A Prediction Method for Floor Water Inrush Based on Chaotic Fruit Fly Optimization Algorithm – Generalized Regression Neural Network

The research was aimed at predicting ﬂ oor water-inrush risk in coal mines and forewarn of such accidents to guide safe production of coal mines in practice. To this end, a prediction method for ﬂ oor water inrush combining the chaotic fruit ﬂ y optimization algorithm (CFOA) and the generalized regression neural network (GRNN) is proposed. Floor water inrush is predicted by virtue of the robust nonlinear mapping capability of the GRNN. However, because the prediction e ﬀ ect of the GRNN is in ﬂ uenced by the smoothing factor, the CFOA is adopted to optimize this factor. In this way, in ﬂ uences of human factors during parameter determination of the GRNN prediction model are decreased, and the prediction accuracy and applicability of the model are improved. Results show that the CFOA – GRNN prediction model has an accuracy of 93.2% for whether ﬂ oor water inrush will occur or not. Compared with the BPNN, RNN, and GRU network prediction model, the CFOA – GRNN model is superior in the prediction accuracy and generalization, and it can more accurately predict ﬂ oor water inrush.


Introduction
With the increasing depletion of shallow coal resources and the increasing intensity of coal mining, more and more coal mines will encounter deep mining issues [1][2][3][4][5]. Compared with shallow coal mining, deep rock mass is in a typical complex mechanical environment of "three highs and one disturbance" (high ground stress, high karst water pressure, high ground temperature, and strong mining disturbance), showing large deformation and uncoordinated deformation and impact deformation [6][7][8][9][10][11][12][13][14][15]. Due to the characteristics of deep rock mechanics that are significantly different from those of shallow rock mechanics, coupled with the complexity of the occurrence environment, a series of catastrophic accidents in deep resource mining have greatly increased in frequency, intensity, and scale. Coal-rock dynamic disasters such as pressure appearance, floor water inrush, mine earthquake, rock burst, and coal and gas outburst become more frequent, and the disaster mechanism will become more complex [16]. In recent years, several major accidents in coal mines in my country are mostly secondary disasters, which have caused the expansion of accidents and increased the catastrophic nature of accidents. For example, in 2005, Fuxin Sunjiawan Coal Mine caused coal and gas outbursts due to rock bursts, and then, a huge gas explosion occurred, killing 214 people and injuring 30 people. During the mining of the 4th coal seam in Huafeng Coal Mine, due to the frequent occurrence of rock bursts, a large amount of water from the roof abscission flowed into the working face. As mining depths increase, coal seams bear increasing karst aquifer pressure, and therefore, the floor water-inrush risk increases: this has been one of the greatest hidden dangers for safe production of coal mines in China. In such context, predicting floor water-inrush risk is important in preventing accidents arising from such disasters in coal mines and ensuring safe mining above high-pressure aquifers.
Much theoretical analysis and numerical simulation has been conducted on the principle and prediction of water inrush from coal floors. For examples, Hu et al. [17] built a physical model with similar materials of the fracture zone in the synclinal axis above a confined aquifer and studied the mechanism of floor water inrush under the combined effect of a confined aquifer and a fracture zone. Numerous scholars also evaluated the influences of confining pressure and permeation pressure on water inrush from coal floors and obtained the mechanism of water inrush from coal floors under the coupled effect of seepage field and stress field [18][19][20][21], studied the effects of faults on stability of the aquifuge of coal floors, deduced the critical water pressure formula for failure of the aquifuge under influences of the fault, and proposed the corresponding mechanical criterion for floor water inrush. Li and Wang [22] reproduced the formation and evolution process of water-inrush channels through numerical simulation using FLAC (3D), which provides insights into formation and evolution characteristics of water-inrush channels in coal floors under high pressure. Ma et al. [23] combined theoretical analysis and numerical simulation with rock failure process analysis and microseismic monitoring to study failure characteristics and damage depth of coal floors above a confined aquifer. The method overcomes the limitations of a single method in previous research and also provides a reference for solving the water-inrush problems in roadways and selection of proper reinforcement measures. Shao et al. [24] proposed a catastrophe prediction model for floor water inrush in coal mines and deduced formulae for critical stress and energy release at failure of the floor system, providing a new theoretical approach for predicting water inrush from coal floors. By using the Mohr-Coulomb criterion and theory of fracture mechanics, Zhang et al. [25] studied the failure mechanism of floor water inrush and found that the higher the breaking energy of fractures, the more significant the floor water-inrush risk in coal mines. Existing theoretical formulae for floor water inrush generally only consider a few influencing factors and therefore are inapplicable to other coal mines. In addition, laboratory tests simplify the mining conditions, so the results are only of reference significance in prediction. Although numerical calculation method develops apace, it is still unable to simulate the complex geological and hydrogeological conditions encountered in deep mining.
In recent years, several risk evaluation methods and prediction models from multiple aspects have been proposed based on nonlinear statistical theory. Zhang and Yang [26] proposed a dynamic GRU (gated recurrent unit) neural network prediction model, the model is able to predict water inrush from coal floor with high accuracy. Zhang et al. [27] established a MFIM-TOPSIS variable weight model, which combines a multifactor interaction matrix (MFIM) and the technique for order performance by similarity to ideal solution (TOPSIS) to implement the risk assessment of floor water inrush in coal mines. Zhang et al. [28] presented a mathematical assessment method for coal-floor water-inrush risk integrating the hierarchy-variable-weight model (HVWM) with collaboration-competition theory (CCT). Zhao et al. [29] proposed a novel and promising assessment model for water inrush based on random forest (RF), which was more practicable to assess the waterinrush risk than PNN. Dong et al. [30] combined the Fisher feature extraction and support vector machine (SVM) methods, and this new combined model was more accurate and efficient in discriminating water-inrush sources than the traditional SVM model. Wang et al. [31] established PCA-(principal component analysis-) BP (Back Propagation) neural network classification model which can effectively identify coal mine water inrush. These methods have been applied in practical work, while still showing certain drawbacks. For instance, the distance discriminant analysis correlates the discriminant distance with units of indices and considers various different indices and variables equally, which sometimes fails to meet the actual requirements, thus leading to less accurate predictions. The SVM does not provide general solutions to nonlinear problems, so it needs to be further improved. The BP neural networks have shortcomings that the BP neural network needs a large number of data samples for training and also has too many optimized parameters [32].The generalized regression neural network (GRNN) is a kind of radial basis function neural network proposed by Specht, which has a strong ability for nonlinear mapping [33]. Compared with the BPNN and the SVM, the GRNN has fewer adjustment parameters, does not easily fall into local minima, and is good at processing large-scale training samples. The generalized regression neural network (GRNN) is highly superior in approximation capability, learning rate, and prediction accuracy, and it can reduce computation complexity and better predict floor water-inrush risk [34,35].
On this basis, the GRNN model is established to predict floor water inrush based on the theory of nonlinear regression by combining relevant water-inrush data of numerous working faces. At the same time, the chaotic fruit fly optimization algorithm (CFOA) is used to optimize the smoothing factor of the GRNN. The novelty of CFOA-GRNN model includes the following three aspects: (a) The fruit fly optimization algorithm achieves the goal of finding the global optimal solution of complex functions in space by simulating the competition and cooperation behavior of fruit fly individuals. The algorithm has the advantages of simple calculation process and fast convergence speed. (b) Generalized regression neural network (GRNN) has the advantages of strong nonlinear mapping ability, single setting parameters, high fault tolerance, and robustness and has high prediction accuracy and stability. (c) The GRNN algorithm is easy to fall into the shortcoming of local optimum. The CFOA algorithm can find the global optimal solution for complex functions in space, and the CFOA algorithm is combined with the GRNN prediction model to make up for the shortcomings of the GRNN algorithm that is easy to fall into local optimality, quickly find the global optimal solution, and improve the prediction efficiency. And accuracy can be greatly improved. The prediction results can provide reference for prediction of floor water inrush and safe production of working faces.

Influencing Factors of Floor Water Inrush in
Coal Mines 2.1. Aquifer Pressure. Head pressure of confined aquifers below coal floors is the precondition and power for floor water inrush. To cause floor water inrush, the head pressure of underlying aquifers should be large enough. Under the same conditions of the aquifuge for coal floors, the confined water pressure below coal floors is directly proportional to the probability of occurrence of water inrush. Particularly, when the aquifuge is affected by mining activities or encounters a fault, the water pressure exerts significant influences on water inrush. Therefore, aquifer pressure is an important basis from which to study floor water inrush.

Aquifuge
Thickness. An aquifuge for coal floors is an intact stratum between a coal floor and the top of an aquifer. The aquifuge exerts influences different from other factors and plays a critical role in preventing groundwater of a confined aquifer from entering the mining space of a mine. It is the only inhibiting factor for floor water inrush and forms a safety barrier for mining above confined aquifers. Aquifuges can obstruct floor water inrush, and the capability depends on aquifuge thickness, mechanical strength of rock, and integrity of aquifuges. When keeping other conditions unchanged, the thicker and the stronger the aquifuge, the lower the probability of water inrush, and vice versa [15]. According to statistical analysis of 343 water-inrush records in typical mining areas in China, the relationship between the aquifuge thickness and the number of water inrush is revealed (Table 1).

Dip Angle of Coal Seams.
According to dip angles, coal seams can be classified into nearly horizontal, gently inclined, inclined, deeply inclined, and steeply inclined, separately corresponding to dip angles of less than 8°, between 8~25°, 25~45°, and 35~65°, and greater than 45°. Previous research has shown that when the dip angle of faults is small, shear failure is likely to occur during coal mining, which induces fractures in aquifers and finally water-inrush accidents. Numerous engineering cases have proven that deeply inclined coal seams are more likely to encounter waterinrush accidents.

Fault Throw.
Damage of faults to coal and rock mass is mainly manifest as increased fractures and pores in, and greatly decreased strength of, coal and rock mass nearby a fault. Different fault throws may produce different contact relationships between coal seams and aquifers in two plates of a fault. Analysis shows that the larger the fault throw and the deeper the cut, the greater the influences of faults and the greater the probability of floor water inrush.
Mining conditions such as mining height and mining methods also affect the initial stress state of the coal and rock mass and the damage depth of coal floors and further influence floor water inrush. Six factors including water pressure (MPa), mining height (m), aquifuge thickness (m), fault throw (m), dip angle of coal seams (°), and distance from a fault to a working face (m) are taken as main influencing factors of floor water inrush. The original data selected are listed in Table 2. The sample data is obtained from the statistics of some mines in my country, mainly including the water-inrush data from the working face and floor of the typical large-water mining areas, such as Hebei Fengfeng, Jinglong, Hebi Hebi, and Shandong Zibo, and the measured data of normal mining.

Principles Underpinning Various Algorithms
3.1. CFOA. Fruit flies can accurately locate distant food sources because of their special sense organs. The fruit fly optimization algorithm (FOA) is an algorithm deduced for searching for the optimal results based on foraging behaviors of fruit flies. FOA simulates the optimization process of fruit flies according to their foraging behavior and then finds the optimal solution. It is characterized by advantages including understandable logic, no need to adjust data and parameters, and rapid convergence [36][37][38]. When searching in a complex environment, FOA is likely to be trapped in local extremums and leads to a large deviation between the results and reality. FOA has been applied in neural network training [39], financial distress model solving [40], power load forecasting [41], multidimensional knapsack problem [42], web auction logistics service [43], and so on [44][45][46].
Chaos theory is universal in its applicability to such problems, and its methods can avoid being trapped in local extrema. Therefore, the CFOA is used to compensate for the drawback of the FOA. The steps are briefly described as follows: Step 1. The initial location (InitX, InitY) of a fruit fly is randomly determined.
Step 2. Random directions and distances are assigned to fruit flies to search for food.
Step 3. The distance (Dist) of a fruit fly to the origin is estimated, and then, the judgment value of smell concentration (S) is calculated, which is the reciprocal of the distance.
Step 4. The judgment value of smell concentration (S) is substituted into the judgment function of smell  Step 5. The fruit fly with the highest smell concentration in the population is found.
Step 6. The location of the fruit fly with the optimal smell concentration is retained, to which the fruit fly population flies.
Step 7. Iterative optimization is conducted, and Steps 2~5 are repeated. Whether the smell concentration is better than the previous iteration or not is judged. If yes, Step 6 is performed; otherwise, the prediction results are output.
Chaos Fruit Fly Optimization Algorithm (CFOA) is the optimal position of each generation obtained in the iterative optimization process of the fruit fly optimization algorithm, adding chaotic disturbance and performing secondary optimization, which can make the population jump out of the local optimal solution, implementing global search. Other variants of FOA often fall into local extrema when searching for complex environments, which affects the computational accuracy and efficiency.

GRNN.
GRNN is based on the nonparametric kernel regression and allows nonparametric estimation taking sample data as the verification condition of posterior probability, so it has favorable learning ability. The most prominent advantage of GRNN is the setting of network parameters which is so convenient that its network performance can be adjusted only by setting the smoothing factor in the kernel function. The first layer of the GRNN is an input layer, on which the number of neurons is same as the dimensions of the input vectors of learning samples and each neuron is a simple distributed network unit. These neurons directly transfer the input variables into the hidden layer. GRNN uses sample data as the verification condition for posterior probability and nonparametric estimation. Finally, to obtain the regression of dependent variables relative to independent variables, the correlation density function between    Figure 2: Flowchart of the CFOA-GRNN prediction model. 6 Geofluids dependent variables and independent variables in the GRNN is calculated using the training samples. The calculation formula is shown as follows: For an unknown probability density function f ðX, YÞ, the following formula is obtained through nonparametric estimation: where X i and Y i separately refer to the observed values of random variables X and Y, δ is a smoothing factor, and n and p separately denote the sample size and dimension of x. The following can be attained according to Formulae (3) and (4): This can be simplified to Formula (6) is the expression for the final output of the GRNN. Based on the calculation formula, the output error of the GRNN is mainly dependent on its smoothing factor δ. When the smoothing factor is very large, Y tends to the mean of dependent variables of all samples; on the contrary, if the smoothing factor tends to 0, Y is approximated to the training samples. Dependent variables of all samples can be considered only when δ is set to a moderate value, thus obtaining favorable results. Therefore, satisfactory results can be obtained by simply adjusting the smoothing factor of the prediction model. The structure of the GRNN is illustrated in Figure 1      convert the distance between a fruit fly and the origin into the smoothing factor (through use of the neural network toolbox in MATLAB™); through training of the GRNN model, the output samples are attained; the prediction error of GRNN is used as the judgment function of smell concentration to find the location of the individual with the lowest error corresponding to all smoothing factors; the above operation is repeated until the condition of convergence is met or the maximum number of iterations is reached. The specific steps are shown as follows: (1) Influencing factors are selected and data collected (2) The initial position (InitX,Inity) of a fruit fly is set at random, which searches within the range (X min, Xmax), (Y min, Ymax). After adding chaotic disturbance C, searched locations of the fruit fly can be obtained on the X and Y-axes (3) The distance DðiÞ between the fruit fly and the origin is calculated according to coordinates of the fruit fly (4) The calculation function of smell concentration is determined using the distance function DðiÞ, and the optimal fitness function is searched. The fitness function is updated, and the variable values are optimized. Then, the local optimal location of the fruit fly is sought in accordance with the chaotic sequences (5) After finishing the iterative loop, the location of the fruit fly with the largest coverage is recorded, and the maximum smell concentration is retained (6) Search of the CFOA is stopped when the number of iterations K is bigger than K max; otherwise, the operation returns to Step 2 to collect the spread of GNRR  Figure 3 shows the training error curves of each model. As can be seen from Figure 4, compared with the other three models, the CFOA-GRNN prediction model has a faster optimization and convergence speed, and the prediction error is relatively stable. Water-inrush level of the 12 groups of data that occurred last in the sample set, that is, the 49th-60th group of sample data, was selected for testing. Establish CFOA-GRNN,   For the analysis of the evaluation results, the following evaluation indicators can be used to evaluate the feasibility and pros and cons of the model.
(1)Overall accuracy (OA) refers to the proportion of the number of correctly classified samples to the total number of samples, which reflects the accuracy of the model's prediction of all levels. The expression is as follows: In the formula, N t is the total number of test samples, and N t is the number of samples whose predicted level is equal to the original level of the Nc model.
(2)Local accuracy (LA) refers to the ratio of the number of correctly classified samples of the ith level to the total number of samples of the ilevel, reflecting the accuracy of the model's prediction of a certain level, and its expression is as follows: In the formula, LAðiÞ is the accuracy of water-inrush level i, NðiÞ t is the number of test samples with waterinrush level i, and NðiÞ c is the number of samples at level i equal to the original level.
(3)Operation time T: it reflects the operation speed of the model The prediction results of the model are evaluated using the above evaluation indicators, and the evaluation results are shown in Table 3. In terms of overall accuracy, the overall accuracy of the CFOA-GRNN model is 16.7% higher than that of the BPNN model, 25% higher than that of the RNN model, and 33.4% higher than that of the GRU model. From the perspective of local accuracy, the introduction of CFOA can effectively improve the local accuracy of the neural network model for the prediction of water inrush at each level and greatly improve the prediction accuracy of the water inrush from the floor. In terms of operation time Tm, the operation time of the CFOA-GRNN model is 18.9% less than that of the BPNN model, 25.9% less than that of RNN, and 21.3% less than that of GRU. Therefore, in summary, the introduction of CFOA can greatly improve the accuracy of the GRNN neural network prediction model for water inrush from the bottom of the model and also significantly reduce the computing time.
Compared with the prediction results of the other three algorithms, it can be seen that the overall accuracy of the other three prediction models is not high. The overall accuracy of the BPNN neural network prediction model, the RNN neural network prediction model, and the GRU (gated recurrent unit) neural network prediction model is 75%, 66.7%, and 58.3%, while the overall accuracy of the CFOA-GRNN neural network prediction model is 91.7%. From the perspective of LAðiÞ, the local accuracy of the CFOA-GRNN neural network prediction model introduced with the chaotic fruit fly optimization algorithm is also significantly improved compared with the other three neural network prediction models. The superiority of the proposed prediction model is confirmed from the three aspects of overall accuracy, local accuracy, and computation time. The prediction result of CFOA-GRNN model on whether water inrush occurs in actual engineering is very close to the actual situation, and its accuracy is significantly higher than that of the other three models. This result shows that the CFOA-GRNN model is reliable in predicting whether there is a risk of water inrush from the floor in actual engineering.

Conclusion
In order to solve the floor water-inrush issue, CFOA-GRNN model is established to predict floor water inrush based on the theory of nonlinear regression by combining relevant water-inrush data of numerous working faces and derived the following conclusions: (1) The prediction effect of GRNN is affected by the smoothing factor, so the CFOA is used to optimize the smoothing factor, which reduces influences of human factors on the parameter determination in the GRNN prediction model and improves the prediction accuracy and applicability of the model (2) By comprehensively analyzing causes of floor water inrush, six main factors are selected to construct the CFOA-GRNN prediction model for floor water inrush (3) The accuracy of the CFOA-GRNN prediction model is 91.7%, the established prediction model has a high accuracy, and the prediction results are in agreement with reality, so it can be used to predict floor water inrush in coal mines in China to guide safe production (4) In the established CFOA-GRNN model, it is found that the fruit fly search function has a great influence on the convergence of the prediction results. In future research, the optimization of the fruit fly search function will be explored in depth to reduce the prediction error caused by the change of the search function

Data Availability
The original contributions presented in the study are included in the article, and further inquiries can be directed to the corresponding author.