CN111784136A - A Dynamic Early Warning Method of Impact Risk Based on Analytic Hierarchy Process and Fuzzy Mathematics - Google Patents

Abstract

The invention discloses a dynamic early warning method for shock risk based on AHP and fuzzy mathematics. The early warning method includes the following steps: Step 1: Determine the early warning object and the shock risk influencing factor applicable to the early warning object, that is, the early warning index; Step 2, Determine the impact risk classification of each early warning index, and form a shock risk early warning index system; step 3, based on the APH (analytic hierarchy process) theory, determine the weight of each early warning index, and form a fuzzy weight vector A; step 4, based on fuzzy mathematics theory, Establish a single-factor fuzzy early-warning set of each index, which is composed of a factor early-warning fuzzy matrix R; Step 5: Calculate the fuzzy comprehensive evaluation vector B=A×R of the early-warning object; Step 6. Determine the impact risk level of the early-warning object according to the principle of maximum membership degree . The present invention comprehensively considers a variety of rockburst early warning indicators, adopts the early warning model to carry out the early warning of the shock danger to the early warning object, the early warning is more scientific, the early warning efficiency is higher, and the result is more reliable.

Description

A Dynamic Early Warning Method of Impact Risk Based on Analytic Hierarchy Process and Fuzzy Mathematics

technical field

The invention relates to the technical field of coal mine safety, in particular to a dynamic early warning method for impact risk based on AHP and fuzzy mathematics.

Background technique

With the increase of mining depth and mining intensity of coal mines in my country, the situation of coal mines facing rockburst is becoming more and more severe, and rockburst evaluation and real-time monitoring and early warning are effective measures to prevent rockburst. At the same time, the "Detailed Rules for the Prevention and Control of Rock Burst in Coal Mine" issued in 2018 stipulates that when mining rock burst coal seams, comprehensive prevention measures such as rock burst risk prediction, monitoring and early warning, prevention and treatment, effect inspection, and safety protection must be taken; Rockburst mines must establish a regional and local impact risk monitoring system. Regional monitoring should cover the mining area of the mine, and local monitoring should cover the rockburst danger zone. Regional monitoring can use microseismic monitoring, and local monitoring can use drilling. Chip method, stress monitoring method, electromagnetic radiation method, etc. However, at present, most of my country's shock risk early warning adopts a single indicator or a combination of simple models for multi-indicator early warning, and the efficiency and accuracy of early warning cannot meet the practical needs of coal mines.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a dynamic early warning method of shock risk based on AHP and fuzzy mathematics. The early warning is more efficient, the results are more reliable, and it is more practical for guiding mines to carry out rockburst prevention and control.

The technical solution adopted by the present invention is:

A dynamic early warning method for impact risk based on AHP and fuzzy mathematics, the early warning method includes the following steps:

Step 1. Determine the early warning object and the shock risk early warning index applicable to the early warning object

Select the applicable shock risk early warning index set U according to the early warning object, and use u _i to represent each early warning index, then U=(u ₁ , u ₂ , u ₃ , u ₄ ... u _i , ... u _n ), where n is Number of early warning indicators;

Step 2: Classify the impact risk of each early warning index to form a shock risk early warning index system

According to the classification of early warning levels, the impact risk of each early warning index is classified; by establishing the classification set v _i of each early warning index, the impact risk early warning index system V of the early warning object is obtained;

Step 3: Determine the weight of each early warning indicator to form a fuzzy weight vector

According to the APH analytic hierarchy process and the 1-9 scale table, the contribution degree of each early warning index to the impact risk of the early warning object is determined, and then the fuzzy weight vector A composed of each index is obtained;

Step 4. Establish a single-factor fuzzy early-warning set of each early-warning index, and form a factor early-warning fuzzy matrix

According to the monitoring results of a certain early warning indicator, combined with the early warning membership function, the set of all membership degrees of the early warning indicator can be determined; then the single factor fuzzy early warning set corresponding to each early warning indicator can be obtained in turn; The fuzzy early warning set R _i is the i-th row, and the composition factor early warning fuzzy matrix R;

Step 5. Calculate the fuzzy comprehensive evaluation vector of the early warning object

Calculate the fuzzy weight vector A that reflects the influence degree of each early warning index on rock burst and the factor early warning fuzzy matrix R, which is composed of the membership degrees of all indicators, so as to obtain the fuzzy comprehensive evaluation vector of each rock burst early warning B=A× R=(b ₁ , b ₂ , b ₃ , b ₄ );

Step 6: Determine the impact hazard level of the warning object

In step 5 (b ₁ , b ₂ , b ₃ , b ₄ ) respectively correspond to the membership degrees of the four evaluation results (no impact risk, weak impact risk, medium impact risk, and strong impact risk); according to the principle of maximum membership degree, The impact risk level of the warning object can be obtained.

In the above step 2, the impact risk of each early warning indicator can be divided into 5 levels, namely none, weak, medium, strong and unsafe. The number of impact risk classifications of each early warning index in step 2 is inconsistent with the number of impact risk classifications of the final early warning object in step 6, but it does not affect the application effect of the method.

In the above-mentioned step 3, a matrix can be obtained by comparing the early warning indicators u _i pairwise and assigning values corresponding to the scale tables 1 to 9, and the eigenvectors of the matrix can be obtained to obtain a fuzzy weight vector A=(a ₁ , a ₂ , ...a _i , ...a _n ), normalized to (a' ₁ , a' ₂ , ...a' _i , ...a' _n ).

In the above step 4, the membership function is shown in formula (1):

In formula (1), x is the test value, and S ₁ , S ₂ , S ₃ and S ₄ correspond to the four grading thresholds of the early warning indicators, respectively.

In the above-mentioned step 6, the principle of the maximum membership degree means that, by comparing the sizes of b ₁ to b ₄ , if the maximum value is b _i , and the value of i is 1, 2, 3, or 4, then the warning object is the ith level impact danger. The impact hazard level is divided into four categories: the impact hazard level belongs to level 1, which means no impact hazard; the impact hazard level belongs to level 2, which is a weak impact hazard; the impact hazard level belongs to level 3, which is a medium impact hazard; the impact hazard level belongs to Level 4 is a strong shock hazard.

The beneficial technical effects of the present invention are:

The invention comprehensively considers a variety of rockburst early warning indicators, assigns different weight values through a mathematical model according to different working conditions, and then uses the early warning model to carry out early warning on the impact risk of the early warning object, the early warning is more scientific, and the early warning efficiency is higher. more reliable. In addition, this early warning method is suitable for early warning equipment for real-time monitoring in engineering, that is, the impact risk early warning results are real-time and dynamic. The early warning method of the invention can be used to guide coal mines to carry out rockburst prevention and control work, and has important practical significance for ensuring the safe production of coal mines.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:

Fig. 1 is the flow chart of the dynamic early warning method of impact risk based on AHP and fuzzy mathematics of the present invention;

FIG. 2 is a schematic diagram of a shock risk early warning index system established in a specific application example of the present invention.

Detailed ways

As shown in Figure 1, a dynamic early warning method of shock risk based on AHP and fuzzy mathematics, the early warning method is suitable for coal mines, and includes the following steps:

Step 1. Determine the early warning object and the impact risk factor applicable to the early warning object, that is, the early warning index

The object of early warning can be a range, including mine, mining area (panel or level), mining face and roadway, or a section of roadway and a monitoring point. Take the monitoring point as an example, select the applicable shock risk early warning index set U according to the early warning object, and use u _i to represent each early warning index, then U=(u ₁ , u ₂ , u ₃ , u ₄ ... u _i , ... u _n ), where n is the number of early warning indicators, including "mining stress", "roadway displacement", "roof separation amount", "anchor bolt working load", "anchor cable working load" and "support resistance", etc.

Step 2: Classify the impact risk of each early warning index to form a shock risk early warning index system

According to the classification of early warning levels, the impact risk of each early warning index is classified into 5 levels, namely none, weak, medium, strong and unsafe. Taking mining stress σ as an example, the classification set of early warning indicators v ₁ = (none, weak, moderate, strong, unsafe) = (σ≤1.5σ _normal , 1.5σ _normal <σ≤3σ _normal , 3σ _normal <σ≤4.5 σ _{is normal} , 4.5σ is _normal <σ≤6σ _{is normal} , σ>6σ _{is normal} ). By establishing the graded set vi of each early warning index, the early warning index system _V of shock risk of early warning objects such as monitoring points is obtained.

Step 3: Determine the weight of each early warning indicator to form a fuzzy weight vector

The weight represents the contribution of each early warning index to the impact risk of the monitoring point, such as the weight of mining stress, roadway displacement, etc., respectively, on the impact risk of the monitoring point.

According to the corresponding relationship between the previous mining stress, roadway displacement and other monitoring data and the impact, combined with the APH analytic hierarchy process and the 1-9 scale table, the contribution of each early warning index to the impact risk of the monitoring point is determined, and then each index is obtained. Composed of fuzzy weight vector A.

Step 4. Establish a single-factor fuzzy early-warning set of each early-warning index, and form a factor early-warning fuzzy matrix

Apply fuzzy mathematics to determine the degree to which each early warning index belongs to different early warning levels in the early warning level set, which is called membership degree, and is represented by r _ij . According to the monitoring results (actual test results) of a certain early warning indicator, combined with the early warning membership function, the set of all membership degrees of the early warning indicator can be determined, which is a single-factor early warning matrix; and then the corresponding early warning indicators can be obtained in turn. Single factor fuzzy early warning matrix or early warning set. According to different early warning indicators, arrange each row from top to bottom, take the i-th single-factor fuzzy early-warning set R _i as the i-th row, and make up the factor early-warning fuzzy matrix R. For example, the factor warning fuzzy matrix R can be n rows and 4 columns.

Step 5. Calculate the fuzzy comprehensive evaluation vector of the early warning object

The fuzzy comprehensive early warning considers the influence of all factors on the monitoring points, and calculates the fuzzy weight vector A that reflects the influence degree of each early warning index on rockburst and the factor early warning fuzzy matrix R synthesized by the membership degrees of all indicators, so as to obtain each impact Fuzzy comprehensive evaluation vector of ground pressure warning B=A×R=(b ₁ , b ₂ , b ₃ , b ₄ ).

Step 6: Determine the impact hazard level of the warning object

In step 5, (b ₁ , b ₂ , b ₃ , b ₄ ) respectively correspond to the membership degrees of the four judgment results (no shock risk, weak shock risk, medium shock risk, and strong shock risk). According to the principle of maximum membership degree, the impact risk level reflected by the monitoring data of the monitoring point for a period of time can be obtained.

In the above-mentioned step 3, the scale table of 1 to 9 is shown in Table 1 below.

Table 1

Scaling express meaning 1 Element i and element j are equally important 3 Element i is slightly more important than element j 5 Element i is significantly more important than element j 7 Element i is strongly more important than element j 9 Element i is extremely important than element j 2,4,6,8 between the above scales reciprocal Indicates that a_ij and a_ij are reciprocals of each other

By comparing the early warning indicators u _i pairwise and assigning them to Table 1, the matrix G can be obtained, and the eigenvectors of the matrix G can be obtained to obtain the fuzzy weight matrix A=(a ₁ , a ₂ ,...a _i ,...a _n ), normalized to (a' ₁ , a' ₂ ,...a' _i ,...a' _n ).

In step 4, the membership degree r _ij is obtained by calculating the membership degree function, and the membership degree function is shown in formula (1).

In formula (1), x is the test value, and S ₁ , S ₂ , S ₃ and S ₄ correspond to the four grading thresholds of the early warning indicators, respectively.

In step 6, the maximum membership degree principle means that, by comparing the sizes of b ₁ to b ₄ , if the maximum value b _i , i takes a value of 1, 2, 3 or 4, the warning object is the ith level impact risk. . The impact hazard level is divided into four categories; the impact hazard level belongs to level 1, which means no impact hazard; the impact hazard level belongs to level 2, which is a weak impact hazard; the impact hazard level belongs to level 3, which is a medium impact hazard; the impact hazard level belongs to level 4 , for a strong shock hazard.

The following takes a coal mine in Henan as a specific application example to further introduce the dynamic early warning method of shock risk based on AHP and fuzzy mathematics.

Background: A coal mine in Henan is a typical rockburst mine. There have been many rockburst accidents during the mining of 2-3 coal. The stress meter and displacement meter are installed for real-time monitoring during the excavation of the roadway on the 13200 working face of the mine, and this method is now used to provide real-time early warning of the impact risk during the excavation of the roadway.

(1) Determine the early warning object and the impact risk early warning index applicable to the early warning object: According to the installation position of the stress meter and displacement meter, determine the 500-600m section of the early warning object 13200 upper lane from the entrance, and determine the impact risk early warning index as the stress gradient ▽σ and the displacement gradient ▽ε.

(2) Determine the impact risk classification of each early warning index, and form a shock risk early warning index system, as shown in Figure 2.

(3) Determine the weight of each early warning index and form a fuzzy weight vector: according to the comparison of the importance of each early warning index, combined with the APH theory and the 1-9 scale table, the fuzzy weight matrix A = (a ₁ ', a ₂ ')=(0.1667, 0.8333).

(4) Establish a single-factor fuzzy early-warning set of each index, and form a factor early-warning fuzzy matrix. The grading thresholds of each early warning index refer to Figure 2, and the factor early warning fuzzy matrix R is calculated as

(5) Calculate the fuzzy comprehensive evaluation vector of the warning object: B=A×R=(0.9603, 0.0397, 0, 0).

(6) Determine the impact risk level of the early warning object: According to the principle of maximum membership degree, the fuzzy comprehensive evaluation index of this measuring point is 0.9603, and the impact risk level is none.

According to the monitoring results of on-site drilling cuttings volume and the dynamic display situation, it can be seen that the drilling cuttings volume did not exceed the standard during the monitoring time period, and there was no dynamic display on the site. It can be seen that the monitoring point has no impact risk, which is different from the dynamic impact risk based on AHP and fuzzy mathematics. The results of the early warning method were consistent.

The parts not mentioned in the above manner can be realized by adopting or learning from the existing technology.

Of course, the above description is not intended to limit 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 essential scope of the present invention should also belong to the present invention. the scope of protection of the invention.

Claims (4)

1. A dynamic early warning method for impact danger based on hierarchical analysis and fuzzy mathematics is characterized by comprising the following steps:

step one, determining an early-warning object and an impact risk early-warning index applicable to the early-warning object

Selecting an applicable impact risk early warning index set U according to the early warning object, and using U_iIf each warning indicator is represented, U is equal to (U)₁，u₂，u₃，u₄…u_i，…u_n) Wherein n is the number of early warning indicators;

step two, classifying the impact dangerousness of each early warning index to form an impact danger early warning index system

Classifying according to the early warning grades, and grading the impact risks of the early warning indexes; by establishing a hierarchical set v of each pre-warning indicator_iObtaining an impact risk early warning index system V of the early warning object;

step three, determining the weight of each early warning index to form a fuzzy weight vector

Determining the contribution degree of each early warning index to the impact risk of the early warning object according to an APH (advanced persistent threat) analytic hierarchy process and a 1-9 standard table, and further obtaining a fuzzy weight vector A formed by each index;

step four, establishing a single-factor fuzzy early warning set of each early warning index to form a factor early warning fuzzy matrix

Aiming at the monitoring result of a certain early warning index, a set of all membership degrees of the early warning index can be determined by combining an early warning membership function; and then a single-factor fuzzy early warning set corresponding to each early warning index can be obtained in sequence; the ith single-factor fuzzy early warning set R_iForming a factor early warning fuzzy matrix R for the ith row;

step five, calculating a fuzzy comprehensive judgment vector of the early warning object

Calculating a factor early warning fuzzy matrix R synthesized by a fuzzy weight vector A reflecting the influence degree of each early warning index on the rock burst and all index membership degrees, thereby obtaining a fuzzy comprehensive judgment vector B of each rock burst early warning, wherein the fuzzy comprehensive judgment vector B is A × R (B)₁，b₂，b₃，b₄)；

Step six, determining the impact danger level of the early warning object

In step five (b)₁，b₂，b₃，b₄) Respectively corresponding to the membership degrees of the four judgment results (no impact risk, weak impact risk, medium impact risk and strong impact risk); according to the maximum membership principle, the impact danger level of the early warning object can be obtained.

2. The dynamic early warning method for impact risk based on hierarchical analysis and fuzzy mathematics as claimed in claim 1, wherein: in the third step, each early warning index u is used_iPairwise comparison is carried out and the value is assigned corresponding to a 1-9 scale table, a matrix can be obtained, the characteristic vector is solved aiming at the matrix, and a fuzzy weight vector A (a) is obtained₁，a₂，…a_i，…a_n) And is (a ') after normalization treatment'₁，a’₂，…a’_i，…a’_n)。

3. The dynamic early warning method for impact risk based on hierarchical analysis and fuzzy mathematics as claimed in claim 1, wherein: in the fourth step, the membership function is shown as formula (1):

in the formula (1), x is a test value, S₁、S₂、S₃And S₄And the four grading threshold values respectively correspond to the early warning indexes.

4. The dynamic early warning method for impact risk based on hierarchical analysis and fuzzy mathematics as claimed in claim 1, wherein: in the sixth step, the principle of maximum membership degree means that b is compared₁～b₄Size, if maximum value is b_iIf i takes values of 1, 2, 3 and 4, the early warning object is the ith-level impact risk; impact hazard grade fractionIs classified into four types: the impact danger level belongs to level 1 and is no impact danger; the impact risk grade belongs to grade 2 and is a weak impact risk; the impact risk rating is class 3, which is a medium impact risk; the impact hazard classification belongs to class 4 and is a strong impact hazard.

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