Rockburst; Forecast and forecast; Distance discriminant analysis; Coal mine; disaster
Introduction to 0
Since 1738, rock burst occurred for the first time in the coal field of South Staffordshire, England, almost all coal mining countries have experienced rock burst, which seriously threatened the safety of underground production and workers' lives. It has become one of the most serious natural disasters in mines all over the world, and has always been a key research topic in the field of geology and mining at home and abroad. In China, rockburst has the following characteristics besides sudden, instantaneous vibration and destructiveness:
① Various types and different disaster severity;
② The occurrence conditions are extremely complicated;
(3) With the increase of mining depth, the number of mines with rockburst disasters has obviously increased, and the degree of harm has become increasingly serious.
Therefore, the prediction and prevention of rockburst has very important practical value and practical significance.
At present, the traditional methods for predicting rockburst mainly include empirical analogy analysis, drilling cuttings method, ground sound monitoring method, microseismic monitoring method, water content determination method and electromagnetic radiation method. The above methods have achieved certain results in engineering practice. However, the occurrence of rockburst is a complex problem with many influencing factors. Therefore, using a single risk index of rock burst may cause a large prediction error, which will seriously affect the personal safety and production safety of mining enterprises. In recent years, many scholars have introduced grey system method, neural network method and support vector machine model into rockburst prediction, and achieved many research results.
Discriminant analysis is an effective multivariate data analysis method, which can extract the information of each group from each training sample and scientifically judge what type the sample belongs to, and has been widely used in many fields. Based on the comprehensive consideration of many factors affecting rockburst in practical engineering, the author introduces the distance discriminant analysis method into rockburst prediction, which overcomes the influence of human factors in prediction, improves the accuracy and reliability of prediction, and provides a new way for rockburst prediction.
1 distance discriminant analysis method
Firstly, the principle and process of distance discriminant analysis are introduced. Set population
Is a multivariate population, in which the sample
manufacture
Then the population mean vector is
. The covariance matrix of population g is
Then the Mahalanobis distance between sample X and population G is defined as
There are k p-ary populations: G 1, G2, …, Gk, the mean vectors are μ 1, μ2, …, μk, and the covariance matrices are ∑ 1, ∑2, …, ∑k, respectively. Calculate the Mahalanobis distance from the new sample X to each population, and compare these k distances to determine that the new sample X belongs to the population with the shortest Mahalanobis distance.
Assuming that the population covariance matrix is equal, take two populations Gi, Gj at will, and investigate the square difference of Mahalanobis distance from x to population Gi, Gj:
Among them,
It's easy to see
We can get the distance criterion of multiple populations under the condition that the covariance matrices of the populations are equal: If the population Gj0 satisfies
Then X∈Gj0.
The population mean vector μ 1, μ2, …, μk and the common covariance matrix ∑ are generally unknown, and can be estimated by using the training samples of each population.
set up
It is a training sample from the population Gj, j = 1, 2, …, k. remember
rule
Is the unbiased estimate of μj, and the unbiased estimate of Σ is
along with
(i.e.
), s (i.e.
) instead of μj and Σ, the corresponding estimated value of Wj(X) can be obtained by the following formula.
Among them,
In this way, the distance criterion of multiple groups is that if the group Gj0 satisfies:
Then X∈Gj0.
In order to examine the superiority of a given criterion, it is necessary to examine the probability of misjudgment. Take two populations G 1 and G2 as examples, that is, consider the probability that X belongs to G 1 and is misjudged as G2, or the probability that X belongs to G2 and is misjudged as G 1. Let the capacity of the two populations be n 1 and n2 respectively, and take all the training samples as n 1+n2 new samples, and substitute them into the established criteria one by one to determine their ownership. This process is called back judgment. Let n 12 be the number of samples that belong to G 1 and are misjudged as G2; N2 1 means that the number of misjudged samples belonging to G2 is G 1, and the total number of misjudged samples is n 12+n2 1. Then there is the misjudgment rate.
The recursive estimate of is
Distance discriminant analysis method for rockburst prediction
2. 1 Determination of influencing factors of rockburst
There are many factors that affect rockburst, and they are interrelated and mutually restricted, showing a complex nonlinear relationship. Often in a rockburst mine, many influencing factors work at the same time. Therefore, in the study of rockburst prediction, we must first make clear the main influencing factors in order to achieve good results.
Referring to relevant research results, starting from mine geological factors and mining technical conditions, it is considered that there are eight main factors affecting rock burst: coal seam mining depth (m), roof lithology, geological structure complexity, coal seam dip angle (O), coal seam thickness (m), mining method, presence or absence of coal pillars, blasting mining or fully mechanized mining. Among them, the first five items belong to geological factors, and the last three items belong to mining technology factors.
2.2 Data processing and distance discriminant analysis model establishment
When assigning values to variables, we can use the binary variable assignment method in quantitative theory to deal with qualitative variables in input variables, that is, "0" and "1" are used to represent "nothing" and "existence" of a certain attribute. Qualitative variables refer to five influencing factors: roof lithology, complexity of geological structure, presence or absence of coal pillar, mining method, blasting or fully mechanized mining. The results of each variable will be used as training samples to establish a distance discriminant analysis model.
According to the provisions of the Interim Measures for Safe Mining of Rock Burst Coal Seam, the risk degree of rock burst is divided into three levels:
Grade I-serious impact danger zone, expressed as grade I (g1);
Grade II-moderate impact danger zone, represented by Grade II (G2);
Class III-No collision danger zone, denoted by III (G3).
On this basis, the distance discriminant analysis model is established, and the discriminant factor of the input layer is 14, which corresponds to 14 variables divided by 8 influencing factors. The output layer has three layers, corresponding to the three levels of rockburst risk. I, II and III risk areas are regarded as three different populations, and the covariance matrices of the three populations are assumed to be equal. The distance discriminant analysis model is established as shown in the following figure.
Schematic diagram of distance discriminant analysis model
3 engineering application
The geological structure of the mining area is complex, and the occurrence conditions of coal seams are nearly horizontal, inclined and steep, with different thicknesses. In the process of the mining area extending to the complex geological structure zone and deep, the problem of rockburst prediction is constantly prominent. According to the historical data of the mining area, a considerable amount of rockburst risk data has been accumulated. Taking historical data as an example, a distance discriminant analysis model is established to learn 18 samples, and the remaining 6 samples are discriminated. After the model learning is completed, the learning samples are judged by recursive estimation method, all of which are accurate and the misjudgment rate is zero (see table 1).