CN115619277A - Rock burst comprehensive evaluation method based on normal cloud and uncertain measure - Google Patents

Rock burst comprehensive evaluation method based on normal cloud and uncertain measure Download PDF

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CN115619277A
CN115619277A CN202211345625.2A CN202211345625A CN115619277A CN 115619277 A CN115619277 A CN 115619277A CN 202211345625 A CN202211345625 A CN 202211345625A CN 115619277 A CN115619277 A CN 115619277A
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黄麟淇
胡星淼
李夕兵
王钊炜
张鸿忠
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Abstract

The invention discloses a normal cloud and uncertain measure-based rock burst comprehensive evaluation method, and belongs to the technical field of underground mine rock burst disaster evaluation. The method comprises the following steps: 1) Establishing an evaluation object index value system; 2) Constructing a single index evaluation system; 3) Determining index combination weight; 4) Constructing a single index measure matrix by using a normal cloud model; 5) Calculating the comprehensive measure of multiple indexes; 6) And determining an evaluation result. The invention is based on rock uniaxial compressive strength sigma c Coefficient of tangential stress σ θ /σ c Brittleness index σ c /σ t The elastic strain energy index Wet4 indexes are used for establishing a rock burst grade evaluation system, a nonlinear measurement function is established based on a normal cloud model, and single index measurement is determined, so that the defects of a single index measurement method in the traditional uncertain measurement evaluation method are overcome, and the method is further characterized in thatThe characteristics of fuzziness and randomness of the rock burst are fully considered, the accuracy of rock burst evaluation is improved, and scientific reference is provided for prevention and control of rock burst disasters.

Description

Rock burst comprehensive evaluation method based on normal cloud and uncertain measure
Technical Field
The invention belongs to the technical field of rock burst disaster evaluation of underground mines, and particularly relates to a rock burst comprehensive evaluation method based on normal cloud and uncertain measure.
Background
The rock burst is a geological disaster frequently occurring in deep high-stress hard rock mining engineering, is one of the primary threats to deep hard rock mining safety, is very easy to cause personal casualties, roadway damage and equipment damage, and can cause local earthquakes seriously. The evaluation of rock burst tendency is an important reference basis for rock burst disaster prevention and control measures. The study is carried out on the scholars at home and abroad, and different rock burst criteria and grading standards are provided, such as Hoek criteria, barton criteria, pottery and astronomy criteria and the like. However, because the occurrence of the rock burst is influenced by a plurality of factors together, and the single criterion is difficult to accurately predict the rock burst tendency, the researchers provide a comprehensive evaluation method combining a plurality of criteria on the basis of the former, wherein an uncertain measure evaluation method obtains a good evaluation effect, but still has a few defects, and a simple linear piecewise function is adopted in the calculation of the index measure, so that the randomness and the uncertainty characteristics of the rock burst are difficult to well characterize. The normal cloud model is a model capable of representing uncertainty, and shows certain superiority in conversion of quantitative indexes and qualitative concepts. Meanwhile, index weight in the traditional evaluation method is also an important factor influencing evaluation accuracy, different weighting methods have respective limitations in the aspects of subjective factors and objective factors, and a large number of research results show that the subjective and objective factor influence of weight can be well balanced by combined weighting.
Disclosure of Invention
The invention mainly aims to make up the defects of the traditional uncertain measurement evaluation method and provide a rock burst comprehensive evaluation method based on normal cloud and uncertain measurement theories, which more fully considers the characteristics of fuzziness and randomness of the rock burst and improves the accuracy of rock burst evaluation.
In order to achieve the purpose, the invention adopts the following technical scheme:
a rock burst comprehensive evaluation method based on normal cloud and an uncertain measurement theory comprises the following steps:
1) Establishing an evaluation object index value system
Obtaining a plurality of groups of rock uniaxial compressive strength sigma according to field sampling, indoor tests and calculation c Coefficient of tangential stress σ θ /σ c Brittleness index σ c /σ t Elastic strain energy index W et Index value; let the sample space composed of rock burst evaluation objects of different groups be R = (R) 1 ，R 2 ，…，R n ) Each evaluation sample contains 4 influencing factors I 1 、I 2 、I 3 、I 4 I.e. representing 4 evaluation indexes, I = (I) 1 ，I 2 ，I 3 ，I 4 ) Is an index set;
2) Construction of Single index evaluation System
Constructing a single index evaluation system according to rock burst grade grading standards, and indicating the intervals of index values corresponding to different rock burst grades under the condition of a single index; wherein, the rock burst grade is divided into 4 types C = (C) 1 ，C 2 ，C 3 ，C 4 ) Corresponding to no rock burst, weak rock burst, medium rock burst and strong rock burst respectively;
3) Determining indicator combining weights
Firstly, respectively weighting 4 indexes by using a CRITIC weighting method and an AHP weighting method, and then obtaining a combination weight by using a game theory combination weight method to represent the importance degree of different evaluation indexes in the comprehensive rockburst evaluation process;
4) Method for constructing single index measure matrix by utilizing normal cloud model
Calculating the digital characteristic parameter expectation Ex of the cloud model according to the single index evaluation system constructed in the step 2) ij Entropy En ij Hyper entropy He ij Substituting the characteristic index value into a forward cloud generator to obtain a nonlinear measurement function, and finally substituting the index value and the digital characteristics into a normal cloud model to obtain a parameter u representing the membership relationship between the index value and the rock burst level ij And constructing a single index measure matrix (mu) based on the measure matrix ij ) 4×4 ；
5) Computing multi-index synthetic measures
According to the comprehensive weight w obtained in the step 3) i (i =1,2,3,4), and the single index measure matrix μ = (μ) constructed in step 4) ij ) 4×4 (i＝1,2,3,4；j＝1,2,3,4)，μ ij The degree of the ith evaluation index representing the evaluation object belonging to the jth rock burst grade is obtained by the comprehensive measure v according to the formula (1):
Figure BDA0003917111660000021
6) Determination of evaluation results
Identifying the evaluation result by using the confidence criterion, as shown in formula (2):
Figure BDA0003917111660000022
lambda is confidence coefficient, usually 0.6 or 0.7 is taken, and the comprehensive evaluation grade of the rock burst of the evaluation object is judged to be C through formula (2) k0 . Further, in an embodiment of the present invention, the AHP authorization in step 3) is implemented as follows:
a. a judgment matrix A is constructed, and the maximum eigenvalue lambda of the judgment matrix is obtained by the scaling method shown in Table 1 max And corresponding feature vector w 1 ；
TABLE 1 decision matrix scaling method
Figure BDA0003917111660000023
Figure BDA0003917111660000031
b. And (3) consistency check, namely determining the consistency of the judgment matrix, and if the check result is not in the allowable consistency range, indicating that the constructed judgment matrix is poor in consistency and needing to readjust the judgment matrix to reach the allowable consistency range, wherein the consistency check formula is as follows:
Figure BDA0003917111660000032
Figure BDA0003917111660000033
wherein CI is deviation consistency index, n is matrix order, RI is random consistency index, RI value refers to the value in Table 2, CR is consistency ratio, when CR is<At 0.1, the degree of inconsistency of A is considered to be within an allowable range, and the normalized feature vector can be used as the weight vector w 1 ；
TABLE 2 random consistency index RI reference values
Figure BDA0003917111660000034
Further, in some preferred embodiments of the present invention, the CRITIC entitlement step in step 3) is as follows:
a. the normalization processing of data, the calculation of the coefficient of variation, the processing and the calculation method are shown in the formulas (5) to (8):
Figure BDA0003917111660000035
Figure BDA0003917111660000036
Figure BDA0003917111660000037
Figure BDA0003917111660000038
wherein x is ij In order to evaluate the value of the object index,
Figure BDA00039171116600000311
is the average value of the j index, s j Is the j index standard deviation, V j The variation coefficient of the j-th index.
b. The correlation coefficient and the collision coefficient are calculated using the normalized data as shown in equations (9) to (11):
Figure BDA0003917111660000039
Figure BDA00039171116600000310
Figure BDA0003917111660000041
wherein,
Figure BDA0003917111660000045
to normalize the mean value of the j-th index, r ij As a correlation coefficient of a normalized index, R j And (4) the item j index conflict coefficient.
c. And (3) calculating the comprehensive information quantity of each index, and determining the index weight as shown in formulas (12) and (13):
η j ＝V j ×R j (12)
Figure BDA0003917111660000042
wherein eta is j Is the combined information quantity of the j-th index, w j Is the weight of the j index.
Further, in some preferred embodiments of the present invention, the game theory combining weight method in step 3) is implemented as follows:
a. the CRITIC weighting method and the AHP weighting method are recorded, and the arbitrary linear combination of the two weight vectors is w, as shown in the formula (14):
w＝α 1 w 1 +α 2 w 2 (14)
wherein, w 1 、w 2 Weights, α, for CRITIC and AHP weighting 1 、α 2 Is the linear combination coefficient, w is the combination weight;
b. and (3) obtaining the optimal combination weight w by taking the dispersion and the digestion between w and each basic weight value as targets, namely, the optimal combination weight w satisfies the formula (15):
min||w-w i || 2 (i＝1,2) (15)
the optimized first derivative condition of equation (15) can be converted to the following system of equations, as shown in equation (16), and the coefficient α is solved;
Figure BDA0003917111660000043
α＝[α 1 ,α 2 ] (17)
wherein alpha is a combined coefficient vector;
c. the coefficients are normalized and the combining weights are calculated as shown in equations (18) (19):
Figure BDA0003917111660000044
w * ＝α' 1 w 1 +α' 2 w 2 (19)
wherein, alpha' i Combining coefficients for normalized weights, w * Is the optimal combining weight.
Further, in some preferred embodiments of the present invention, the specific steps of constructing the single index measurement matrix by using the normal cloud model in step 4) are as follows:
a. determining cloud model characteristic parameters as shown in formulas (20) - (22):
Figure BDA0003917111660000051
Figure BDA0003917111660000052
He ij ＝k (22)
wherein, B max And B min Respectively corresponding to the upper and lower limit values of the ith index corresponding to the jth rock burst grade standard in the index evaluation system, and substituting the value limit of the example data for the lacking boundary value, ex ij For the expectation of the ith index corresponding to the jth grade standard interval, en ij Entropy, he, of the grade standard interval corresponding to the jth item index ij The hyper-entropy of the ith index corresponding to the jth grade standard interval is expressed as cloud thickness, is uncertainty measurement of En, and can be taken according to the size of En, wherein generally the larger the En is, the larger the He is;
b. determining membership parameters u of index values of samples to be evaluated to different rock burst grades by using nonlinear calculation method ij And constructing a single index measure matrix, wherein the calculation method is shown as the formula (23) and (24):
Figure BDA0003917111660000053
Figure BDA0003917111660000054
wherein x is i To evaluate the index value, en' ij To be covered with En ij To be expected, with He ij Normal random number with standard deviation, i.e. satisfying En' - (En, he) 2 )，u ij Is a membership parameter, mu ij Is a single index measure and satisfies the non-negative borderline: 0 is less than or equal to mu ij (x∈C j ) Less than or equal to 1; normalization:
Figure BDA0003917111660000055
adding property:
Figure BDA0003917111660000056
the invention has the beneficial technical effects that:
the invention is based on rock uniaxial compressive strength sigma c Coefficient of tangential stress σ θ /σ c Brittleness index σ c /σ t And an elastic strain energy index Wet4 index establishes a rock burst grade evaluation system, and provides a nonlinear measurement function constructed based on a normal cloud model to improve a calculation method of single index measurement in the traditional uncertain measurement evaluation method and determine a single index measurement matrix. Meanwhile, in order to balance the influence of subjective factors and objective factors in index weighting, a game combination weighting method is adopted, an AHP weighting method and a CRITIC weighting method are integrated, index combination weighting is calculated, and finally the rockburst level is identified according to a confidence criterion. The method can make up the defects of the traditional uncertain measure evaluation method, more fully considers the characteristics of fuzziness and randomness of the rock burst, improves the accuracy of rock burst evaluation, and provides scientific reference for the prevention and treatment of rock burst disasters.
Drawings
FIG. 1 is a flow chart of a comprehensive evaluation method for rock burst based on normal cloud and uncertain measures according to an embodiment of the invention;
FIG. 2 is a graph representing a uniaxial compressive strength index nonlinear single index metric function according to an embodiment of the invention;
FIG. 3 is a tangential stress coefficient index nonlinear single index metric function representation according to an embodiment of the present invention;
FIG. 4 is a graph of a brittle index nonlinear single index metric function representation in accordance with an embodiment of the present invention;
fig. 5 is a representation of an elastic strain energy index nonlinear single index measure function according to an embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures 1 to 5 are described in detail below, and it is apparent that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
Examples
As shown in fig. 1, the comprehensive evaluation method for rock burst based on normal cloud and unknown measure provided in this embodiment includes:
1) Establishing an evaluation object index value system
Obtaining a plurality of groups of rock uniaxial compressive strength sigma according to field sampling, indoor test and calculation c Tangential stress coefficient sigma θ /σ c Brittleness index σ c /σ t Elastic strain energy index W et Index value; the data of the present examples are referred to published document [1 ]]Example data in (1) is shown in table 3.
[1].Zhao H and Chen B.Data-Driven Model for Rockburst Prediction.Mathematical Problems in Engineering,2020.2020:p.1-14.
TABLE 3 evaluation object index value System
Figure BDA0003917111660000061
2) Construction of rock burst single index evaluation system
Constructing a single index evaluation system according to rock burst grade grading standards, and indicating the intervals of index values corresponding to different rock burst grades under the condition of a single index; as shown in table 4, the present embodiment adopts the existing rock burst criterion, and the rock burst class is classified into class 4C = (C) 1 ，C 2 ，C 3 ，C 4 ) Corresponding to no rock burst, weak rock burst, medium rock burst and strong rock burst.
TABLE 4 rock burst single index evaluation system
Figure BDA0003917111660000071
3) Calculating a combination weight of evaluation indexes
Firstly, respectively weighting 4 indexes by using a CRITIC weighting method and an AHP weighting method, and then obtaining a combined weight by using a game theory combined weight method to represent the importance degree of different evaluation indexes in the comprehensive rockburst evaluation process;
a. using AHP (Analytic Hierarchy Process) to assign right
Constructing a judgment matrix A:
Figure BDA0003917111660000072
λ max ＝4.01
Figure BDA0003917111660000073
Figure BDA0003917111660000074
therefore, the consistency of the matrix A is judged to be in an allowable range, and the maximum eigenvalue of the matrix A corresponds to the normalized eigenvector w 1 ＝[0.23,0.12,0.23,0.42]I.e. AHP weighting to σ c, σ θ /σ c 、σ c /σ t 、W et The weights are 0.23, 0.12, 0.23, 0.42, respectively.
b. Weighting by CRITIC (criterion impact high Interfrieria Correlation)
The evaluation target index values were normalized by the formulas (5) to (7), and the results are shown in table 5.
Figure BDA0003917111660000075
Figure BDA0003917111660000081
Figure BDA0003917111660000082
Figure BDA0003917111660000083
TABLE 5 standardized evaluation object index value system
Figure BDA0003917111660000084
And (3) calculating quantization coefficients of index variability and conflict through formulas (9) to (13), and determining index weight:
Figure BDA0003917111660000085
Figure BDA0003917111660000086
Figure BDA0003917111660000087
η j ＝V j ×R j (12)
Figure BDA0003917111660000088
obtaining:
V＝[0.96,0.48,0.59,0.69]
Figure BDA0003917111660000091
R＝[1.45,1.71,1.36,1.02]
η＝[1.40,0.82,0.80,0.71]
w＝[0.37,0.22,0.21,0.20]
c. game theory combined weight method weighting
The combined weight of the CRITIC weighting method and the AHP weighting method is calculated by equations (16) to (19).
Figure BDA0003917111660000092
α＝[α 1 ,α 2 ] (17)
Figure BDA0003917111660000093
w * ＝α' 1 w 1 +α' 2 w 2 (19)
Solving the following steps:
α 1 ＝0.680
α 2 ＝0.394
α 1 '＝0.633
α 2 '＝0.367
w * ＝[0.28,0.16,0.22,0.34]
4) Determining cloud model feature parameters
Cloud model characteristic parameters are calculated by equations (20) to (22), and the calculation results are shown in table 6.
Figure BDA0003917111660000094
Figure BDA0003917111660000095
He ij ＝k (22)
TABLE 6 cloud model feature parameters
Figure BDA0003917111660000096
Figure BDA0003917111660000101
5) Constructing a nonlinear measurement function by using a normal cloud model, wherein the function representation is shown in figures 2-5, calculating single index measurement, and constructing a single index measurement matrix; the calculation method is shown in the formulas (23) and (24):
Figure BDA0003917111660000102
Figure BDA0003917111660000103
wherein, en' ij Is defined by En ij To be expected, with He ij Normal random number with standard deviation, i.e. satisfying En' - (En, he) 2 ) Can be randomly generated using MATLAB, and μ ij Satisfy non-negative boundless: 0 is less than or equal to mu ij (x∈C j ) Less than or equal to 1; normalization:
Figure BDA0003917111660000104
adding property:
Figure BDA0003917111660000105
obtaining a single index measure matrix of each evaluation object:
Figure BDA0003917111660000106
Figure BDA0003917111660000111
Figure BDA0003917111660000112
Figure BDA0003917111660000113
Figure BDA0003917111660000114
6) Computing multi-index synthetic measures
Calculating the multi-index comprehensive measure by formula (1):
Figure BDA0003917111660000115
obtaining:
v 1 ＝[0.28,0.34,0.38,0] v 2 ＝[0,0.16,0.01,0.84]
v 3 ＝[0,0.16,0.1,0.74] v 4 ＝[0.74,0.04,0.22,0]
v 5 ＝[0.37,0.39,0.24,0] v 6 ＝[0,0.38,0.28,0.34]
v 7 ＝[0.76,0.02,0.22,0] v 8 ＝[0,0.42,0.37,0.21]
v 9 ＝[0,0.28,0.25,0.47] v 10 ＝[0.76,0.02,0.22,0]
7) Identifying evaluation results using confidence criteria
The evaluation results were identified using confidence criteria and calculated by equation (2), where λ is 0.6.
Figure BDA0003917111660000116
The discrimination results of the method of the present invention and the conventional uncertain measure evaluation method are compared, and the results are shown in table 7.
TABLE 7 comprehensive evaluation results of rock burst
Figure BDA0003917111660000117
Figure BDA0003917111660000121
The result shows that the rock burst comprehensive evaluation model has all correct evaluation results, has higher accuracy and good effect compared with the traditional uncertain measurement evaluation method, and solves the problem that the traditional uncertain measurement evaluation method is difficult to better characterize the randomness and the uncertainty of the rock burst. Meanwhile, the game combination weighting method is adopted to well balance the influence of subjective and objective factors of the weight.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (5)

1. The rock burst comprehensive evaluation method based on normal cloud and uncertain measurement theory is characterized by comprising the following steps:
1) Establishing an evaluation object index value system
Obtaining a plurality of groups of rock uniaxial compressive strength sigma according to field sampling, indoor test and calculation c Tangential stress coefficient sigma θ /σ c Brittleness index σ c /σ t Elastic strain energy index W et Index value; let the sample space composed of different groups of rock burst evaluation objects be R = (R) 1 ，R 2 ，…，R n ) Each evaluation sample contains 4 influencing factors I 1 、I 2 、I 3 、I 4 I.e. representing 4 evaluation indexes, I = (I) 1 ，I 2 ，I 3 ，I 4 ) Is an index set;
2) Construction of Single index evaluation System
Constructing a single index evaluation system according to rock burst grade grading standards, and indicating the intervals of index values corresponding to different rock burst grades under the condition of a single index; wherein the rockClass 4 class C = (C) 1 ，C 2 ，C 3 ，C 4 ) Respectively corresponding to no rock burst, weak rock burst, medium rock burst and strong rock burst;
3) Determining indicator combining weights
Firstly, respectively weighting 4 indexes by using a CRITIC weighting method and an AHP weighting method, and then obtaining a combined weight by using a game theory combined weight method to represent the importance degree of different evaluation indexes in the comprehensive rockburst evaluation process;
4) Method for constructing single index measure matrix by utilizing normal cloud model
Calculating the expected Ex of the digital characteristic parameters of the cloud model according to the single index evaluation system constructed in the step 2) ij Entropy En ij He of super entropy ij Substituting the nonlinear measurement function into a forward cloud generator to obtain a nonlinear measurement function, and finally substituting the index value and the digital characteristics into a normal cloud model to obtain a parameter u representing the membership relationship between the index value and the rock burst level ij And constructing a single index measure matrix (mu) based on the measure matrix ij ) 4×4 ；
5) Computing multi-index synthetic measures
Based on the integrated weight w obtained in step 3) i (i =1,2,3,4), and the single index measure matrix μ = (μ) constructed in step 4) ij ) 4×4 (i＝1,2,3,4；j＝1,2,3,4)，μ ij The degree of the ith evaluation index representing the evaluation object belonging to the jth rock burst grade is obtained by the formula (1):
Figure FDA0003917111650000011
6) Determining the evaluation result
The evaluation results are identified using confidence criteria, as shown in equation (2):
Figure FDA0003917111650000012
λ is confidence, usually 0.6 or 0.7, and is determined by equation (2)Giving out the comprehensive evaluation grade of the rock burst of the evaluation object as C k0 。
2. The comprehensive rock burst evaluation method based on normal cloud and uncertain measure theory according to claim 1, wherein the AHP weighting method in step 3) is realized by the following steps:
a. a judgment matrix A is constructed, and the maximum eigenvalue lambda of the judgment matrix is obtained by the scaling method shown in Table 1 max And corresponding feature vector w 1 ；
TABLE 1 decision matrix Scale method
Figure FDA0003917111650000021
b. And (3) consistency check, namely determining the consistency of the judgment matrix, and if the check result is not in the allowable consistency range, indicating that the constructed judgment matrix is poor in consistency and needing to readjust the judgment matrix to reach the allowable consistency range, wherein the consistency check formula is as follows:
Figure FDA0003917111650000022
Figure FDA0003917111650000023
wherein CI is deviation consistency index, n is matrix order, RI is random consistency index, RI value refers to the value in Table 2, CR is consistency ratio, when CR is<At 0.1, the degree of inconsistency of A is considered to be within an allowable range, and the normalized feature vector can be used as the weight vector w 1 。
TABLE 2 reference value of random consistency index RI
Figure FDA0003917111650000024
3. The comprehensive rock burst evaluation method based on normal cloud and uncertain measure theory according to claim 1, wherein the CRITIC weighting method in step 3) comprises the following steps:
a. the data is normalized, the coefficient of variation is calculated, and the processing and calculation methods are shown in formulas (5) to (8):
Figure FDA0003917111650000025
Figure FDA0003917111650000026
Figure FDA0003917111650000031
Figure FDA0003917111650000032
wherein x is ij In order to evaluate the value of the object index,
Figure FDA0003917111650000033
is the average value of the j index, s j Is the j index standard deviation, V j The j index variation coefficient;
b. the correlation coefficient and the collision coefficient are calculated using the normalized data as shown in equations (9) to (11):
Figure FDA0003917111650000034
Figure FDA0003917111650000035
Figure FDA0003917111650000036
wherein,
Figure FDA0003917111650000037
to normalize the mean value of the j-th index, r ij For the correlation coefficient of the normalization index, R j The j index conflict coefficient;
c. and (3) calculating the comprehensive information quantity of each index, and determining the index weight as shown in formulas (12) and (13):
η j ＝V j ×R j (12)
Figure FDA0003917111650000038
wherein eta j Is the comprehensive information quantity of the jth index, w j Is the weight of the j index.
4. The comprehensive rock burst evaluation method based on the normal cloud and the uncertain measure theory according to claim 1, wherein the game theory combination weight method in the step 3) is realized by the following steps:
a. the two weight vectors of CRITIC weighting method and AHP weighting method are combined into w in an arbitrary linear way, as shown in formula (14):
w＝α 1 w 1 +α 2 w 2 (14)
wherein w 1 、w 2 Weights, α, for CRITIC and AHP weighting 1 、α 2 Is a linear combination coefficient, w is a combination weight;
b. and (3) obtaining an optimal combination weight w by taking the minimum dispersion between w and each basic weight value as a target, namely satisfying the formula (15):
min||w-w i || 2 (i＝1,2) (15)
the optimized first derivative condition of equation (15) can be converted to the following system of equations, as shown in equation (16), and the coefficient α is solved;
Figure FDA0003917111650000039
α＝[α 1 ,α 2 ] (17)
wherein, alpha is a combined coefficient vector;
c. the coefficients are normalized and the combining weights are calculated as shown in equations (18) (19):
Figure FDA0003917111650000041
w * ＝α′ 1 w 1 +α′ 2 w 2 (19)
wherein, alpha' i For normalized weight combining coefficients, w * Is the optimal combining weight.
5. The comprehensive rock burst evaluation method based on normal cloud and uncertain measurement theory according to claim 1, wherein the specific steps of constructing the single index measurement matrix by using the normal cloud model in the step 4) are as follows:
a. determining cloud model characteristic parameters as shown in formulas (20) - (22):
Figure FDA0003917111650000042
Figure FDA0003917111650000043
He ij ＝k (22)
wherein, B max And B min Respectively corresponding to the upper and lower limit values of the ith index corresponding to the jth rock burst grade standard in the index evaluation system, and substituting the value limit of the example data for the lacking boundary value, ex ij For the expectation of the i-th index corresponding to the j-th grade standard interval, en ij Entropy, he, of the grade standard interval corresponding to the jth item index ij The hyper-entropy of the ith index corresponding to the jth grade standard interval is expressed as cloud thickness, is uncertainty measurement of En, and can be taken according to the size of En, wherein generally the larger the En is, the larger the He is taken.
b. Determining membership parameters u of index values of samples to be evaluated to different rock burst grades by using nonlinear calculation method ij And constructing a single index measure matrix, wherein the calculation method is shown as the formula (23) (24):
Figure FDA0003917111650000044
Figure FDA0003917111650000045
wherein x is i For evaluation index value, en' ij Is defined by En ij To be expected, with He ij Normal random number with standard deviation, i.e. satisfying En' - (En, he) 2 )，u ij Is a membership parameter, mu ij Is a single index measure and meets the following non-negative limitation: 0 is less than or equal to mu ij (x∈C j ) Less than or equal to 1; normalization:
Figure FDA0003917111650000046
adding property:
Figure FDA0003917111650000047
CN202211345625.2A 2022-10-31 2022-10-31 Rock burst comprehensive evaluation method based on normal cloud and uncertain measure Pending CN115619277A (en)

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