CN109359393B - Mine four-quantity reasonable mining period determining method under uncertain information condition - Google Patents
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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
Technical Field
The invention relates to the technical field of mine safety exploitation, in particular to a method for determining four reasonable mining periods of a mine under the condition of uncertain information.
Background
In the coal production process, maintaining the mining balance is a precondition for ensuring normal, continuous and stable production of a mine, and is also an important means for reducing the maintenance cost of tunneling engineering. With the rapid development of the coal industry, the technological progress of coal production, the complexity of mining conditions and the like in China, the mining disorder gradually appears in the ' three-quantity ' regulation ' which is formulated by China to ensure the smooth succession of mines, and the mining disorder cannot adapt to the requirements of the succession of the mines in the current stage. The four-quantity method for determining the coal quantity, the preparation coal quantity period, the recovery coal quantity and the four-quantity reasonable recovery period improves the defect of the traditional three-quantity theory in the aspect of gas pre-extraction to a great extent, so that a referential theoretical basis is provided when the reasonable recovery period of the high-gas and gas outburst mine is calculated.
At present, production practice activities of mines are increasingly affected by various uncertain information conditions, such as: unpredictable complex geological abrupt changes, sudden disasters, external economic and market demands, reasonable allocation and exploitation methods and the like, which are not predeterminable in terms of internal factors possibly encountered in the production process and external factors brought by the surrounding environment, but have non-negligible influence on the reasonable mining period of four-volume mines. However, at present, the research on the change rule of the reasonable four-amount mining period under the condition of uncertain information of the mine is very few, and no borrowable results are available in the aspects of the risk and the reliability of the four-amount mining period.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a method for determining four reasonable mining periods of a mine under uncertain information conditions, which is used for carrying out risk analysis and reliability analysis on the four reasonable mining period models by exploring the change rule of the four reasonable mining periods under uncertain information conditions, so as to obtain the risk function of the four reasonable mining period models and provide guidance for normal production connection of a working face.
In order to achieve the purpose, the method for determining the four reasonable mining periods of the mine under the condition of uncertain information comprises the following steps:
step 1: determining a four-quantity reasonable mining period model;
step 2: determining a change rule of a four-quantity reasonable mining period under the uncertain information condition, and measuring the influence of the uncertain information condition on the four-quantity reasonable mining period by taking the tunneling speed as a random variable;
step 3: analyzing uncertain information conditions which cause the failure of a four-quantity reasonable mining period model through a main logic diagram, and quantitatively calculating the risk of the model based on probability calculation of a fault tree and an event tree;
step 4: and (5) carrying out reliability analysis on the four-quantity reasonable mining period model.
Further, in the step 3, 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 leading to mining imbalance be H 1 ,H 2 ,H 3 ,...,H n And there is an intersection between the factors, the calculation formula of the total probability of the mining unbalance is as follows:
(2) Probability calculation of event tree:
the m accident sequence groups of the event tree in the four-quantity reasonable mining period model are ASG 1 ,ASG 2 ,...,ASG m And the j-th link event contained in the accident sequence set is T j1 ,T j2 ,...,T jl The calculation formula of the conditional probability of the j-th accident sequence set is as follows:
wherein P (ASG) j I IE) is the probability of occurrence of the j-th consecutive accident event when the uncertain event IE occurs, p (T) kl ) The probability of occurrence of the first link event in the accident sequence group;
(3) Risk probability calculation of a reasonable mining period model of four quantities:
the risk probability calculation formula for obtaining the "four-quantity" reasonable mining period model according to the total probability of mining unbalance and the conditional probability of each accident sequence group is as follows:
P(A)=∑ i ∑ j P(IE i )P(ASG j |IE i )P(A|ASG j );
wherein P (A) is the failure probability of a reasonable sampling period model with 'four quantities', and P (IE) i ) To generate the ith probability of an uncertain event that may cause mining imbalance, P (ASG) j |IE i ) To determine the probability of occurrence of the jth consecutive accident event at the occurrence of event i, P (A|ASG) j ) Is the probability of whether the j-th cascading accident event results in model failure.
Further, the method for performing reliability analysis on the "four-volume" reasonable mining period model in the step 4 is as follows:
subjecting a continuous random variable X to a gamma distribution of parameter (alpha, lambda), denoted X-Ga (alpha, lambda), wherein alpha > 0 and lambda > 0, the mathematical expectation and variance of the variable X being respectivelyAnd->The probability density function of the variable X is:
the cumulative distribution function of the gamma function obtained by MATLAB calculation is as follows:
wherein X is any reasonable sampling period in the reasonable sampling period of four quantities, X is a variable value under a function of the reasonable sampling period, and igamma is inverse gamma distribution;
then, given the reliability, the equation F is calculated to be satisfied x (x) And the reliability of the reasonable mining period model is given to the value x of the reliability, namely the reliability of the 'four-quantity' reasonable mining period model corresponding to the value x.
The invention has the beneficial effects that:
the invention provides a mine four-quantity reasonable mining period determining method considering the influence of uncertain information conditions, researches the change rule of a four-quantity reasonable mining period model under various uncertain information conditions, perfects the traditional four-quantity reasonable mining period calculation model and theoretical basis, establishes a corresponding mathematical model by analyzing the risk and reliability of the model under the uncertain information conditions, provides guidance opinion for the establishment of mine safety production plans, and provides theoretical basis for normal production connection of working faces.
Drawings
FIG. 1 is a flow chart of a method for determining four reasonable mining periods of a mine considering the influence of uncertain information conditions in the embodiment of the invention;
FIG. 2 is a schematic diagram of a theoretical gamma distribution in an embodiment of the present invention;
FIG. 3 is a schematic diagram of the gamma distribution actually applied in combination with the "four-volume" reasonable mining period of the mine in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. The specific embodiments described herein are to be considered in an illustrative sense only and are not intended to limit the invention.
A method for determining four reasonable mining periods of a mine considering influence of uncertain information conditions is shown in a figure 1, and the concrete method is as follows:
step 1: determining a four-quantity reasonable mining period model;
in this embodiment, the "four-volume" reasonable recovery period model is as follows:
1) The development of the reasonable mining period model of the coal quantity is as follows:
wherein T is k To develop reasonable recovery period of coal quantity, L k For the total length of the tunneling engineering, p is the average tunneling team number in the development process, V k To develop the average tunneling speed of the process, T k0 To form the average preparation succession time from the development of the coal quantity to the preparation of the coal quantity, T z2 For the average pre-pumping time of the cross-cut coal uncovering, T z3 Average pre-pumping time for uncovering coal of shaft, V d In order to influence the reduced maximum average tunneling speed by complex geological structures during tunneling,to slow down the influence coefficient of the speed, and +.>Is interval [0,1 ]]An internal constant;
2) The reasonable mining period model of the coal quantity is prepared as follows:
wherein T is z To prepare reasonable coal quantity in the recovery period L z For the total length of tunneling required for preparation work, q is the average tunneling queue number in the preparation process, V z To prepare the average tunneling speed of the process, T z0 To average preparation succession time from the preparation coal quantity to the recovery coal quantity z1 The average pre-pumping time before the coal bed is revealed for preparing the roadway;
3) The reasonable recovery mining period model of the recovery mining amount is as follows:
T h =L m /(V J -φV d )+max{T o ,T c };
wherein T is h T is the reasonable recovery period of the stope coal quantity o Setting debugging time for working face average equipment, T c For the average gas extraction standard reaching time of the working face, L m Total length of tunnelling required for stoping work, V J The average tunneling speed of the working face is set;
4) The reasonable mining period model of the gas extraction standard coal quantity is as follows:
T w =kT h ;
wherein T is w The gas extraction reaches the standard of the coal quantity in the period of the extraction, k is the safety coefficient of gas pre-extraction, andS 1 s is the area of the coal recovery 2 The area of the gas pre-extraction coal is defined.
Step 2: determining a change rule of a four-quantity reasonable mining period under the uncertain information condition, and measuring the influence of the uncertain information condition on the four-quantity reasonable mining period by taking the tunneling speed as a random variable;
in this embodiment, taking unpredictable complex geological structures as an example, by analysis, the structures may cause that too many structures cannot be recovered after the original planned recoverable coal amount is excavated, the previously excavated roadway may be scrapped, so that the increase of invalid roadway is caused, which is equivalent to the decrease of the roadway excavation speed, and the recovery work depends on whether the excavation work can be successfully completed or not, so that the unpredictable geological structures can be considered as the reasonable recovery period increase of four-amount caused by the decrease of the excavation speed. Similarly, for other uncertain information conditions, such as: sudden disasters, external economy and market demands, reasonable allocation and exploitation methods and the like can be directly or indirectly converted into reduction of tunneling speed, so that the reasonable exploitation period of four quantities is prolonged.
Step 3: analyzing uncertain information conditions which cause the failure of a four-quantity reasonable mining period model through a main logic diagram, and quantitatively calculating the risk of the model based on probability calculation of a fault tree and an event tree;
the method for quantitatively calculating the risk of the model based on probability calculation of the fault tree and the event tree comprises the following steps:
(1) Probability calculation of fault tree:
let n factors leading to mining imbalance be H 1 ,H 2 ,H 3 ,...,H n And there is an intersection between the factors, the calculation formula of the total probability of the mining unbalance is as follows:
(2) Probability calculation of event tree:
the m accident sequence groups of the event tree in the four-quantity reasonable mining period model are ASG 1 ,ASG 2 ,...,ASG m And the j-th link event contained in the accident sequence set is T j1 ,T j2 ,...,T jl The calculation formula of the conditional probability of the j-th accident sequence set is as follows:
wherein P (ASG) j I IE) is the j-th chain incident event when the uncertain event IE occursProbability of occurrence, p (T kl ) The probability of occurrence of the first link event in the accident sequence group;
(3) Risk probability calculation of a reasonable mining period model of four quantities:
the risk probability calculation formula for obtaining the "four-quantity" reasonable mining period model according to the total probability of mining unbalance and the conditional probability of each accident sequence group is as follows:
P(A)=∑ i ∑ j P(IE i )P(ASG j |IE i )P(A|ASG j );
wherein P (A) is the failure probability of a reasonable sampling period model with 'four quantities', and P (IE) i ) To generate the ith probability of an uncertain event that may cause mining imbalance, P (ASG) j |IE i ) To determine the probability of occurrence of the jth consecutive accident event at the occurrence of event i, P (A|ASG) j ) Is the probability of whether the j-th cascading accident event results in model failure.
In this embodiment, in the "four-volume" reasonable-mining-period model, the Main Logic Diagram (MLD) describes the necessary conditions for the occurrence of the risk accident in a grading manner, and from an unexpected working face mining imbalance, the model is developed from top to bottom by adopting a strategy of dividing and controlling the model, so as to gradually decompose the accident into sub-blocks described by the initial events until all possible initial event sets. Event Tree Analysis (ETA) is to obtain an accident sequence group ASG caused by factors causing mining unbalance through accident sequence examination and accident development analysis. Event nodes in the event tree represent the resulting events that may be caused by the event of the previous layer. Each uncertainty factor for the event tree requires establishing a joint probability of occurrence to determine the probability of occurrence for that point. Fault Tree (FTA) is a process of deductive reasoning that generally provides more detailed details of failure link events of an event tree. It is clear from the FTA what uncertainty factor the model is due to, and thus the primary cause of the mining imbalance is found. In practical application, the probability of failure of the four-quantity reasonable mining period model or the probability of incapability of normal connection in the production process can be obtained exactly by using a quantitative calculation method through statistics of related data, so that corresponding adjustment can be made on a production plan in advance according to practical conditions, and loss caused by risk is reduced to the minimum.
Step 4: and (5) carrying out reliability analysis on the four-quantity reasonable mining period model.
The method for carrying out reliability analysis on the four-quantity reasonable mining period model comprises the following steps:
subjecting a continuous random variable X to a gamma distribution of parameter (alpha, lambda), denoted X-Ga (alpha, lambda), wherein alpha > 0 and lambda > 0, the mathematical expectation and variance of the variable X being respectivelyAnd->The probability density function of the variable X is:
the cumulative distribution function of the gamma function obtained by MATLAB calculation is as follows:
wherein X is any reasonable sampling period in the reasonable sampling period of four quantities, X is a variable value under a function of the reasonable sampling period, and igamma is inverse gamma distribution;
on the premise of the given reliability, the x value satisfying the equation F (x) under the given reliability is calculated, namely the reliability of the reasonable 'four-quantity' mining-period model under the corresponding x value.
The theoretical gamma function distribution is shown in FIG. 2, in this embodiment, the reasonable recovery period T is given by the recovery coal h Performing reliability analysis, wherein the reliability (probability) is 0.9 when the tunneling time is calculated, and the problem is that the calculation satisfies the equationThe lower x value is the recovery coal quantity recovery period T which can realize successful butt joint of the recovery under 90 percent probability h =x, and x appears as a value at k in the gamma function profile.
In this embodiment, taking a certain gas outburst mine as an example, by combining statistical data of staff with actual experience, the probability that a working face must be re-excavated under the influence of faults is 80% under the condition that the mining process is not predicted in advance and a large fault is encountered; the probability that other sudden disasters of the surrounding environment can occur under the influence of the fault is 60%; the probability of model failure caused by the influence of the subsequent sudden disasters is 70%, and the probability of model failure in the reasonable mining period of four quantities is finally obtained as follows:
P(A)=∑ i ∑ j P(IE i )P(ASG j |IE i )P(A|ASG j )=33.6%;
the calculation result shows that the probability of failure of the reasonable recovery period of four quantities reaches 33.6 percent due to the influence of unpredictable faults, and obviously brings greater risk to the normal connection of the production process.
In this embodiment, the gamma function distribution in practical application is shown in fig. 3, so as to reduce risk of production connection caused by uncertain information conditions, thereby obtaining the optimal reasonable recovery period T of the recovery coal h The tunneling time of the model under 90% reliability is calculated as follows:
after counting the tunneling time of several adjacent roadways in a certain mining area of the mine, calculating to obtain the expected E (X) and the variance Var (X) of 8.95 and 2.01 respectively, wherein the parameters alpha and lambda are 40.051 and 4.475 respectively, and because the X in the embodiment is time, positive values are needed, the parameters alpha and lambda are substituted into the following formula to solve the X:
the time x was 7.192, i.e. the value of the k point in fig. 3, was determined by MATLAB.
As can be seen from fig. 3, under the premise of uncertain information conditions, the reasonable recovery period of the coal recovery amount is 7.192 months, so that the probability of normal continuation of mine production can reach more than 90%, guidance comments can be provided for the production plan of the mine, and normal continuation of production is ensured.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art will understand that; the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the invention, which is defined by the following claims.
Claims (2)
1. The method for determining the four reasonable mining periods of the mine under the condition of uncertain information is characterized by comprising the following steps of:
step 1: determining a four-quantity reasonable mining period model;
step 2: determining a change rule of a four-quantity reasonable mining period under the uncertain information condition, and measuring the influence of the uncertain information condition on the four-quantity reasonable mining period by taking the tunneling speed as a random variable;
step 3: analyzing uncertain information conditions which cause the failure of a four-quantity reasonable mining period model through a main logic diagram, and quantitatively calculating the risk of the model based on probability calculation of a fault tree and an event tree;
step 4: reliability analysis is carried out on the four-quantity reasonable mining period model;
in the step 3, 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 leading to mining imbalance be H 1 ,H 2 ,H 3 ,...,H n And there is an intersection among the factors, resulting inThe calculation formula of the total probability of mining imbalance is as follows:
(2) Probability calculation of event tree:
the m accident sequence groups of the event tree in the four-quantity reasonable mining period model are ASG 1 ,ASG 2 ,...,ASG m And the j-th link event contained in the accident sequence set is T j1 ,T j2 ,...,T jl The calculation formula of the conditional probability of the j-th accident sequence set is as follows:
wherein P (ASGj|IE) is the probability of occurrence of the jth chain accident event when the uncertain event IE occurs, P (T) kl ) The probability of occurrence of the first link event in the accident sequence group;
(3) Risk probability calculation of a reasonable mining period model of four quantities:
the risk probability calculation formula for obtaining the "four-quantity" reasonable mining period model according to the total probability of mining unbalance and the conditional probability of each accident sequence group is as follows:
P(A)=∑ i ∑ j P(IE i )P(ASG j |IE i )P(A|ASG j );
wherein P (A) is the failure probability of a reasonable sampling period model with 'four quantities', and P (IE) i ) To generate the ith probability of an uncertain event that may cause mining imbalance, P (ASG) j |IE i ) To determine the probability of occurrence of the jth consecutive accident event at the occurrence of event i, P (A|ASG) j ) Is the probability of whether the j-th cascading accident event results in model failure.
2. The method for determining four reasonable mining periods of a mine under the condition of uncertain information according to claim 1, wherein the method for performing reliability analysis on the four reasonable mining period model in the step 4 is as follows:
subjecting a continuous random variable X to a gamma distribution of parameter (alpha, lambda), denoted X-Ga (alpha, lambda), wherein alpha > 0 and lambda > 0, the mathematical expectation and variance of the variable X being respectivelyAnd->The probability density function of the variable X is:
the cumulative distribution function of the gamma function obtained by MATLAB calculation is as follows:
wherein X is any reasonable sampling period in the reasonable sampling period of four quantities, X is a variable value under a function of the reasonable sampling period, and igamma is inverse gamma distribution;
on the premise of the given reliability, the x value satisfying the equation F (x) under the given reliability is calculated, namely the reliability of the reasonable 'four-quantity' mining-period model under the corresponding x value.
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