CN109359393B - Method for Determination of Reasonable Mining Period of Four Quantities in Mine Under Uncertain Information Conditions - Google Patents

Abstract

The invention provides a method for determining four reasonable mining periods of a mine under uncertain information conditions, and relates to the technical field of mine safety mining. The method comprises the following steps: determining a four-quantity reasonable mining period model; measuring the influence of uncertain information conditions on the reasonable sampling period of four quantities; analyzing uncertain information conditions which cause model failure, and quantitatively calculating the risk of the model; and (5) performing reliability analysis on the model. The method for determining the four reasonable mining periods of the mine under the uncertain information condition provided by the invention researches the change rule of the four reasonable mining period models under various uncertain information conditions, perfects the traditional four reasonable mining period calculation models and theoretical basis, establishes a corresponding mathematical model by analyzing the risk and reliability of the models under the uncertain information condition, provides guidance opinion for the establishment of a mine safety production plan, and provides theoretical basis for normal production connection of a working face.

Description

Method for determining the reasonable mining period of four quantities in a mine under uncertain information conditions

Technical Field

The invention relates to the technical field of safe mining of mines, and in particular to a method for determining a reasonable mining period of four quantities in a mine under uncertain information conditions.

Background Art

In the process of coal production, maintaining the balance between mining and excavation is a prerequisite for ensuring the normal, continuous and stable production of the mine, and is also an important means to reduce the maintenance cost of the tunneling project. With the rapid development of my country's coal industry, the progress of coal production science and technology, and the continuous changes in the complexity of mining conditions, the "Three Quantities" regulations formulated by the state to ensure the smooth succession of mines have gradually become unbalanced in mining and excavation and cannot meet the needs of mine succession at this stage. The "four quantities" are the development coal quantity, the preparation coal quantity period, and the recovery coal quantity, and the method for determining the reasonable mining period of the "four quantities" has greatly improved the shortcomings of the traditional "three quantities" theory in gas pre-extraction, providing a theoretical basis for reference when calculating the reasonable mining period of high-gas and gas outburst mines.

At present, the production practice of mines is increasingly affected by a variety of uncertain information conditions, such as: unforeseen complex geological mutations, sudden disasters, external economic and market demand, reasonable allocation and mining, and pioneering mining methods. These factors, whether internal factors that may be encountered in the production process or external factors brought by the surrounding environment, cannot be determined in advance, but they have an impact on the reasonable mining period of the "four quantities" of the mine that cannot be ignored. However, there is currently little research on the changing laws of the reasonable mining period of the "four quantities" under the conditions of uncertain information in mines, and there is no reference to the risk and reliability of the mining period of the "four quantities".

Summary of the invention

In view of the problems existing in the prior art, the present invention provides a method for determining the reasonable mining period of four quantities in a mine under uncertain information conditions. By exploring the changing law of the reasonable mining period of the "four quantities" under uncertain information conditions, risk analysis and reliability analysis are performed on the reasonable mining period model of the "four quantities", so as to obtain the risk function of the reasonable mining period model of the "four quantities", which provides guidance for the normal production continuation of the working face.

In order to achieve the above purpose, a method for determining the reasonable mining period of four quantities in a mine under uncertain information conditions includes the following steps:

Step 1: Determine the reasonable mining period model of the "four quantities";

Step 2: Determine the changing rules of the reasonable recoverable period of the "four quantities" under uncertain information conditions, and use the tunneling speed as a random variable to measure the impact of uncertain information conditions on the reasonable recoverable period of the "four quantities";

Step 3: Analyze the uncertain information conditions that lead to the failure of the "four quantities" reasonable recoverable period model through the main logic diagram, and quantitatively calculate the risk of the model based on the probability calculation of the fault tree and event tree;

Step 4: Conduct reliability analysis on the reasonable mining period model of the “four quantities”.

Furthermore, the method for quantitatively calculating the risk of the model based on the probability calculation of the fault tree and the event tree in step 3 is as follows:

(1) Probability calculation of fault tree:

Let n factors that lead to mining imbalance be H ₁ , H ₂ , H ₃ , ..., H _n , and there is an intersection between the factors, then the calculation formula for the total probability of leading to mining imbalance is as follows:

(2) Probability calculation of event tree:

Let the m accident sequence groups in the event tree of the “four-quantity” reasonable mining period model be ASG ₁ , ASG ₂ , ... , ASG _m , and the l link events contained in the jth accident sequence group be T _j1 , T _j2 , ... , T _jl , then the calculation formula for the conditional probability of the jth accident sequence group is as follows:

Where, P(ASG _j |IE) is the probability of the jth chain accident event occurring when the uncertain event IE occurs, and p(T _kl ) is the probability of the lth link event occurring in the accident sequence group;

(3) Risk probability calculation of the “four quantities” reasonable mining period model:

According to the total probability of causing mining imbalance and the conditional probability of each accident sequence group, the risk probability calculation formula of the "four quantities" reasonable mining period model is as follows:

P(A)=∑ _i ∑ _j P(IE _i )P(ASG _j |IE _i )P(A|ASG _j );

Where P(A) is the failure probability of the reasonable mining period model of the “four quantities”, P(IE _i ) is the probability of the occurrence of the i-th uncertain event that may cause mining imbalance, P(ASG _j |IE _i ) is the probability of the occurrence of the j-th chain accident event when the uncertain event i occurs, and P(A|ASG _j ) is the probability of whether the j-th chain accident event will lead to model failure.

Furthermore, the method for performing reliability analysis on the reasonable mining period model of the "four quantities" in step 4 is as follows:

和

故变量X的概率密度函数为：Let the continuous random variable X obey the gamma distribution with parameters (α, λ), denoted as X~Ga(α, λ), where α＞0 and λ＞0, then the mathematical expectation and variance of the variable X are

and

Therefore, the probability density function of variable X is:

The cumulative distribution function of the gamma function calculated by MATLAB is:

Among them, X is any reasonable mining period among the “four quantities”, x is the variable value under the reasonable mining period function, and igamma is the inverse gamma distribution;

Under the premise of a given reliability, the value of x that satisfies the equation F _x (x) is calculated to be the value of x under the given reliability, that is, the reliability of the reasonable mining period model of the "four quantities" corresponding to the value of x.

Beneficial effects of the present invention:

The present invention proposes a method for determining the reasonable mining period of four quantities in a mine taking into account the influence of uncertain information conditions, studies the changing law of the reasonable mining period model of the "four quantities" under various uncertain information conditions, improves the traditional "four quantities" reasonable mining period calculation model and theoretical basis, and establishes a corresponding mathematical model by analyzing the risk and reliability of the model under uncertain information conditions, which provides guidance for the formulation of mine safety production plans and provides a theoretical basis for the normal production continuation of the working face.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for determining a reasonable mining period of four quantities in a mine taking into account the influence of uncertain information conditions in an embodiment of the present invention;

FIG2 is a schematic diagram of a theoretical gamma distribution in an embodiment of the present invention;

3 is a schematic diagram of the gamma distribution actually applied in combination with the reasonable mining period of the “four quantities” of a mine in an embodiment of the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

A method for determining the reasonable mining period of four quantities in a mine considering the influence of uncertain information conditions, the process is shown in Figure 1, and the specific method is as follows:

Step 1: Determine the reasonable mining period model of the "four quantities";

In this embodiment, the reasonable mining period model of the “four quantities” is as follows:

1) The model of reasonable mining period of coal development is as follows:

为减缓速度的影响系数，且

为区间[0，1]内的常数；Where, _Tk is the reasonable mining period of the development coal volume, _Lk is the total length of the tunneling project, p is the average number of tunneling teams in the development process, _Vk is the average tunneling speed in the development process, _Tk0 is the average preparation replacement time from the formation of the development coal volume to the formation of the preparation coal volume, _Tz2 is the average pre-pumping time for coal uncovering in the stone gate, _Tz3 is the average pre-pumping time for coal uncovering in the shaft, _Vd is the maximum average tunneling speed reduced by the influence of complex geological structures during the tunneling process,

is the influence coefficient of slowing down speed, and

is a constant in the interval [0, 1];

2) Prepare a reasonable mining period model for coal quantity as follows:

Where, _Tz is the reasonable mining period of the prepared coal volume, _Lz is the total excavation length required for the preparation work, q is the average number of excavation teams in the preparation process, _Vz is the average excavation speed in the preparation process, _Tz0 is the average preparation replacement time from the formation of the prepared coal volume to the formation of the recovered coal volume, and _Tz1 is the average pre-extraction time before the preparation roadway exposes the coal seam;

3) The model of reasonable recoverable period of coal recovery volume is as follows:

T _h =L _m /(V _J -φV _d )+max{T _o , T _c };

Where, _Th is the reasonable period of coal recovery at the working face, _To is the average equipment installation and commissioning time at the working face, _Tc is the average gas extraction standard time at the working face, _Lm is the total excavation length required for the recovery work, and _VJ is the average excavation speed at the working face;

4) The model of reasonable recoverable period of coal volume that meets gas extraction standards is as follows:

_Tw = _kTh ;

S₁为回采煤量面积，S₂为瓦斯预抽煤量面积。Where _Tw is the period of coal mining that meets the gas extraction standard, k is the gas pre-extraction safety factor, and

_S1 is the area of recovered coal volume, and _S2 is the area of gas pre-extraction coal volume.

Step 2: Determine the changing rules of the reasonable recoverable period of the "four quantities" under uncertain information conditions, and use the tunneling speed as a random variable to measure the impact of uncertain information conditions on the reasonable recoverable period of the "four quantities";

In this embodiment, taking unforeseen complex geological structures as an example, through analysis, these structures may lead to the discovery that there are too many structures that cannot be mined after the originally planned mineable coal is excavated, and the previously excavated tunnels may also be scrapped, resulting in an increase in invalid tunnels, which is equivalent to a reduction in the tunnel mining speed. The mining work depends on whether the excavation work can be completed smoothly. Therefore, it can be considered that unforeseen geological structures cause the increase of the reasonable mineable period of the "four quantities" by causing a reduction in the excavation speed. Similarly, for other uncertain information conditions, such as sudden disasters, external economic and market demand, reasonable allocation and mining, and development mining methods, they can be directly or indirectly converted into a reduction in the excavation speed, causing an increase in the reasonable mineable period of the "four quantities".

Step 3: Analyze the uncertain information conditions that lead to the failure of the "four quantities" reasonable recoverable period model through the main logic diagram, and quantitatively calculate the risk of the model based on the probability calculation of the fault tree and event tree;

The method for quantitatively calculating the risk of the model based on the probability calculation of the fault tree and the event tree is as follows:

(1) Probability calculation of fault tree:

Let n factors that lead to mining imbalance be H ₁ , H ₂ , H ₃ , ..., H _n , and there is an intersection between the factors, then the calculation formula for the total probability of leading to mining imbalance is as follows:

(2) Probability calculation of event tree:

Let the m accident sequence groups in the event tree of the “four-quantity” reasonable mining period model be ASG ₁ , ASG ₂ , ... , ASG _m , and the l link events contained in the jth accident sequence group be T _j1 , T _j2 , ... , T _jl , then the calculation formula for the conditional probability of the jth accident sequence group is as follows:

Where, P(ASG _j |IE) is the probability of the jth chain accident event occurring when the uncertain event IE occurs, and p(T _kl ) is the probability of the lth link event occurring in the accident sequence group;

(3) Risk probability calculation of the “four quantities” reasonable mining period model:

According to the total probability of causing mining imbalance and the conditional probability of each accident sequence group, the risk probability calculation formula of the "four quantities" reasonable mining period model is as follows:

P(A)=∑ _i ∑ _j P(IE _i )P(ASG _j |IE _i )P(A|ASG _j );

Where P(A) is the failure probability of the reasonable mining period model of the “four quantities”, P(IE _i ) is the probability of the occurrence of the i-th uncertain event that may cause mining imbalance, P(ASG _j |IE _i ) is the probability of the occurrence of the j-th chain accident event when the uncertain event i occurs, and P(A|ASG _j ) is the probability of whether the j-th chain accident event will lead to model failure.

In this embodiment, in the "four-quantity" reasonable mining period model, the main logic diagram (MLD) describes the necessary conditions for the occurrence of risk accidents in a hierarchical manner. Starting from an undesirable mining imbalance at a working face, the model is developed from top to bottom with a divide-and-conquer strategy, and the accident is gradually decomposed into sub-blocks described by the initial event until all possible initial events are collected. Event tree analysis (ETA) obtains the accident sequence group ASG caused by the factors causing mining imbalance through accident sequence review and accident development analysis. The event node in the event tree represents the consequence event that may be caused by the event of the previous layer. For each uncertain factor in the event tree, it is required to establish a joint probability of occurrence to determine the probability of occurrence at that point. Fault tree (FTA) is a process of deductive reasoning, which usually provides more detailed details for the failure link events of the event tree. Through FTA, it is possible to clearly understand which uncertain factors cause the model to fail, so as to find out the basic cause of mining imbalance. In practical applications of the reasonable mining period of the "four quantities", by statistically analyzing relevant data and using quantitative calculation methods, we can accurately obtain the probability of failure of the reasonable mining period model of the "four quantities" or the probability of failure to continue normally during the production process. This will enable us to make corresponding adjustments to the production plan in advance based on actual conditions and minimize the losses caused by risks.

Step 4: Conduct reliability analysis on the reasonable mining period model of the “four quantities”.

The method for performing reliability analysis on the reasonable mining period model of the "four quantities" is as follows:

和

故变量X的概率密度函数为：Let the continuous random variable X obey the gamma distribution with parameters (α, λ), denoted as X~Ga(α, λ), where α＞0 and λ＞0, then the mathematical expectation and variance of the variable X are

and

Therefore, the probability density function of variable X is:

The cumulative distribution function of the gamma function calculated by MATLAB is:

Among them, X is any reasonable mining period among the “four quantities”, x is the variable value under the reasonable mining period function, and igamma is the inverse gamma distribution;

Under the premise of a given reliability, the x value that satisfies the equation F(x) is calculated to be the value of x under the given reliability, that is, the reliability of the "four quantities" reasonable mining period model corresponding to the x value.

下的x值，即在90％概率下可实现采掘顺利对接的回采煤量可采期T_h＝x，且在伽马函数分布图中x表现为在k点处的取值。The theoretical distribution of the gamma function is shown in FIG2. In this embodiment, the reliability analysis is performed based on the reasonable recoverable period of the recovered coal volume T _h. In the problem of calculating the excavation time, the reliability (probability) is given as 0.9, and the problem is to calculate the equation satisfying

The x value under this condition, that is, the recoverable period of coal volume that can achieve smooth mining and excavation connection under 90% probability is _Th = x, and in the gamma function distribution diagram, x is represented as the value at point k.

In this embodiment, a gas outburst mine is taken as an example. Through the statistical data collected by the staff and the actual experience, it is known that when the mining process is not predicted in advance and a large fault is encountered, the probability that the working face must be re-excavated due to the influence of the fault is 80%; the probability that other sudden disasters in the surrounding environment may occur due to the influence of the fault is 60%; the probability of model failure due to the influence of subsequent sudden disasters is 70%. Finally, the failure probability of the "four quantities" reasonable mining period model is obtained as follows:

P(A)=∑ _i ∑ _j P(IE _i )P(ASG _j |IE _i )P(A|ASG _j )=33.6%;

The calculation results show that due to the influence of unpredictable faults, the probability of failure of the reasonable mining period of the "four quantities" reaches 33.6%, which obviously brings great risks to the normal continuation of the production process.

In this embodiment, the gamma function distribution in actual application is shown in FIG3 . In order to reduce the risk of uncertain information conditions to production continuity, and thus obtain the optimal reasonable recoverable period _Th of the recovered coal volume, the excavation time of the calculation model under a reliability of 90% is calculated as follows:

After counting the excavation time of several adjacent tunnels in a mining area of the mine, the expected E(X) and variance Var(X) are calculated to be 8.95 and 2.01 respectively, and the parameters α and λ are 40.051 and 4.475 respectively. Since x is time in this embodiment and needs to be a positive value, the parameters α and λ are substituted into the following formula to solve x:

The time x is obtained by MATLAB as 7.192, which is the value of point k in Figure 3.

As can be seen from Figure 3, under the premise of uncertain information conditions, the reasonable recoverable period of coal recovery is 7.192 months, which can make the probability of normal mine production continuation reach more than 90%, and can provide guidance for the mine's production plan, thereby ensuring the normal continuation of production.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features therein may be replaced by equivalents. Therefore, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims (2)

1. A method for determining the reasonable mining period of four quantities in a mine under uncertain information conditions, characterized in that it comprises the following steps: Step 1: Determine the reasonable mining period model of the "four quantities"; Step 2: Determine the changing rules of the reasonable recoverable period of the "four quantities" under uncertain information conditions, and use the tunneling speed as a random variable to measure the impact of uncertain information conditions on the reasonable recoverable period of the "four quantities"; Step 3: Analyze the uncertain information conditions that lead to the failure of the "four quantities" reasonable recoverable period model through the main logic diagram, and quantitatively calculate the risk of the model based on the probability calculation of the fault tree and event tree; Step 4: Conduct reliability analysis on the reasonable mining period model of the “four quantities”; The method for quantitatively calculating the risk of the model based on the probability calculation of the fault tree and the event tree in step 3 is as follows: (1) Probability calculation of fault tree: Let n factors that lead to mining imbalance be H ₁ , H ₂ , H ₃ , ..., H _n , and there is an intersection between the factors, then the calculation formula for the total probability of leading to mining imbalance is as follows:

(2) Probability calculation of event tree: Let the m accident sequence groups in the event tree of the “four-quantity” reasonable mining period model be ASG ₁ , ASG ₂ , ... , ASG _m , and the l link events contained in the jth accident sequence group be T _j1 , T _j2 , ... , T _jl , then the calculation formula for the conditional probability of the jth accident sequence group is as follows:

Where, P(ASGj|IE) is the probability of the jth chain accident event occurring when the uncertain event IE occurs, and p(T _kl ) is the probability of the lth link event occurring in the accident sequence group; (3) Risk probability calculation of the “four quantities” reasonable mining period model: According to the total probability of causing mining imbalance and the conditional probability of each accident sequence group, the risk probability calculation formula of the "four quantities" reasonable mining period model is as follows: P(A)=∑ _i ∑ _j P(IE _i )P(ASG _j |IE _i )P(A|ASG _j ); Where P(A) is the failure probability of the reasonable mining period model of the “four quantities”, P(IE _i ) is the probability of the occurrence of the i-th uncertain event that may cause mining imbalance, P(ASG _j |IE _i ) is the probability of the occurrence of the j-th chain accident event when the uncertain event i occurs, and P(A|ASG _j ) is the probability of whether the j-th chain accident event will lead to model failure. 2. The method for determining the reasonable mining period of four quantities in a mine under uncertain information conditions according to claim 1 is characterized in that the method for performing reliability analysis on the reasonable mining period model of the "four quantities" in step 4 is as follows: Let the continuous random variable X obey the gamma distribution with parameters (α, λ), denoted as X~Ga(α, λ), where α＞0 and λ＞0, then the mathematical expectation and variance of the variable X are

and

Therefore, the probability density function of variable X is:

The cumulative distribution function of the gamma function calculated by MATLAB is:

Among them, X is any reasonable mining period among the “four quantities”, x is the variable value under the reasonable mining period function, and igamma is the inverse gamma distribution; Under the premise of a given reliability, the x value that satisfies the equation F(x) is calculated to be the value of x under the given reliability, that is, the reliability of the "four quantities" reasonable mining period model corresponding to the x value.

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