Water flowing fractured zone height prediction method

Abstract

The invention discloses a water flowing fractured zone height prediction method. A water flowing fractured zone height prediction method combining segmented regression and generalized Pareto distribution is provided. The method comprises the following steps: firstly, marking an over-limit sample as an extreme interval according to a high threshold of the mining depth or the inclined length of a working face; a generalized Pareto distribution extreme value theory is adopted in the interval, and distribution parameters describing random characteristics of the extreme interval are obtained through maximum likelihood estimation; when the input mining depth or the inclined length of the working face falls into an extreme interval, prediction is carried out based on the model, segment regression continues to be carried out on a conventional section, and a final result is output through weighted fusion; if a new abnormal value occurs in the extreme interval, the extreme value model can be updated or finely adjusted in real time. According to the method, the prediction precision and stability under extreme working conditions such as ultra-large mining depth and high working face inclined length can be remarkably improved.

Description

Technical Field

[0001] The invention relates to a method for predicting the height of a water-conducting fracture zone, and belongs to the technical field of predicting the height of a water-conducting fracture zone. Background Art

[0002] In the field of coal mining, how to accurately predict the height of water-conducting fracture zones is of vital importance to coal mine safety, especially under extreme conditions such as extremely deep mining or obliquely long working faces. Water-conducting fracture zones are fracture zones generated in the overlying rock strata after coal seam mining. Once their development height exceeds the bottom boundary of the aquifer above, they may cause water inrush disasters, seriously threatening underground production and personnel safety. Traditional prediction methods are often based on single regression models or empirical formulas, which cannot fully take into account both conventional and extreme working conditions, and are also difficult to cope with the complex changes under the coupling of multiple factors such as different mining depths, working face lengths, and hard rock lithology ratios.

[0003] In view of the above problems, in the prior art, the height of the water-conducting fracture zone is generally predicted by the following methods:

[0004] 1) Based on empirical formula or linear regression: Traditional practices usually rely on simplified empirical formulas for factors such as coal seam mining thickness and burial depth, or perform simple multivariate linear regression on this basis. Although this method is relatively simple to calculate, under geological conditions of extremely deep mining, high mining thickness, or complex soft and hard rock combinations, the model's extrapolation ability is often insufficient, making it difficult to accurately capture possible mutations or nonlinear trends in extreme intervals.

[0005] 2) Use a single nonlinear regression or neural network model: Some researchers have tried to introduce nonlinear regression, neural network and other methods to improve prediction accuracy. However, a single global nonlinear model may face problems of overfitting or extrapolation distortion caused by complex distribution of training data, multicollinearity and scarcity of extreme values. Especially under the conditions of extremely deep mining or extremely long working face, the lack of sufficient extreme samples can easily lead to numerical instability of the model.

[0006] Therefore, the current technical methods generally have the following limitations:

[0007] 1) It is impossible to take into account both the normal interval and the extreme interval at the same time: simple empirical formulas or linear regression are prone to distortion when extrapolating to the extreme interval, and complex nonlinear models may overfit the normal interval and ignore the characteristics of the extreme interval.

[0008] 2) Lack of specialized modeling for extreme intervals: Traditional methods usually treat the entire data as a whole training, ignoring the fact that when the mining depth or the inclined length of the working face exceeds a certain threshold, the rock formation failure mechanism may change significantly, thereby increasing the prediction error. Summary of the invention

[0009] The technical problem to be solved by the present invention is to provide a method for predicting the height of a water-conducting fracture zone to overcome the deficiencies of the prior art.

[0010] The technical solution of the present invention is: a method for predicting the height of a water-conducting fracture zone, the method comprising the following steps:

[0011] According to the high value threshold of mining depth or inclined length of working face, the sample data exceeding the threshold is marked as extreme interval;

[0012] In the extreme interval, a generalized Pareto distribution extreme value theoretical model is selected, and the distribution parameters describing the highly random characteristics of the water-conducting fracture zone in the extreme interval are obtained by using an extreme value parameter estimation method;

[0013] When the input mining depth or the oblique length of the working face falls into the extreme interval, the height of the water-conducting fracture zone is predicted according to the generalized Pareto distribution extreme value theoretical model;

[0014] The segmented regression model is used to predict the results in the conventional section, and the prediction results are weighted and fused in the extreme interval to finally output the predicted value of the water-conducting fracture zone height.

[0015] Furthermore, the method also includes: by continuously evaluating the actual mining depth and working face oblique length monitoring values ​​and subsequent observation data, if new mining depth or working face oblique length abnormal values ​​appear in the extreme interval, updating or fine-tuning the parameters of the extreme value model.

[0016] Furthermore, the extreme value parameter estimation method is a maximum likelihood estimation method.

[0017] The beneficial effects of the present invention are as follows: compared with the prior art, the present invention aims at the problem that traditional methods are difficult to take into account both conventional working conditions and extreme working conditions, and proposes a method of combining separate modeling of extreme intervals based on generalized Pareto distribution with segmented regression of conventional sections, so that when the mining depth or the inclined length of the working face exceeds the high value threshold, the height of the water-conducting fracture zone can be more accurately extrapolated and predicted, and the regression results of the conventional sections can be combined through weighted fusion to achieve overall output. Through the special modeling of extreme intervals, not only the numerical distortion or overfitting problems of a single model under the condition of scarcity of extreme values ​​are effectively avoided, but also the extreme value model parameters can be updated or fine-tuned in time when new extreme data arrives, so as to maintain adaptability to complex underground geological conditions. This significantly improves the accuracy and stability of the prediction of the height of the water-conducting fracture zone, and provides a more reliable technical guarantee for the prevention and control of water hazards in coal mine roofs. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0019] Implementation Example 1: This implementation example proposes a method for predicting the height of a water-conducting fracture zone for extreme working conditions such as extremely deep mining or oblique long working faces in coal mines. By separately modeling extreme samples that exceed the set threshold and using a segmented regression model to achieve prediction fusion in conventional sections, the accuracy of extrapolation of the height of a water-conducting fracture zone in extreme intervals can be effectively improved, overcoming the limitation of existing technologies that cannot take into account both conventional intervals and extreme intervals.

[0020] To enable those skilled in the art to implement, reference is made to Figure 1 This implementation example provides a complete process and mathematical derivation from data preprocessing to extreme value distribution estimation and then to fusion prediction, which is convenient for application in actual working conditions underground in coal mines.

[0021] Step 1: Data collection and threshold setting

[0022] Data collection: Data were collected from multiple coal mining areas. Sample, where S i Indicates mining depth, L i Indicates the oblique length of the working surface, H f,i Indicates the corresponding height of the water-conducting fracture zone.

[0023] Threshold setting: Set the high threshold S based on empirical analysis or statistical distribution. max With L max When S i ≥S max or L i ≥L max , the sample is judged to be in the extreme range.

[0024] Step 2: Extreme interval identification and data classification

[0025] 1. Extreme interval data: All data that meet

[0026] S i ≥S max or L i ≥L max

[0027] 2. The samples are recorded as extreme interval data sets

[0028] 3. Regular segment data: the remaining samples (S i max And L i <L max ) is classified as a regular segment data set

[0029] Step 3: Train a segmented regression model on regular segments

[0030] right ​For data within , piecewise regression can be used to improve local fitting accuracy. The following uses multivariate linear segmentation as an example for easy explanation:

[0031] 1. Segment division: set several thresholds {T S,k},{T L,k}, divide the regular segment into several sub-intervals Ω k .

[0032] 2. Regression model diagram: For each subinterval Ω k Create a regression equation, such as

[0033]

[0034] Where M is the mining thickness and b is the hard rock lithology ratio coefficient. k,j It can be obtained by least squares or other fitting methods.

[0035] Step 4: Modeling the Generalized Pareto Distribution (GPD) in the extreme interval

[0036] (1) Background of Extreme Value Theory

[0037] When the mining depth or the inclined length of the working face exceeds a certain high value threshold, the traditional regression lacks sufficient samples or is difficult to characterize the tail distribution. The present invention selects the generalized Pareto distribution (GPD) to perform separate modeling of extreme intervals.

[0038] (2) GPD mathematical form Let the super-threshold sample be {X i}(such as S i ≥S max The corresponding water-conducting fracture zone height {H f,i}), then the GPD distribution function can be written as:

[0039]

[0040] Among them, σ>0 is the scale parameter, ξ is the shape parameter, and u is the high value threshold (which can be compared with S max or L max correspond).

[0041] (3) GPD parameter estimation

[0042] Using the maximum likelihood estimation method to obtain Let the sample be {X1,X2,…,X n}, its log-likelihood function is

[0043]

[0044] Through numerical optimization, we find the solution that maximizes l(σ,ξ) This process can use Newton iteration, BFGS or other numerical methods.

[0045] Step 5: Extrapolate forecasts to extreme ranges

[0046] When the new mining depth or working face inclined length (S new ,L new ) When the GPD model enters the extreme range, it can be used for extrapolation prediction. Common methods include:

[0047] (1) Independent extrapolation mode

[0048] The height of the water-conducting fracture zone in the extreme range is recorded as X (or ΔH f ),like If the extreme value theory has been used to fit the distribution, the expected value or quantile can be directly extracted from the GPD distribution for prediction. For example, if ξ<1, the expectation of GPD can be written as

[0049] (when ξ<1),

[0050] This gives additional height in extreme cases.

[0051] (2) Weighted Fusion Mode

[0052] If the conventional segment already has segmented regression results It can be corrected within the limit.

[0053]

[0054] in represents the extrapolated result calculated by extreme value distribution, and α∈[0,1] is the weighting coefficient. Step 6: Final fusion output and model update

[0055] · Fusion output: In conventional sections: directly use the segmented regression model for output; in extreme intervals: output the estimated value of the height of the water-conducting fracture zone based on the GPD model or after weighted correction of the segmented regression model. · Model update: If the subsequent downhole monitoring data continues to increase, and new abnormal mining depths or oblique lengths of working faces appear in the extreme interval samples, they can be included in the extreme value distribution for re-estimation ( parameters, etc.), so that the model remains accurate and robust in the ever-changing mining environment.

[0056] Derivation of mathematical formulas

[0057] The following is a derivation process of several key mathematical expressions in this implementation example to help those skilled in the art understand:

[0058] 1. GPD distribution and its log-likelihood function

[0059] After setting the threshold u, (Xu) represents the excess part, then the GPD probability density function is

[0060]

[0061] Log-likelihood function

[0062]

[0063] Taking its partial derivative and setting it to zero gives the parameter estimation equation, which is solved by numerical iteration.

[0064] 2. Weighted Fusion Formula

[0065] When entering the extreme interval, in order to take into account the characteristics of conventional regression and extreme value extrapolation, let

[0066]

[0067] Where α(x) can change with the distance from the threshold, or be set to a constant value.

[0068] 3. Model Update

[0069] When the extreme value {X j} arrives, it can be included in the extreme value distribution for refitting:

[0070]

[0071] Where n is the number of original extreme samples, and m is the number of newly added extreme samples. This allows for adaptive updating of extreme distribution over time.

[0072] The above method can take into account the modeling requirements of both conventional sections and extreme sections, avoid excessive extrapolation errors caused by lack of extreme values ​​in conventional sections, and prevent distortion problems caused by too little data in extreme sections to support model training. Actual test cases have shown that this method can maintain higher prediction accuracy and model stability under conditions of ultra-deep mining or ultra-long working faces, thereby more effectively preventing and controlling water inrush risks and ensuring safe production in coal mines.

[0073] The parts not described in detail in the present invention are all known technologies to those skilled in the art. Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention is described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for predicting the height of a water-conducting fracture zone, characterized in that: The method comprises the following steps: According to the high-value threshold of the mining depth or the inclined length of the working face, the sample data exceeding the threshold is marked as an extreme interval; within the extreme interval, the generalized Pareto distribution extreme value theory model is selected, and the distribution parameters describing the highly random characteristics of the water-conducting fracture zone in the extreme interval are obtained through the extreme value parameter estimation method; When the input mining depth or the oblique length of the working face falls into the extreme interval, the height of the water-conducting fracture zone is predicted according to the generalized Pareto distribution extreme value theoretical model; The segmented regression model is used to predict the results in the conventional section, and the prediction results are weighted and fused in the extreme interval to finally output the predicted value of the water-conducting fracture zone height.

2. The method for predicting the height of a water-conducting fracture zone according to claim 1, characterized in that: The method also includes: by continuously evaluating the actual mining depth and working face oblique length monitoring values ​​and subsequent observation data, if new mining depth or working face oblique length abnormal values ​​appear in the extreme interval, updating or fine-tuning the parameters of the extreme value model.

3. The method for predicting the height of a water-conducting fracture zone according to claim 1, characterized in that: The extreme value parameter estimation method is the maximum likelihood estimation method.

Images