h2\u003e\n \u003cp\u003eIn this section, we evaluate the performance of the coal mine water inrush prediction algorithm proposed in this paper and test it on water inrush data extracted from actual working faces in typical mining areas in North China. Comparison algorithms include \u003cem\u003eIWOA-SVM, PCA-OPF, PCA-Fisher\u003c/em\u003e and other recent water inrush prediction algorithms (Lian C, Mei Y, et al \u003cspan\u003e2021\u003c/span\u003e, Jiang Zehua, et al 2021, Qiu Xingguo, LiJing 2022), as well as the oversampling algorithms \u003cem\u003eSMOTE\u003c/em\u003e and \u003cem\u003eBorderline-SMOTE\u003c/em\u003e. The \u003cem\u003eSMOTE\u003c/em\u003e parameters are set to \u003cem\u003ek1\u0026thinsp;=\u0026thinsp;5\u003c/em\u003e, and the \u003cem\u003eBL-SMOTE\u003c/em\u003e parameters are set to \u003cem\u003ek1\u0026thinsp;=\u0026thinsp;5\u003c/em\u003e and \u003cem\u003ek2\u0026thinsp;=\u0026thinsp;5\u003c/em\u003e.\u003c/p\u003e\n \u003cp\u003eClassification algorithms generally use \u003cem\u003eAccuracy\u003c/em\u003e as the main result analysis indicator. \u003cem\u003eRecall\u003c/em\u003e and the \u003cem\u003eF-measure\u003c/em\u003e are also used for performance evaluation.\u003c/p\u003e\n \u003cdiv id=\"Equ15\"\u003e\n \u003cdiv id=\"FileID_Equ15\" name=\"EquationSource\"\u003e$$\\begin{gathered} Accuracy=\\frac{{TP+TN}}{{TP+TN+FP+FN}} \\hfill \\\\ Recall=\\frac{{TP}}{{TP+FN}} \\hfill \\\\ F - measure=\\frac{{{{(1+\\beta )}^2}*recall*precision}}{{{\\beta ^2}*recall*precision}} \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\n \u003cdiv\u003e15\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe accuracy is calculated as the ratio of the number of correct classifications of the algorithm to the total number of samples. The higher the \u003cem\u003eAccuracy\u003c/em\u003e is, the better the performance of the prediction algorithm. \u003cem\u003eF1\u003c/em\u003e is the harmonic mean of precision and recall, mainly focusing on the minority class. The \u003cem\u003eRecall\u003c/em\u003e indicates the number of positive samples correctly predicted by the algorithm among the original samples present in the dataset samples.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\"\u003e\n \u003ch2\u003eWater inrush dataset experiment\u003c/h2\u003e\n \u003cp\u003eAll water inrush data used in the experiments in this section are collected from the Internet of Things Research Center of the China University of Mining and Technology, who measured water inrush data on working faces in typical mining areas in North China. A total of \u003cem\u003e80\u003c/em\u003e sets of collected data is used in the experiments. After the data collection is completed, all water inrush instance data is standardized. The standardization formula is as follows:\u003c/p\u003e\n \u003cdiv id=\"Equ16\"\u003e\n \u003cdiv id=\"FileID_Equ16\" name=\"EquationSource\"\u003e$${x_{norm}}=\\frac{{x - {x_{\\hbox{min} }}}}{{{x_{\\hbox{max} }} - {x_{\\hbox{min} }}}}$$\u003c/div\u003e\n \u003cdiv\u003e16\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cstrong\u003eNaN-ISMOTE-MISAE\u003c/strong\u003e \u003cstrong\u003ealgorithm ablation experiment\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eThe \u003cem\u003eNaN-ISMOTE-MISAE\u003c/em\u003e algorithm proposed in this article first uses natural neighbors to remove noise points and outliers and then uses different interpolation methods for data expansion according to the different areas where the minority class samples are located. Second, the prediction model uses the \u003cem\u003eMISAE\u003c/em\u003e algorithm to extract highly relevant water inrush features. Therefore, two \u003cem\u003eSMOTE\u003c/em\u003e prediction models without natural neighbors data preprocessing and refined sampling methods are used to verify the effectiveness of the proposed oversampling method. The prediction results of the \u003cem\u003eSAE\u003c/em\u003e and \u003cem\u003eMISAE\u003c/em\u003e are compared using the same dataset to verify the effectiveness of the proposed water inrush feature extraction method. Figure\u0026nbsp;\u003cspan\u003e7\u003c/span\u003e and Table\u0026nbsp;\u003cspan\u003e2\u003c/span\u003e shows the prediction curves of the different models.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 2\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eAblation experiment results\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tabc\" border=\"1\"\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNaN-ISMOTE-MISAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNaN-ISMOTE-SAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBLSMOTE-MISAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSMOTE-MISAE\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eAccuracy\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9375\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8750\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eRecall\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9524\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9259\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9245\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9057\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eF1 Score\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9362\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9346\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9245\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9057\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe prediction value obtained based on the prediction model proposed in this article is more consistent with the actual water inrush sample label. Under the same operating environment and dataset, the ability of the proposed method to predict mine floor water inrush is stronger. The data augmentation algorithm can effectively increase the number of water inrush samples in the dataset, increase the diversity of the synthetic dataset, and provide sufficient water inrush occurrence characteristics. A comparison of the prediction results of the \u003cem\u003eNaN-ISMOTE-MISAE\u003c/em\u003e and \u003cem\u003eNaN-ISMOTE-SAE\u003c/em\u003e shows that in the traditional \u003cem\u003eSAE\u003c/em\u003e model, the noise information of irrelevant variables in water inrush samples will propagate to high-dimensional features, causing the model to extract irrelevant variable information and affecting the feature extraction performance of the water inrush prediction model. The \u003cem\u003eMISAE\u003c/em\u003e resets the weight of feature neurons with a smaller correlation to \u003cem\u003e0\u003c/em\u003e, retains neurons that are beneficial to the expression of water inrush features, improves feature extraction capabilities, and obtains better prediction accuracy. Comparing the results of the \u003cem\u003eNaN-ISMOTE-MISAE\u003c/em\u003e, \u003cem\u003eSMOTE-MISAE\u003c/em\u003e and \u003cem\u003eBLSMOTE-MISAE\u003c/em\u003e oversampling algorithms, the model results proposed in this article are better. This is due to the introduction of natural neighbors theory to preprocess the dataset. Using natural neighbors theory to eliminate noise and outliers and create a normally distributed data set. This enhanced the prediction model\u0026apos;s capacity for generalization. In the borderline sample and center sample regions, the \u003cem\u003eNaN-ISMOTE\u003c/em\u003e algorithm simultaneously employs two sampling techniques. Among these, the risk of noise produced when borderline samples are oversampled is efficiently decreased by random interpolation of natural nearest neighbor intermediate points. The use of spatial random interpolation method in the center sample can improve the diversity of the synthetic data set. Therefore, the \u003cem\u003eNaN-ISMOTE\u003c/em\u003e algorithm improves the accuracy of subsequent prediction algorithms.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eComparison between the\u003c/strong\u003e \u003cstrong\u003eNaN-ISMOTE-MISAE\u003c/strong\u003e \u003cstrong\u003ealgorithm and water inrush prediction algorithms in recent years\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eThe comparison results between the prediction algorithm proposed in this paper and the coal mine floor water inrush prediction algorithm proposed in recent years are shown in Fig.\u0026nbsp;\u003cspan\u003e8\u003c/span\u003e and Table\u0026nbsp;\u003cspan\u003e3\u003c/span\u003e. The \u003cem\u003eNaN-ISMOTE\u003c/em\u003e expanded water inrush dataset is used. Compared with traditional algorithms such as \u003cem\u003ePCA\u003c/em\u003e, the \u003cem\u003eMISAE\u003c/em\u003e algorithm causes less damage to the secondary features in the water inrush data and can more completely preserve the feature vector of the sample. Compared with the \u003cem\u003eIWOA-SVM\u003c/em\u003e, the shallow network has difficulty mining the complex mapping relationship between water inrush characteristics and accident occurrence. Therefore, the \u003cem\u003eMISAE\u003c/em\u003e is needed to extract hidden features from water inrush data and reduce the impact of irrelevant feature information on model expression. Moreover, compared with other classification algorithms such as the \u003cem\u003eFisher\u003c/em\u003e and \u003cem\u003eOPF\u003c/em\u003e algorithms, the \u003cem\u003eMISAE\u003c/em\u003e has greater advantages in the field of water inrush prediction and is highly suitable for analyzing and predicting nonlinear and complex floor water inrush data.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eThe simulation results\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eNaN-ISMOTE-MISAE\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eIWOA-SVM\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ePCA-OPF\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ePCA-Fisher\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eAccuracy\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9375\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8625\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8625\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eRecall\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9444\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9412\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9375\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eF1 Score\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9533\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9231\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8932\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8911\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eTo solve the problems of small numbers of floor water inrush data samples and difficulty in extracting water inrush features, the NaN-ISMOTE and MISAE methods were introduced to improve the prediction model. The NaN-ISMOTE algorithm is used to expand the water burst dataset, and at the same time, it addresses the shortcomings of being unable to distinguish noise data and easily changing the distribution pattern of the dataset. This paper introduces the natural neighbors theory to reduce the risk of overfitting of the prediction model by removing outliers and noise samples ​​from the water inrush dataset. The water inrush data samples are divided into center minority class samples and borderline minority class samples, and two targeted oversampling methods are proposed for oversampling. These two methods improve the diversity of the synthetic data and enhances the coverage of the minority class data area by synthetic samples while retaining the distribution pattern of the original data and reducing the impact of borderline samples on oversampling. The MISAE is used to extract water inrush accident features, and mutual information is used to evaluate the importance of neurons in the hidden layer of the model for predicting the target. Suppressing the interference of factors that are less relevant to the occurrence of water inrush accidents in the model improves the feature extraction performance of the classifier and increases the model prediction accuracy. The experimental results show that the model proposed in this paper can more accurately analyze the characteristics of water inrush accidents, improve the accuracy of water inrush accident prediction, and promote the application of deep learning and data expansion in coal mine water inrush prediction.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe funding was provided by Key Technologies Research and Development Program (Grant No.2017YFF0205500).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Publish\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors:\u003c/p\u003e\n\u003cp\u003e(1)\u0026nbsp;This material has not been published in whole elsewhere;\u003c/p\u003e\n\u003cp\u003e(2)\u0026nbsp;The manuscript is not currently being considered for publication in another journal;\u003c/p\u003e\n\u003cp\u003e(3)\u0026nbsp;All authors have been personally and actively involved in substantive work leading to the manuscript, and will hold themselves jointly and individually responsible for its content.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Shoufeng Tang and Ye Zhang. The manuscript was written by Ye Zhang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo potential conflict of interest was reported by the authors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eA. Wahid, C.S.R. Annavarapu, (2021) NaNOD: A natural neighbourbased outlier detection algorithm, Neural Comput.Appl 33(6) 2107\u0026ndash;2123.\u003c/li\u003e\n\u003cli\u003eCao QK, Zhao F (2011) Prediction of water inrush from coal floor based on genetic-support vector regression. J Coal 36(12):2097\u0026ndash;2101\u003c/li\u003e\n\u003cli\u003eDu CL, Zhang XY, Fenglian Li (2014) Application of improved CART algorithm in prediction of water inrush from coal seam floor. Ind Mine Autom 40(12):52\u0026ndash;56. https://doi.org/10.13272/j.issn.1671- 251x.2014.12.014\u003c/li\u003e\n\u003cli\u003eDan Liu, Shisheng Zhong, Lin Lin, Minghang Zhao, Xuyun Fu, Xueyun Liu, (2023) Deep attention SMOTE: Data augmentation with a learnable interpolation factor for imbalanced anomaly detection of gas turbines, Computers in Industry, 151, https://doi.org/10.1016/j.compind.2023.103972.\u003c/li\u003e\n\u003cli\u003eD.Elreedy, A.F.Atiya (2019) A comprehensive analysis of synthetic minority oversampling technique(SMOTE)for handling class imbalance, Inform.Sci.50532\u0026ndash;64.\u003c/li\u003e\n\u003cli\u003eG.Douzas, F.Bacao, (2019) Geometric smote a geometrically enhanced drop-in replacement for smote, Information Sciences 501:118\u0026ndash;135.\u003c/li\u003e\n\u003cli\u003eHao H, Jingming W (2015) Research on water inrush from the blind fault of coal floor by physical experiment. J North China Inst Sci Technol (nat Sci) 12(1):11\u0026ndash;16\u003c/li\u003e\n\u003cli\u003eJ.Li, Q.Zhu, Q.Wu, et al. (2021) SMOTE-NaN-DE: Addressing the noisy and borderline examples problem in imbalanced classification by natural neighbors and differential evolution, Knowl.-Based Syst.223107056.\u003c/li\u003e\n\u003cli\u003eJiang Zehua, et al (2021) Prediction of Coal Seam Floor Water Inrush Based on PCA-OPF Model, 36(1):6\u003c/li\u003e\n\u003cli\u003eLiu Z, Jin D, Liu Q (2009) Prediction of water inrush from seam floor based on binomial logistic regression model and CART tree. Coal Geol Explor 37(1):56\u0026ndash;61\u003c/li\u003e\n\u003cli\u003eLiu Z, Jin D, Liu Q (2011) Prediction of water inrush through coal floors based on data mining classification technique. Procedia Earth Planet Sci 3:166\u0026ndash;174. https://doi.org/10.1016/j.proeps.2011.09.079\u003c/li\u003e\n\u003cli\u003eLeng, Q, Guo, J , Jiao, E. , Meng, X , Wang, C (2023) Nanbdos: adaptive and parameter-free borderline oversampling via natural neighbor search for class-imbalance learning. Knowledge-based systems.\u003c/li\u003e\n\u003cli\u003eLi J, Zhu Q, Wu Q,et al (2021) A novel oversampling technique for class-imbalanced learning based on SMOTE and natural neighbors. Information Sciences 565:438-455.\u003c/li\u003e\n\u003cli\u003eLian C, Mei Y, et al (2021) Application of Pca-Fisher Discriminant Model in Prediction of Water Inrush From Coal Seam Floor Journal of Mathematics in Practice and Theory, 51(6):9.\u003c/li\u003e\n\u003cli\u003eN.V.Chawla, K.W.Bowyer, L.O.Hall, et al. (2002) SMOTE: Synthetic minorityover-sampling technique, J. Artificial Intelligence Res.16321\u0026ndash;357\u003c/li\u003e\n\u003cli\u003ePan, T., Zhao, J., Wu, W., Yang, J (2020) Learning imbalanced datasets based on SMOTE and Gaussian distribution. Information Sciences, 512, 1214-1233.\u003c/li\u003e\n\u003cli\u003eP.Soltanzadeh, M.Hashemzadeh, (2021) Rcsmote: range-controlled synthetic minority over-sampling technique for handling the class imbalance problem, Information Sciences: 542:92\u0026ndash;111.\u003c/li\u003e\n\u003cli\u003eQiao Y (2010) Application research of genetic algorithm and artificial neural networks in the prediction of mine water gushing-out. Xi\u0026rsquo;an University of Architecture and Technology, Xi\u0026rsquo;an (in Chinese)\u003c/li\u003e\n\u003cli\u003eQiu Xingguo, Li Jing (2022) Prediction model of water inrush in coal mine based on IWOA-SVM, 48(1):7\u003c/li\u003e\n\u003cli\u003eShi LQ, Han J (2004) Floor water inrush mechanism and prediction. China University of Mining and Technology Press, Xuzhou\u003c/li\u003e\n\u003cli\u003eShi L, Gao W, Han J et al (2017) A nonlinear risk evaluation method for water inrush through the seam floor. Mine Water Environ 34(4):1\u0026ndash;9. https://doi.org/10.1007/s10230-017-0449-1\u003c/li\u003e\n\u003cli\u003eShi L (2012) Analysis of water inrush coefficient and its applicability. J Shandong Univ Sci Technol 31(6):6\u0026ndash;9. https://doi.org/10.16452/j.cnki.sdkjzk.2012.06.002\u003c/li\u003e\n\u003cli\u003eS.Susan, A.Kumar, (2019) Ssomaj-smote-ssomin:Three-step intelligent pruning of majority and minority samples for learning from imbalanced datasets, Applied Soft Computing 78:141\u0026ndash;149.\u003c/li\u003e\n\u003cli\u003eWeitao L, Shanghui L, Shiliang L et al (2015) Principal component logistic regression analysis in application of water outbursts from coal seam floor. J Liaoning Tech Univ 34(8):905\u0026ndash;909\u003c/li\u003e\n\u003cli\u003eZhigang Y, Haibo B, Hairong Z (2008) A novel SVM model for the analysis and prediction of water inrush from coal mine. J Chin Secur Sci 18(7):166\u0026ndash;170. https://doi.org/10.1016/S1005-8885(08)60096-5\u003c/li\u003e\n\u003cli\u003eZhao Z, Hu M (2014) Multi-level forecasting model of coal mine water inrush based on self-adaptive evolutionary extreme learning machine. Appl Math Inf Sci Lett 2(3):103\u0026ndash;110. https://doi.org/10.12785/amisl/020305\u003c/li\u003e\n\u003cli\u003eZhao Z, Li P, Xu X (2013) Forecasting model of coal mine water inrush based on extreme learning machine. Appl Math Inf Sci 7(3):1243\u0026ndash;1250. https://doi.org/10.12785/amis/070349\u003c/li\u003e\n\u003cli\u003eZhao D, Wu Q, Cui F, Xu H, Zeng Y, Cao Y, Du Y (2018) Using random forest for the risk assessment of coal-floor water inrush in Panjiayao Coal Mine, northern China. Hydrogeol J 26(7):2327\u0026ndash;2340. https://doi.org/10.1007/s10040-018-1767-5\u003c/li\u003e\n\u003cli\u003eZ. Xu, D. Shen, Y. Kou, et al (2022) A synthetic minority oversampling technique based on Gaussian mixture model filtering for imbalanced data classification, IEEE Trans. Neural Netw.Learn.Syst. 1\u0026ndash;14, http://dx.doi.org/10.1109/TNNLS.2022.3197156.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"stochastic-environmental-research-and-risk-assessment","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"serr","sideBox":"Learn more about [Stochastic Environmental Research and Risk Assessment](https://www.springer.com/journal/477)","snPcode":"477","submissionUrl":"https://submission.nature.com/new-submission/477/3","title":"Stochastic Environmental Research and Risk Assessment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Mine water inrush, Feature extraction, Natural neighbors theory, Improved SMOTE, Mutual information dropout, Sparse autoencoder","lastPublishedDoi":"10.21203/rs.3.rs-4385835/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4385835/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe accuracy of coal mine water inrush prediction models is affected mainly by the small number of samples and difficulty in feature extraction. In this paper, a new data augmentation water inrush prediction method is proposed. This method uses a natural neighbors theory and mutual information dropout sparse autoencoder -improved \u003cem\u003eSMOTE\u003c/em\u003e to augment and predict the risk of water inrush in coal mines. By learning water intrusion features through the autoencoder, we can achieve better separation between classes and weaken the influence of data overlap between classes in the original sample. Then, the natural neighbors search algorithm is used to determine the intrinsic neighbor relationships between samples, remove outliers and noise samples, and use different oversampling methods for borderline samples and center samples in the minority class. Synthetic samples are generated in the feature space, mapped back to the original space and merged with the original samples to form an expanded water inrush dataset. Finally, the effectiveness of the proposed method is confirmed by comparing the measured water inrush data and prediction model results in typical mining areas in North China. The results from this study can be used to more accurately analyze the characteristics of water inrush accidents, improve the accuracy of water inrush accident prediction, and promote the application of machine learning in water inrush prediction.\u003c/p\u003e","manuscriptTitle":"An Evaluation of the Mine Water Inrush based on the Data expansion and Deep learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-21 15:12:31","doi":"10.21203/rs.3.rs-4385835/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorAssigned","content":"","date":"2024-05-10T16:29:18+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-09T10:55:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"Stochastic Environmental Research and Risk Assessment","date":"2024-05-08T01:52:55+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"stochastic-environmental-research-and-risk-assessment","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"serr","sideBox":"Learn more about [Stochastic Environmental Research and Risk Assessment](https://www.springer.com/journal/477)","snPcode":"477","submissionUrl":"https://submission.nature.com/new-submission/477/3","title":"Stochastic Environmental Research and Risk Assessment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d31b5bc7-4cdb-4686-aed9-68c11cbc5825","owner":[],"postedDate":"May 21st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-05-21T15:12:31+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-21 15:12:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4385835","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4385835","identity":"rs-4385835","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}