Coal mine water inflow prediction method based on combined model and dynamic collaborative weight distribution

Abstract

The invention discloses a coal mine water inflow prediction method based on a combined model and dynamic collaborative weight distribution, and belongs to the technical field of coal mining, and the method comprises the following steps: 1, collecting and preprocessing time sequence historical data of mine water inflow, and defining the preprocessed data as an original time sequence data set; step 2, constructing an ARIMA model; step 3, constructing a GM (1, 1) model; and 4, constructing an ARIMA-GM combination model to predict the water inflow of the mine, introducing a time attenuation factor, an error sensitivity coefficient and an adjustment factor, and constructing a dynamic collaborative weight distribution mechanism to update and optimize the weight. According to the invention, the precision and stability of mine water inflow prediction can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of coal mine exploitation, and particularly relates to a method for predicting the water inflow of a coal mine based on a combined model and dynamic collaborative weight allocation. Background Technique

[0002] During the coal mine exploitation process, mine water inrush is an important issue in the safe production of coal mines. The change of the water inflow of a mine will not only affect the normal production process, but may also cause property losses and casualties. Therefore, accurately predicting the water inflow of a mine has important practical significance for the safe production of coal mines and flood prevention and control.

[0003] The existing methods for predicting the water inflow of a mine mainly include traditional empirical formulas, groundwater dynamics methods, large well methods, horizontal gallery methods, etc. Although these methods can achieve certain effects under certain conditions, they generally have problems such as poor prediction accuracy, poor stability, weak adaptability, and limited application scope. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a method for predicting the water inflow of a coal mine based on a combined model and dynamic collaborative weight allocation, which fuses the ARIMA model and the GM(1,1) model to construct an ARIMA-GM combined model, and introduces a dynamic collaborative weight allocation mechanism to dynamically adjust the weights according to real-time monitoring data and prediction errors, so as to improve the prediction accuracy and stability of the water inflow of a mine.

[0005] The technical solution of the present invention is as follows: A method for predicting the water inflow of a coal mine based on a combined model and dynamic collaborative weight allocation, comprising the following steps: Step 1: Collect the historical time series data of the water inflow of a mine and perform preprocessing, and define the preprocessed data as the original time series data set; Step 2: Construct an ARIMA model; Step 3: Construct a GM(1,1) model; Step 4: Construct an ARIMA-GM combined model to predict the water inflow of a mine, and introduce a time decay factor, an error sensitivity coefficient, and a regulation factor to construct a dynamic collaborative weight allocation mechanism for weight update and optimization.

[0006] Further, in the above step 1, during preprocessing, it is necessary to perform data integrity, stability, and correlation tests; the specific process is as follows: Step 1.1: Check the data integrity, and for missing data, supplement it by interpolation method; Step 1.2: Perform a stability test. If the data is not stationary, perform a difference operation and then a white noise test. If the data is stationary, directly perform a white noise test; Step 1.3: Conduct a correlation test using white noise; the specific process is as follows: Perform a differencing operation on the data to obtain a residual sequence, calculate the autocorrelation function and partial autocorrelation function based on the residual sequence, and plot the corresponding autocorrelation function graph or partial autocorrelation function graph. If the values of the autocorrelation function or partial autocorrelation function decay rapidly within the confidence interval, it indicates that the residuals are close to white noise and meet the modeling requirements of the ARIMA model; if they do not meet the modeling requirements of the ARIMA model, re-collect the data for preprocessing, or return to Step 1.1 to re-preprocess the data.

[0007] Further, the specific process of Step 2 is as follows: Determine the regression order p and the mean order q of the ARIMA model based on the autocorrelation function and partial autocorrelation function calculated in Step 1.3, and directly use the determined ARIMA model to predict the future water inflow. When predicting, directly input the time series historical data of the preprocessed mine water inflow into the ARIMA model to obtain the ARIMA model prediction sequence , where is the th data in the ARIMA model prediction sequence.

[0008] Further, in Step 3, the specific working process of the GM(1,1) model is as follows: Step 3.1: Given an original time series data set , after a first-order accumulation, obtain a first-order accumulated time series data set ; the formula for the first-order accumulation is: (1); where , are respectively the th and th data in the original time series data set; , are respectively the th and th data in the first-order accumulated time series data set; Step 3.2: Conduct a smoothness test on each data in the original time series data set: (2); where is the smoothness ratio of the th data; is the th data in the first-order accumulated time series data set; If it satisfies and When it is, this sequence data is considered a quasi-smooth sequence, meeting the modeling requirements of the GM(1,1) model; Step 3.3: Calculate the adjacent mean value and generate a set of adjacent mean value sequences ; The calculation formula for the adjacent mean value is: (3); Where, and are respectively the th and th data in the set of adjacent mean value sequences; Step 3.4: Establish a grey differential equation: (4); Where, and are different undetermined parameters; Step 3.5: The corresponding white differential equation is: (5); Where, is the cycle serial number; Define the parameter column: (6); (7); (8); Where, is the determinant constructed by the undetermined parameters; is the transpose; is the matrix constructed by the adjacent mean values; is the matrix composed of the original data; Substitute and into formula (6) to solve for the estimated values of the undetermined parameters and ; Step 3.6: Solve the grey differential equation and the white differential equation to obtain the set of accumulated time response sequences ; (9); Where, and and are respectively the predicted values of and and ; is the th data in the set of first-order accumulated time series data; is the natural constant; Step 3.7: Perform subtraction reduction to obtain the predicted value: (10); wherein, is the th predicted value in the GM(1,1) model prediction sequence; The GM(1,1) model prediction sequence is ; is the th predicted value in the GM(1,1) model prediction sequence.

[0009] Furthermore, the specific process of step 4 is as follows: Step 4.1: Initialize the time decay factor, error sensitivity coefficient, and adjustment factor, and define the prediction error calculation formula as: (11); wherein, is the prediction error of the model in the th period; is the root mean square error of the model in the th period; Step 4.2: Calculate the weight numerator: (12); wherein, is the weight numerator of the model ; is the adjustment factor; is the error sensitivity coefficient; is the prediction error of the model in the th period; is the prediction error of the model in the th period; is the time decay factor; Step 4.3: Calculate the normalization coefficient: (13); wherein, is the normalization coefficient; is the weight numerator of the ARIMA model; is the weight numerator of the GM(1,1) model; Step 4.4: Assign weights to the two models: (14); (15); wherein, is the weight of the th period of the ARIMA model; is the weight of the th period of the GM(1,1) model; Step 4.5. Weight and combine the prediction results of the two models to construct an ARIMA-GM combined model for predicting the mine water inflow: (16); where, is the predicted value of the mine water inflow by the combined model; Step 4.6. Perform dynamic parameter optimization; specifically, adjust the parameters dynamically according to the prediction error: If the sum of the prediction errors of the ARIMA model and the GM(1,1) model in the current period is higher than the pre-set threshold, then increase , and the specific increased value is adjusted according to the actual situation; If the environmental stability is high, then reduce , and the specific reduced value is adjusted according to the actual situation; The specific manifestation of high environmental stability is that the water inflow data fluctuates little and has no obvious trend change, and at the same time, the prediction error remains low and fluctuates little for a long time; Step 4.7. Abnormal handling; when the normalization coefficient approaches zero, it is an abnormal situation, and reset the weight of the ARIMA model and the weight of the GM(1,1) model are both the default value 0.5.

[0010] The beneficial technical effects brought by the present invention: The present invention combines the advantages of the ARIMA model and the GM(1,1) model, constructs an ARIMA-GM combined model with combined weighting of the two models, reduces the error caused by the limitations of traditional single models, and improves the prediction accuracy and stability. At the same time, a dynamic collaborative weight allocation mechanism based on real-time data feedback is introduced to dynamically and flexibly adjust the model weights, enabling the system to adapt to the complex and dynamic mine environment and optimize the advantages of different models. The introduction of reinforcement learning enables the system to have an intelligent adaptive ability, and can continuously optimize the weight combination with the change of the environment and the update of data, and improve the long-term prediction performance. Brief Description of the Drawings

[0011] Figure 1 is the flow chart of the coal mine water inflow prediction method based on the combined model and dynamic collaborative weight allocation of the present invention.

[0012] Figure 2 is the curve graph of the original time series data in the embodiment of the present invention.

[0013] Figure 3It is a curve graph after the first-order difference operation processing on the original time series data in the embodiment of the present invention.

[0014] Figure 4 It is the autocorrelation graph of the ARIMA model in the embodiment of the present invention.

[0015] Figure 5 It is the partial autocorrelation graph of the ARIMA model in the embodiment of the present invention.

[0016] Figure 6 It is the residual ACF graph of the ARIMA model in the embodiment of the present invention.

[0017] Figure 7 It is the comparison graph of the prediction results of different models and the true value in the embodiment of the present invention. Specific embodiments

[0018] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments: In order to improve the accuracy and stability of the prediction of mine water inrush. The present invention combines the ARIMA model and the GM(1,1) model and assigns weights, determines the weights by calculating the root mean square error (RMSE) of the two models, and weights and synthesizes the prediction results of the two models to obtain the final predicted value of the water inrush. At the same time, in order to improve the adaptability of the mine water inrush prediction method, the present invention constructs a dynamic collaborative weight allocation mechanism based on real-time data feedback. By introducing the dynamic collaborative weight allocation mechanism based on real-time data feedback, when abnormal data or large prediction errors occur, the system can dynamically adjust the weights of the two models to improve the prediction accuracy. The weights are not statically calculated, but are automatically adjusted according to the real-time model performance and external environment.

[0019] As Figure 1 shown, a coal mine water inrush prediction method based on a combined model and dynamic collaborative weight allocation includes the following steps: Step 1: Collect the time series historical data of the mine water inrush and perform preprocessing, and define the preprocessed data as the original time series data set; during preprocessing, it is necessary to perform data integrity, stability, and correlation tests. The specific process is as follows: Step 1.1: Check the data integrity. For missing data, supplement it by interpolation method; Step 1.2: Perform stability test. If the data is not stationary, perform difference operation processing and then perform white noise test. If the data is stationary, directly perform white noise test; specifically: draw the curve graph of the original time series data time and the water inrush. If there is an obvious linear trend in the curve graph, it means the data is not stationary and difference operation processing is required; Step 1.3. Conduct a correlation test using white noise to ensure that the data meets the modeling requirements of the ARIMA (AutoRegressive Integrated Moving Average) model. The process of the correlation test is as follows: perform a differencing operation on the data to obtain a residual sequence, calculate the autocorrelation function (ACF) and partial autocorrelation function (PACF) based on the residual sequence, and plot the corresponding autocorrelation function graph (ACF graph) or partial autocorrelation function graph (PACF graph). If the values of the autocorrelation function or partial autocorrelation function decay rapidly within the confidence interval, it indicates that the residuals are close to white noise and meet the modeling requirements of the ARIMA model. If it does not meet the modeling requirements of the ARIMA model, re-collect the data for preprocessing, or return to Step 1.1 to re-preprocess the data.

[0020] Step 2. Construct an ARIMA model to predict the future water inflow. The prediction process is as follows: Determine the regression order p and the moving average order q of the ARIMA model according to the autocorrelation function (ACF) and partial autocorrelation function (PACF) calculated in Step 1.3, and directly use the ARIMA model with the determined orders to predict the future water inflow. When predicting, directly input the time series historical data of the preprocessed mine water inflow into the ARIMA model to obtain the ARIMA model prediction sequence , where is the th data in the ARIMA model prediction sequence. The specific rule for determining the orders is: the last significant lag order at which the PACF graph gradually truncates can be used as the autoregressive order p, and the last significant lag order at which the ACF graph gradually truncates can be used as the moving average order q.

[0021] Step 3. Construct a GM(1,1) model. GM(1,1) is a prediction model based on grey system theory. Using grey system theory, new data series are generated by cumulative addition of the original data, and differential equations are established for prediction. Calculate the root mean square error (RMSE) based on the actual data and compare it with the ARIMA model. The working process and formula of the GM(1,1) model are as follows: Step 3.1. Suppose there is an original time series data set , after one-time cumulative addition, a one-time cumulative time series data set is obtained; the formula for one-time cumulative addition is: (1); where , are the th and th data in the original time series data set respectively; , are the individual, the th data; For example, assume a set of original time series data , then the first-order accumulated time series data set is , that is, the th data in the first-order accumulated time series data set is the sum of the first accumulations in the original sequence; Step 3.2. Conduct a smoothness test on each data in the original time series data set: (2); Among them, is the smooth ratio of the th data; is the th data in the first-order accumulated time series data set; If it satisfies and , this sequence data is considered a quasi-smooth sequence, meeting the modeling requirements of the GM(1,1) model.

[0022] Step 3.3. Calculate the adjacent mean and generate the adjacent mean sequence set ; The calculation formula for the adjacent mean is: (3); Among them, , are respectively the th, the th data in the adjacent mean sequence set; Step 3.4. Establish a grey differential equation: (4); Among them, , are different undetermined parameters, which can be determined according to the least squares method; Step 3.5. The corresponding whiting differential equation is: (5); Among them, is the cycle number; Define the parameter column: (6); (7); (8); Among them, is the determinant constructed by undetermined parameters; is the transpose; is a matrix constructed adjacent to the mean value; is a matrix composed of the original data; Substitute and into formula (6) to solve for the undetermined parameters and estimation values; Step 3.6, Solve the grey differential equation and the white differential equation to obtain the set of time response sequences after accumulation ; (9); Among them, , , are the predicted values of , , respectively; is the th data in the set of first-order accumulated time series data; is the natural constant, approximately 2.71828; Step 3.7, Perform inverse accumulation reduction to obtain the predicted value: (10); Among them, is the th predicted value in the GM(1,1) model prediction sequence; The prediction sequence of the GM(1,1) model is ; is the th predicted value in the GM(1,1) model prediction sequence. The GM(1,1) model models the trend through the accumulated generating sequence and then obtains the predicted value of the original sequence through inverse accumulation reduction; due to the mathematical properties of the accumulation and inverse accumulation operations, the prediction result is naturally expressed as a one-step backward sequence of the original sequence, that is, from the 2nd to the th, which is an inherent property of the GM(1,1) model.

[0023] Step 4, Construct an ARIMA-GM combined model for predicting the mine water inflow, introduce a time decay factor, an error sensitivity coefficient, and a regulation factor, and construct a dynamic collaborative weight allocation mechanism for weight update and optimization. The specific implementation is as follows: Step 4.1, Initialize the time decay factor, the error sensitivity coefficient, and the regulation factor; set the initial time decay factor to 0.7 to balance historical and recent errors; the initial error sensitivity coefficient to 0.5 to amplify the error sensitivity of the GM(1,1) model; the initial regulation factor to 0.95, and the regulation factor is the time decay factor; and define the prediction error calculation formula as: (11); Among them, is the prediction error of the th cycle of the model; is the root mean square error of the th cycle of the model; Step 4.2, calculate the weight numerator: (12); Among them, is the weight numerator of the model; is the adjustment factor; is the error sensitivity coefficient; is the th cycle prediction error of the model; is the th cycle prediction error of the model; is the time decay factor; Step 4.3, calculate the normalization coefficient: (13); Among them, is the normalization coefficient; is the weight numerator of the ARIMA model; is the weight numerator of the GM(1,1) model; Step 4.4, assign weights to the two models: (14); (15); Among them, is the weight of the ARIMA model at the th cycle; is the weight of the GM(1,1) model at the th (16); Among them, is the predicted value of the combined model for the mine water inrush volume.

[0024] Step 4.6, perform dynamic parameter optimization; specifically, adjust the parameters dynamically according to the prediction error: If the sum of the prediction errors of the ARIMA model and the GM(1,1) model in the current cycle (i.e., ) If it is higher than a pre-set threshold, then increase to enhance error sensitivity, and the specific increased value is adjusted according to the actual situation; where is the prediction error of the th period of the ARIMA model; is the prediction error of the th period of the GM(1,1) model; If the environmental stability is high, then reduce to enhance the reference weight of historical errors, and the specific reduced value is adjusted according to the actual situation. The specific manifestation of high environmental stability is that the water inflow data fluctuates little and has no obvious trend change, and at the same time the prediction error remains at a low level and fluctuates little for a long time.

[0025] Step 4.7, anomaly handling; when the normalization coefficient approaches zero, it is an abnormal situation, and reset the weights of the ARIMA model and the weights of the GM(1,1) model are both the default value of 0.5 to ensure the robustness of the system.

[0026] Taking a certain coal mine as a specific embodiment, applying the ARIMA-GM combined model to predict its mine water inflow, and comparing it with a single prediction method to verify the effectiveness and superiority of the method of the present invention.

[0027] Taking the monthly water inflow data of a certain coal mine from 2020 to 2022 as experimental data, and taking the monthly water inflow data of 2023 as control data to conduct water inflow prediction.

[0028] Figure 2 is the original time series data. It can be intuitively seen from Figure 2 that the original data does not meet the requirements of data stationarity. Therefore, it is necessary to perform a first-order difference operation on the original time series data, and the processed result is as Figure 3 shown.

[0029] Then, determine the order of the ARIMA model; draw the Figure 4 shown autocorrelation graph (ACF graph) according to the autocorrelation function of the ARIMA model, and draw the Figure 5The partial autocorrelation function (PACF) plot shown. According to the autocorrelation function and the partial autocorrelation function, judge and test the order of the ARIMA model. The last significant lag order at which the PACF plot gradually truncates can be used as the autoregressive order p, and the last significant lag order at which the ACF plot gradually truncates can be used as the moving average order q. By observing the ACF plot and the PACF plot, determine that the model regression order p = 1 and the average order q = 1. Set the differencing order to d = 1, so an ARIMA(1,1,1) model is constructed for predicting the mine water inflow. Conduct a white noise test. After differencing the original time series data, use white noise to conduct a correlation test on the data, and check the ACF plot or PACF plot of the residuals. If it decays rapidly within the confidence interval, it indicates that the residuals are close to white noise. The residual ACF of this model is as Figure 6 shown. After testing, it meets the requirement of rapid decay within the confidence interval, and there is a correlation between the data. Figures 4 - 6 In Figures 4 - 6 , the gray shaded area represents the confidence interval (usually defaulting to a 95% confidence level), and its role is to help judge whether the autocorrelation coefficient or the partial autocorrelation coefficient is statistically significant; the horizontal line in the middle is the reference line of y = 0, indicating no correlation (the correlation coefficient is zero); each lag period corresponds to a vertical line, and the height represents the autocorrelation coefficient (or partial autocorrelation coefficient value) of that lag period.

[0030] Finally, use the established ARIMA model to predict future data, and the prediction results are shown in Table 1 below: Table 1 ARIMA model prediction table .

[0031] According to the data in Table 1, the calculated RMSE is 5.311.

[0032] Use the GM(1,1) model to predict the water inflow data. Substitute the basic water inflow data for each month from 2020 to 2022 to obtain the original time series data set: ; For accumulation can be obtained: ; Conduct a smoothness test on each data in the original time series data set, calculate , after testing, when and , it meets the smoothness.

[0033] The adjacent mean sequence set is: ; After discretization, the gray differential equation is obtained: ; According to the formula, the white differential equation can be obtained: ; Calculation shows that = 0.00169, = 231.645; Take , and substitute , into formula (9) and restore it through formula (10) to obtain the prediction sequence of the GM(1,1) model. The prediction results are shown in Table 2 below: Table 2 Gray Model Prediction Table .

[0034] According to the data in Table 2, the calculated RMSE is 10.618.

[0035] Determine the corresponding weights of the two models according to the RMSE of the two models. After calculation, it can be known that the weights of the ARIMA model and the GM(1,1) model are 66.66% and 33.34% respectively. Finally, use the prediction results of the ARIMA-GM combined model.

[0036] The prediction results are as Figure 7 shown. The prediction trends of the water inflow of the three models are roughly consistent with the change law of the actual value, all showing a trend of first decreasing and then increasing, reaching a peak in August and then decreasing and then increasing again. This prediction trend better reflects the fluctuation characteristics of the actual water inflow, indicating that the model has a certain degree of accuracy and applicability in capturing the periodic changes and peak periods of the water inflow.

[0037] After calculation, it can be known that the root mean square errors predicted by the ARIMA model and the GM(1,1) model are 5.311 and 10.618 respectively, and the root mean square error predicted by the ARIMA-GM model is 3.327. Comparing the two single models, the error precision of the ARIMA-GM combined model is smaller. The goodness of fit R 2 of the ARIMA-GM combined model is approximately 0.9822, close to 1, indicating that the model fitting effect is good and can more accurately predict the future short- and medium-term changes in mine water inflow, providing reference for coal mines.

[0038] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions, or substitutions made by those skilled in the art within the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for predicting the water inrush volume of coal mines based on a combined model and dynamic collaborative weight allocation, characterized in that, It includes the following steps: Step 1: Collect the time series historical data of the mine water inflow and perform preprocessing. Define the preprocessed data as the original time series data set; Step 2: Construct an ARIMA model; Step 3: Construct a GM(1,1) model; Step 4: Construct an ARIMA-GM combined model for predicting the mine water inflow, and introduce a time decay factor, an error sensitivity coefficient, and a regulation factor to construct a dynamic collaborative weight allocation mechanism for weight update and optimization.

2. The method for predicting the water inrush volume of coal mines based on a combined model and dynamic collaborative weight allocation according to claim 1, characterized in that, In Step 1, during preprocessing, it is necessary to perform data integrity, stability, and correlation tests; The specific process is as follows: Step 1.1: Check data integrity. For missing data, supplement it by interpolation method; Step 1.2: Perform stability test. If the data is not stationary, perform differencing operation and then perform white noise test. If the data is stationary, directly perform white noise test; Step 1.3: Use white noise for correlation test; the specific process is as follows: Perform differencing operation on the data to obtain the residual sequence, calculate the autocorrelation function and partial autocorrelation function according to the residual sequence, and draw the corresponding autocorrelation function graph or partial autocorrelation function graph. If the values of the autocorrelation function or partial autocorrelation function decay rapidly within the confidence interval, it indicates that the residual is close to white noise and meets the modeling requirements of the ARIMA model; if it does not meet the modeling requirements of the ARIMA model, re-collect the data for preprocessing, or return to Step 1.1 to preprocess the data again.

3. The method for predicting the water inrush volume of coal mines based on a combined model and dynamic collaborative weight allocation according to claim 2, characterized in that, The specific process of step 2 is as follows: Determine the regression order p and the mean order q of the ARIMA model according to the autocorrelation function and the partial autocorrelation function calculated in step 1.3, and directly use the ARIMA model with the determined order to predict the future water inflow. When predicting, directly input the time series historical data of the preprocessed mine water inflow into the ARIMA model to obtain the ARIMA model prediction sequence , where is the th data in the ARIMA model prediction sequence.

4. The method for predicting the water inrush volume of coal mines based on a combined model and dynamic collaborative weight allocation according to claim 3, characterized in that, In Step 3, the specific working process of the GM(1,1) model is as follows: Step 3.

1. There is a set of original time series data , which is subjected to a first-order accumulation to obtain a set of first-order accumulated time series data ; The formula for the first-order accumulation is: (1)； Among them, and are the -th and -th data in the original time series data set respectively; and are the -th and -th data in the first-order accumulated time series data set respectively; Step 3.2: Perform smoothness test on each data in the original time series data set: (2)； Among them, is the smooth ratio of the th data; is the th data in the set of one-time cumulative time series data; If the following conditions are met and then this sequence data is considered a quasi-smooth sequence, meeting the modeling requirements of the GM(1,1) model; Step 3.3: Calculate the adjacent mean values and generate a set of adjacent mean value sequences ; The calculation formula for the adjacent mean value is as follows: (3)； Among them, , are respectively the th th data in the set of mean sequences, adjacent to each other; Step 3.4: Establish a grey differential equation: (4)； Among them, , are different undetermined parameters; The corresponding white differential equation is: (5)； Among them, is the cycle serial number; Define the parameter column: (6)； (7)； (8)； Among them, The determinant constructed for the undetermined parameters; Is the transpose; Is the matrix constructed by the adjacent means; Is the matrix composed of the original data; Substitute and into formula (6) to solve for the estimated values of the undetermined parameters and ; Step 3.6: Solve the grey differential equation and the white differential equation to obtain the set of accumulated time response sequences ; (9)； Among them, , , are the predicted values for , , respectively; is the th data in the set of first-order accumulated time series data; is the natural constant; Step 3.7: Perform cumulative reduction to obtain the predicted value: (10)； Among them, is the th predicted value in the GM(1,1) model prediction sequence; The predicted sequence of the GM(1,1) model is ; is the th predicted value in the predicted sequence of the GM(1,1) model.

5. The coal mine water inrush prediction method based on the combined model and dynamic collaborative weight allocation according to claim 4, characterized in that, The specific process of Step 4 is as follows: Step 4.1: Initialize the time decay factor, error sensitivity coefficient, and regulation factor, and define the prediction error calculation formula as: (11)； Among them, is the prediction error of the model in the th cycle; is the root mean square error of the model in the th cycle. Step 4.2: Calculate the weight numerator: (12)； Among them, is the weight molecule of the model ; is the adjustment factor; is the error sensitivity coefficient; is the prediction error of the model in the th cycle; is the prediction error of the model in the th cycle; is the time decay factor; Step 4.3: Calculate the normalization coefficient: (13)； Among them, is the normalization coefficient; is the weight numerator of the ARIMA model; is the weight numerator of the GM(1,1) model; Step 4.4: Allocate weights to the two models: (14)； (15)； Among them, is the weight of the th period of the ARIMA model; is the weight of the th period of the GM(1,1) model; Step 4.5: Weightedly combine the prediction results of the two models to construct an ARIMA-GM combined model for predicting the mine water inflow: (16)； Among them, is the predicted value of the combined model for the mine water inflow; Step 4.6: Perform dynamic parameter optimization; specifically, dynamically adjust the parameters according to the prediction error: If the sum of the prediction errors of the current-period ARIMA model and the GM(1,1) model is higher than a pre-set threshold, then increase , and the specific increased value is adjusted according to the actual situation; If the environmental stability is high, it will be reduced , and the specific reduction value is adjusted according to the actual situation; the specific manifestation of high environmental stability is that the water inflow data fluctuates little and has no obvious trend change, and at the same time, the prediction error remains at a low level for a long time and fluctuates little; Step 4.7, Exception handling: When the normalization coefficient approaches zero, it is an abnormal situation, and the weights of the ARIMA model are reset and the weights of the GM(1,1) model are both the default value of 0.5.

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