CN103778480A - Fissure-zone height prediction method based on sensitivity analysis - Google Patents

Abstract

The invention discloses a fissure-zone height prediction method based on sensitivity analysis and belongs to the technical field of 'three-under' exploit and gas extraction. The method is obtained on the basis of collection of actual measurement of national mines so that geographical limitation is overcome. The method takes effects of mining thickness, hard-rock lithologic proportion coefficient and mining depth into consideration so that prediction precision of fissure-zone heights is improved effectively and practicality is higher.

Description

A kind of fissure zone Height Prediction method based on sensitivity analysis

Technical field

The invention belongs to " three times " exploitation and gas pumping technical field, be specifically related to a kind of fissure zone Height Prediction method based on sensitivity analysis.

Background technology

Under mine water body, exploitation must be stayed and establishes barrier pillar, determines that the most important parameter of barrier pillar is the height of water flowing fractured zone, and the staying to establish of barrier pillar is related to the production safety of exploiting under water body.Accurate fissure zone height is the important prerequisite that realizes safe working.

Along with the development of China coal industry and technical equipment, the research of fissure zone development height also makes great progress.Recent decades, the Chinese coal scientific worker take Liu Tianquan academician as representative, accumulated a large amount of achievements in research and practical experience by methods such as theoretical research, practice analysis and experiments.For the safe working of mine provides very large support.

The computing method of the existing fissure zone height of China are mainly the computing method in " buildings, water body, railway and main roadway Coal Pillar Design with press coal mining rules " (hereinafter to be referred as " three times " rules).The method be Liu Tianquan academician in the eighties according to the measured data of North China, applied regression analysis gained, wherein the development height of fissure zone only with adopt thick relevant, do not consider the impact of other factors, therefore predicated error is larger, and selected data have the limitation of region, to Cai Fa with adopt and thickly wait mining conditions restriction larger.

In practice for many years, learn at the scene fissure zone height not only with adopt thick relevant, and with to adopt the factors such as dark, superincumbent stratum lithology and workplace span relevant.(1) adopt thick larger fissure zone height larger; (2) adopt the dark size that directly affects rock pressure [in mine, and rock pressure [in mine affects the motion scale of superincumbent stratum, and then affect the development degree of fissure zone; (3) learn according to the theory of the mechanics of materials, workplace span and rock beam flexibility relation in direct ratio, rock beam flexibility is larger, and rock beam more easily ruptures, and then affects the development height of fissure zone.It is generally acknowledged that span meets while fully adopting, it will weaken the development impact of fissure zone.(4) rock property, particularly shearing strength is larger, is more conducive to stop the growth of fissure zone; Therefore, consider that overall effect factor is very important for the prediction of fissure zone height.

Summary of the invention

The deficiency existing for prior art, the present invention proposes a kind of fissure zone Height Prediction method based on sensitivity analysis, to reach the object that improves fissure zone Height Prediction precision.

A fissure zone Height Prediction method based on sensitivity analysis, comprises the following steps:

Step 1, gather the historical mine data of many groups, every group of data comprise adopts thick, hard rock lithologic proportion coefficient, workplace span and adopts dark four kinds of influence factors;

Step 2, employing Multielement statistical analysis method are determined the relation between influence factor and fissure zone height, specific as follows:

Step 2-1, set up and adopt thick, hard rock lithologic proportion coefficient, workplace span, adopt the regression model between dark and fissure zone height:

y _t=β ₀+β ₁x _t1+β ₂x _t2+β ₃x _t3+β ₄x _t4+ε _t(t=1,2,…,n) (1)

Wherein, y _trepresent the fissure zone height of t group data prediction; β ₀represent constant; β ₁represent to adopt the coefficient of thick influence factor; β ₂represent the coefficient of hard rock lithologic proportion coefficient, β ₃represent the coefficient of workplace span, β ₄represent to adopt dark coefficient; x _t1represent that adopting of t group data is thick; x _t2represent the hard rock lithologic proportion coefficient of t group data; x _t3represent the workplace span of t group data; x _t4represent that adopting of t group data is dark; ε _trepresent stochastic error; N represents total group of number of image data;

Step 2-2, the regression model that four factor value substitutions in the historical data gathering are set up, utilize criterion of least squares to calculate the coefficient that obtains each influence factor, complete the foundation of regression model, complete the relation of determining between influence factor and fissure zone height;

Step 3, carry out significance test to calculating the coefficient of each influence factor obtaining:

Step 3-1, suppose that the numerical value of the coefficient of a certain influence factor is 0, formula is as follows:

Suppose:

β _i=0 (2)

Wherein, β _irepresent the coefficient of a certain influence factor, i=1,2 ..., 4;

Step 3-2, calculating hypothesis are deleted factor beta _ithe regression sum of square of the regression model of gained after corresponding influence factor, with the difference P of regression sum of square of the regression model of setting up _i, formula is as follows:

$P_i={{\widehat{\mathrm{\β}}}_i}^2/l^{\mathrm{ii}}---\left(3\right)$

Wherein, P _irepresent sum of squares of partial regression, hypothesis is deleted factor beta _ithe regression sum of square of the regression model of gained after corresponding influence factor, with regression sum of square poor of the regression model of setting up;

represent the least squares estimator of coefficient vector β, $\widehat{\mathrm{\β}}=\left[\begin{array}{c}{\widehat{\mathrm{\β}}}_0\\ {\widehat{\mathrm{\β}}}_1\\ \·\·\·\·\\ {\widehat{\mathrm{\β}}}_4\end{array}\right],$ According to

determine β _icorresponding

l ⁱⁱrepresenting matrix L ^-1i diagonal element, wherein,

represent the data matrix of former data matrix X centralization, wherein $C=\left[\begin{array}{ccccc}1& x_{11}& x_{12}& \·\·\·& x_{14}\\ 1& x_{21}& x_{22}& \·\·\·& x_{24}\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ 1& x_{n1}& x_{n2}& \·\·\·& x_{n4}\end{array}\right],$ $X=\left[\begin{array}{ccccc}& x_{11}& x_{12}& \·\·\·& x_{14}\\ & x_{21}& x_{22}& \·\·\·& x_{24}\\ & \·& \·& & \·\\ & \·& \·& & \·\\ & \·& \·& & \·\\ & x_{n1}& x_{n2}& \·\·\·& x_{n4}\end{array}\right],$ $Y=\left[\begin{array}{c}{y}_1\\ y_2\\ \·\\ \·\\ \·\\ y_n\end{array}\right];$

Step 3-3, the hypothesis obtaining according to calculating are deleted factor beta _ithe difference P of the regression sum of square of the regression sum of square of rear gained regression model and the regression model of foundation _i, matrix of coefficients β residual sum of squares (RSS) Q and image data total group of number, determine the coefficient test statistics of each influence factor;

Test statistics formula is as follows:

$F_i=\frac{P_i}{Q/(n-4-1)}---\left(4\right)$

Wherein, Q represents the residual sum of squares (RSS) of matrix of coefficients β;

The test statistics of each influence factor that step 3-4, judgement calculating obtain is more than or equal to the probability of test statistics setting value, and then acquisition significance probability value, if significance probability value is greater than significance probability setting value, this influence factor is significant for the impact of fissure zone height, needs to retain; Otherwise this influence factor is inapparent for the impact of fissure zone height, need to delete this influence factor;

The regression model after not appreciable impact factor is deleted in step 3-5, acquisition;

Step 4, employing sensitivity analysis method are determined the susceptibility of the rear lingering effect factor of deletion for fissure zone height;

Step 4-1, determine the value of lingering effect factor in mine historical data, and then the variation range of definite lingering effect factor value calculate mean values, reference value using this mean values as corresponding influence factor, and the reference value substitution of each influence factor is deleted in the regression model after not appreciable impact factor, obtain fissure zone altitude datum value;

Step 4-2, in lingering effect factor, choose at random an influence factor, according to deleting the regression model that obtains after not appreciable impact factor and the reference value of other influences factor, determine the impact for fissure zone height of the influence factor chosen;

Delete in the regression model obtaining after not appreciable impact factor by the reference value substitution of other influences factor, the relational expression of the influence factor that acquisition is chosen and fissure zone height, and according to the variation range of the influence factor value of choosing, determine maximal value and the minimum value of fissure zone height value;

Step 4-3, repeating step 4-2 are until complete all lingering effect factors determining for fissure zone effect of altitude;

Step 4-4, according to the reference value, fissure zone height value of calculating the fissure zone height obtaining corresponding maximal value and minimum value in the variation range of influence factor, determine the susceptibility of the each factor of residue;

The susceptibility formula that calculates the each factor of residue is as follows:

${\mathrm{\η}}_{\left(c_j\right)}=\max \left\{\right[(S{\left(c_j\right)}_{\max }-S^{*})/S^{*}],[(S^{*}-S{\left(c_j\right)}_{\min })/S^{*}\left]\right\}---\left(5\right)$

Wherein,

represent influence factor c _jsusceptibility, wherein, c _jrepresent remaining influence factor, j=1,2 ..., m, m represents lingering effect factor number; S ^*represent fissure zone altitude datum value; S (c _j) _maxrepresent influence factor c _jthe maximal value of fissure zone height in its span, S (c _j) _minrepresent influence factor c _jthe minimum value of fissure zone height in its span;

Step 5, according to the lingering effect factor obtaining for the susceptibility of fissure zone height, be optimized deleting the regression model obtaining after not appreciable impact factor;

Step 5-1, set up susceptibility forecast model, formula is as follows:

η _j△(c _j)/c _j ^*=△S(c _j)/S ^* (6)

Wherein, △ S (c _j) be illustrated in influence factor c _jin situation, fissure zone height change value, △ (c _j) expression influence factor c _jchanging value, c _j ^*for influence factor c _jreference value;

Formula (6) is sued for peace, obtains formula as follows:

$S\left(c\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{S}^{*}{\mathrm{\η}}_j(c_j-{c_j}^{*})/{c_j}^{*}+S^{*}---\left(7\right)$

Wherein, S (c) represents the fissure zone height of prediction; η _jrepresent influence factor c _jsusceptibility; c _jrepresent the value of influence factor, c _j ^*for influence factor c _jreference value;

Step 5-2, according to residue each influence factor susceptibility and reference value, substitution obtain susceptibility forecast model, obtain optimize after fissure zone Height Prediction model;

Step 6, gather that adopting of tested mine is thick, hard rock lithologic proportion coefficient, workplace span and adopt deeply, in the fissure zone Height Prediction model after the optimization that substitution obtains, obtain the prediction fissure zone height of tested mine;

Step 7, judge that prediction fissure zone height whether in the safe range of setting, if so, can continue exploitation and produce, adopt thick or carry out filling mining otherwise need to reduce.

Test statistics setting value described in step 3-4, its span is 0.6～0.8; Described significance probability setting value, its value is 0.95.

Advantage of the present invention:

A kind of fissure zone Height Prediction method based on sensitivity analysis of the present invention, is collecting gained on the actual measurement basis of national mine, has therefore overcome the limitation of region; That the present invention has considered to adopt is thick, hard rock lithologic proportion coefficient and adopt dark impact, therefore, has effectively improved the precision of prediction of fissure zone height, has more practicality.

Accompanying drawing explanation

Fig. 1 is the fissure zone Height Prediction method flow diagram based on sensitivity analysis of an embodiment of the present invention.

Embodiment

Below in conjunction with accompanying drawing, an embodiment of the present invention is described further.

A fissure zone Height Prediction method based on sensitivity analysis, method flow diagram as shown in Figure 1, comprises the following steps:

Step 1, gather the historical mine data of many groups, every group of data comprise adopts thick, hard rock lithologic proportion coefficient, workplace span and adopts dark four influence factors;

In the embodiment of the present invention, by investigation, the measured data of having collected a large amount of colliery fissure zone height.(hard rock lithologic proportion coefficient refers to that roof adds up in height above with adopting thick, hard rock lithologic proportion coefficient to analyze fissure zone height, the ratio of hard rock and statistics height, the hard rock that participates in statistics mainly refers to sandstone, mixed rock, pyrogenic rock), workplace span and adopt the funtcional relationship between dark.

Table 1 fissure zone developmental state statistical form

Using table 1 data as analyzing data.Choose and adopt thick, hard rock lithologic proportion coefficient, workplace span and adopt the dark major influence factors as affecting fissure zone height, the fissure zone developmental state of mine is analyzed.Influence factor using above 4 factors of influence as fissure zone height, application SPSS19.0 software carries out multiple linear regression analysis to it.

Step 2, employing Multielement statistical analysis method are determined the relation between influence factor and fissure zone height, specific as follows:

In the embodiment of the present invention, adopt regression analysis, regretional analysis is most widely used in Practical Project in the various analytical approachs of multivariate statistical analysis.It is the data analysing method of processing relation of interdependence between multiple variablees.Mutual relationship between variable is a large amount of existence in practical problems, and regretional analysis is effective mathematical method of this mutual relationship of research.

Step 2-1, set up and adopts thick, hard rock lithologic proportion coefficient, workplace span and adopt the regression model between dark and fissure zone height;

In the embodiment of the present invention, suppose fissure zone height y _twith adopt thick x _t1, hard rock lithologic proportion coefficient x _t2, workplace span x _t3, adopt dark x _t4influence factor linear dependence, for 28 groups of data y ₁, y ₂..., y ₂₈meet following regression model:

y _t=β ₀+β ₁x _t1+β ₂x _t2+β ₃x _t3+β ₄x _t4+ε _t(t=1,2,…,28) (1)

Wherein, the average E (ε of stochastic error _t)=0; The variance of stochastic error is σ ², i.e. Var (ε _t)=σ ²; The related coefficient of each stochastic error is 0, i.e. Cov (ε _i, ε _{j '})=0 (i ≠ j '), stochastic error meet normal distribution, i.e. ε _t～N (0, σ ²), separate; y _trepresent the fissure zone height of t group data prediction; β ₀represent constant; β ₁represent to adopt the coefficient of thick influence factor; β ₂represent the coefficient of hard rock lithologic proportion coefficient, β ₃represent the coefficient of workplace span, β ₄represent to adopt dark coefficient; x _t1represent that adopting of t group data is thick; x _t2represent the hard rock lithologic proportion coefficient of t group data; x _t3represent the workplace span of t group data; x _t4represent that adopting of t group data is dark; ε _trepresent stochastic error; N represents total group of number of image data;

Step 2-2, the regression model that four factor value substitutions in the historical data gathering are set up, utilize criterion of least squares to calculate the coefficient that obtains each influence factor, complete the foundation of regression model, complete the relation of determining between influence factor and fissure zone height;

In the embodiment of the present invention, adopt the criterion of least squares in SPSS software to calculate the factor beta that obtains each influence factor ₁, β ₂, β ₃and β ₄, the ultimate principle of least square method is the sum of square of deviations minimizing between match value and actual value;

Step 3, carry out significance test to calculating the coefficient of each influence factor obtaining:

Step 3-1, suppose that the numerical value of the coefficient of a certain influence factor is 0;

In the embodiment of the present invention, regression equation significance test is to judge β ₁, β ₁..., β ₄whether be 0 entirely, but can not get rid of certain β _ibe 0, if β _ibe 0 explanation influence factor x _ibe not have influentially to fissure zone height y, should from model, reject, be i.e. the following hypothesis of check:

β _i=0 (2)

Wherein, β _irepresent the coefficient of a certain influence factor, i=1,2 ..., 4;

Step 3-2, calculating hypothesis are deleted factor beta _ithe regression sum of square of the regression model of gained after corresponding influence factor, with the difference P of regression sum of square of the regression model of setting up _i, formula is as follows:

$P_i={{\widehat{\mathrm{\β}}}_i}^2/l^{\mathrm{ii}}---\left(3\right)$

Wherein, P _irepresent sum of squares of partial regression, hypothesis is deleted factor beta _ithe regression sum of square of the regression model of gained after corresponding influence factor, with regression sum of square poor of the regression model of setting up;

represent the least squares estimator of coefficient vector β, $\widehat{\mathrm{\β}}=\left[\begin{array}{c}{\widehat{\mathrm{\β}}}_0\\ {\widehat{\mathrm{\β}}}_1\\ \·\·\·\·\\ {\widehat{\mathrm{\β}}}_4\end{array}\right],$ According to

determine β _icorresponding

l ⁱⁱrepresenting matrix L ^-1i diagonal element, wherein,

represent the data matrix of former data matrix X centralization, wherein $C=\left[\begin{array}{ccccc}1& x_{11}& x_{12}& \·\·\·& x_{14}\\ 1& x_{21}& x_{22}& \·\·\·& x_{24}\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ 1& x_{n1}& x_{n2}& \·\·\·& x_{n4}\end{array}\right],$ $X=\left[\begin{array}{ccccc}& x_{11}& x_{12}& \·\·\·& x_{14}\\ & x_{21}& x_{22}& \·\·\·& x_{24}\\ & \·& \·& & \·\\ & \·& \·& & \·\\ & \·& \·& & \·\\ & x_{n1}& x_{n2}& \·\·\·& x_{n4}\end{array}\right],$ $Y=\left[\begin{array}{c}{y}_1\\ y_2\\ \·\\ \·\\ \·\\ y_n\end{array}\right];$

Step 3-3, the hypothesis obtaining according to calculating are deleted factor beta _ithe difference P of the regression sum of square of the regression sum of square of rear gained regression model and the regression model of foundation _i, matrix of coefficients β residual sum of squares (RSS) Q and image data total group of number, determine the coefficient test statistics of each influence factor;

Test statistics formula is as follows:

$F_i=\frac{P_i}{Q/(n-4-1)}---\left(4\right)$

Wherein, Q represents the residual sum of squares (RSS) of matrix of coefficients β;

The test statistics of each influence factor that step 3-4, judgement calculating obtain is more than or equal to the probability of test statistics setting value, and then acquisition significance probability value, if significance probability value is greater than significance probability setting value, this influence factor is significant for the impact of fissure zone height, needs to retain; Otherwise this influence factor is inapparent for the impact of fissure zone height, need to delete this influence factor; Described test statistics setting value, its span is 0.6～0.8, in the embodiment of the present invention, value is 0.6; Described significance probability setting value, its span is 0.95.

In the embodiment of the present invention, the data importing SPSS software in table 1 is carried out to linear regression analysis.Obtain following data: regression coefficient is respectively 5.183,15.041 ,-0.057,0.022, constant term is 23.809.Workplace span x ₃significance probability value be 0.734, be less than 0.95, therefore delete workplace span x ₃.Weeding face span x ₃after again carry out regretional analysis with SPSS software, obtain result as follows, regression coefficient is respectively 5.164,15.496,0.022, constant term is 13.960.Then check the conspicuousness of this equation coefficient, the significance probability value of three independents variable is 1,0.997,0.997, is all greater than 0.95 requirement, can think and between dependent variable and independent variable, have significant linear dependence.

The regression model after not appreciable impact factor is deleted in step 3-5, acquisition;

In the embodiment of the present invention, equation of linear regression is:

y=5.164x ₁+15.496x ₂+0.022x ₄+13.960 (8)

Formula (8) is fissure zone height and adopts thick, hard rock lithologic proportion coefficient and adopt dark functional relation; Wherein, y represents fissure zone height, x ₁expression is adopted thick, x ₂represent hard rock lithologic proportion coefficient, x ₄represent to adopt dark.

Step 4, employing sensitivity analysis method are determined the susceptibility of the rear lingering effect factor of deletion for fissure zone height;

In the embodiment of the present invention, single Study on Sensitivity of Factors Influencing refers on the basis of getting a certain specific reference factor collection in all influence factors, in the time evaluating the susceptibility of certain factor, suppose that other factor is constant, make each factor change in its possible variation range separately, analyze variation tendency and the intensity of variation of the corresponding generation of fissure zone height.

The first step of sensitivity analysis is the functional relation of setting up between fissure zone height and each factor.Then choose the sensible factor that affects fissure zone height, provide reference factor collection.While analyzing some factors on the affecting of fissure zone height, other each factor is got reference value and is remained unchanged.If the less amplitude of variation of this factor, can cause the larger variation of fissure zone height, illustrate that fissure zone height is to this factor sensitivity, this factor is high sensible factor.If this factors vary is larger, and fissure zone height change is small, illustrates that fissure zone height is insensitive to this factor, this factor is low sensible factor.

Step 4-1, determine the value of lingering effect factor in mine historical data, and then the variation range of definite lingering effect factor value calculate mean values, reference value using this mean values as corresponding influence factor, and the reference value substitution of each influence factor is deleted in the regression model after not appreciable impact factor, obtain fissure zone altitude datum value;

In the embodiment of the present invention, reference factor collection definite be data take table 1 as basis, obtain through comprehensive analysis.Reference factor collection and variation range are in table 2.The reference value that each factor reference value substitution formula (8) calculates fissure zone height is 52.95m.

Table 2 factor reference value and variation range

Step 4-2, in lingering effect factor, choose at random an influence factor, according to deleting the regression model that obtains after not appreciable impact factor and the reference value of other influences factor, determine the impact for fissure zone height of the influence factor chosen;

Delete in the regression model obtaining after not appreciable impact factor by the reference value substitution of other influences factor, the relational expression of the influence factor that acquisition is chosen and fissure zone height, and according to the variation range of the influence factor value of choosing, determine maximal value and the minimum value of fissure zone height value;

Step 4-3, repeating step 4-2 are until complete all lingering effect factors determining for fissure zone effect of altitude;

In the embodiment of the present invention, the impact analysis of each influence factor to fissure zone height:

(1) adopt the thick impact analysis to fissure zone height

Derived by formula (8) that to adopt thick and funtcional relationship fissure zone height be y=5.164x ₁+ 30.44, when adopt thick variation range while changing between 2.1m～7.52m, the height change scope of fissure zone is 41.28m～69.27m.

(2) impact analysis of hard rock lithologic proportion coefficient to fissure zone height

The funtcional relationship of being derived hard rock lithologic proportion coefficient and fissure zone height by formula (8) is y=15.496x ₂+ 45.27, when the variation range of hard rock lithologic proportion coefficient is 0.18～1, the height change scope of fissure zone is 48.06m～60.77m.

(3) adopt the dark impact analysis to fissure zone height

Deriving the funtcional relationship of adopting dark and fissure zone height by formula (8) is y=0.022x ₂+ 44.76, when adopting dark variation range at 86.1m～679m, the height change scope of fissure zone is 46.65m～59.70m.

Step 4-4, according to the reference value, fissure zone height value of calculating the fissure zone height obtaining corresponding maximal value and minimum value in the variation range of influence factor, determine the susceptibility of the each factor of residue;

The susceptibility formula that calculates the each factor of residue is as follows;

${\mathrm{\η}}_{\left(c_j\right)}=\max \left\{\right[(S{\left(c_j\right)}_{\max }-S^{*})/S^{*}],[(S^{*}-S{\left(c_j\right)}_{\min })/S^{*}\left]\right\}---\left(5\right)$

Wherein,

represent influence factor c _jsusceptibility, wherein, c _jrepresent remaining influence factor, j=1,2 ..., m, m represents lingering effect factor number; S ^*represent fissure zone altitude datum value; S (c _j) _maxrepresent influence factor c _jthe maximal value of fissure zone height in its span, S (c _j) _minrepresent influence factor c _jthe minimum value of fissure zone height in its span;

In the embodiment of the present invention, its susceptibility is obtained respectively in the susceptibility definition providing according to formula (5) in the variation range of each factor shown in table 2, and result is as shown in table 3.As can be seen from Table 3, in three factors, adopt thick the most responsively to fissure zone height, hard rock lithologic proportion coefficient takes second place, be then adopt dark, wherein hard rock lithologic proportion coefficient with adopt dark susceptibility and approach.

The susceptibility of the each factor of table 3 to fissure zone height

Step 5, according to the lingering effect factor obtaining for the susceptibility of fissure zone height, be optimized deleting the regression model obtaining after not appreciable impact factor;

Step 5-1, set up susceptibility forecast model, formula is as follows:

η _j△(c _j)/c _j ^*=△S(c _j)/S ^* (6)

Wherein, △ S (c _j) be illustrated in influence factor c _jin situation, fissure zone height change value, △ (c _j) expression influence factor c _jchanging value, c _j ^*for influence factor c _jreference value;

Formula (6) is sued for peace, obtain formula as follows;

$S\left(c\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{S}^{*}{\mathrm{\η}}_j(c_j-{c_j}^{*})/{c_j}^{*}+S^{*}---\left(7\right)$

Wherein, S (c) represents the fissure zone height of prediction; η _jrepresent influence factor c _jsusceptibility; c _jrepresent the value of influence factor, c _j ^*for influence factor c _jreference value;

Step 5-2, according to residue each influence factor susceptibility and reference value, substitution obtain susceptibility forecast model, obtain optimize after fissure zone Height Prediction model;

In the embodiment of the present invention, determined the Prediction Model of fissure zone height by formula (7) according to table 2 and table 3, called after DM-L model:

H _li=22.080+3.741C ₁+14.648C ₂+0.018C ₃ (9)

In formula, H _lifor fissure zone Height Prediction value, C ₁for optimize in rear model adopt thick, C ₂for optimizing the hard rock lithologic proportion coefficient in rear model, C ₃for optimizing adopting deeply in rear model, wherein the span of each influence factor is in table 2.

Step 6, gather that adopting of tested mine is thick, hard rock lithologic proportion coefficient, workplace span and adopt deeply, in the fissure zone Height Prediction model after the optimization that substitution obtains, obtain the prediction fissure zone height of tested mine;

Step 7, judge that prediction fissure zone height whether in the safe range of setting, if so, can continue exploitation and produce, adopt thick or carry out filling mining otherwise need to reduce.

In the embodiment of the present invention, the safety practice of taking is specific as follows:

(1) if fissure zone height involves the aquitard covering, should strengthen mine drainage facility power, accomplish that water burst discharges at any time, assurance personnel safety in production;

(2) if fissure zone height involves superincumbent stratum for compared with strong aquifer, should strengthen the Real-Time Monitoring of mine inflow, carry out in advance and the safety practice such as prevent, withdraw;

(3) if fissure zone height is excessive, stay the protection coal column of establishing can not play impermeable role, should forbid exploitation, in order to avoid cause casualties and accident generation.

In the embodiment of the present invention, DM-L model is applied to and adopts thick scope is between 2.1～7.52m, and hard rock lithologic proportion coefficient is between 0.18～1, and adopting is between 86.1～679m deeply.

The measured data that the fissure zone height that table 4 is collected for investigation is grown.

Table 4 fissure zone developmental state statistical form

The formula that calculates fissure zone height in " three times " rules is as following table 5.

Fissure zone high computational formula in table 5 " three times " rules

In table, M represent in " three times " rules formula adopt thick;

In table 4, on each actual measurement parameter basis, estimate result and the comparative analysis of measured data row with " three times " rules formula and DM-L model, in table 6, what wherein " three times " rules computing formula result was selected is that computational accuracy is the highest.

Table 6 is estimated resultant error contrast table

By in table 6, the final prediction error of the computing formula of " three times " rules and DM-L Prediction Model contrasts known, and the precision of DM-L Prediction Model will be higher than the result of calculation of " three times " rules.And the obvious distortion of computing formula result of calculation in No. 3 and 4 numbers " three times " rules.In production practices, to estimate the height of fissure zone, can calculate by DM-L Prediction Model.

Claims (2)

1. the fissure zone Height Prediction method based on sensitivity analysis, is characterized in that, comprises the following steps:

Step 1, gather the historical mine data of many groups, every group of data comprise adopts thick, hard rock lithologic proportion coefficient, workplace span and adopts dark four kinds of influence factors;

Step 2, employing Multielement statistical analysis method are determined the relation between influence factor and fissure zone height, specific as follows:

Step 2-1, set up and adopt thick, hard rock lithologic proportion coefficient, workplace span, adopt the regression model between dark and fissure zone height:

y _t=β ₀+β ₁x _t1+β ₂x _t2+β ₃x _t3+β ₄x _t4+ε _t(t=1,2,…,n) (1)

Wherein, y _trepresent the fissure zone height of t group data prediction; β ₀represent constant; β ₁represent to adopt the coefficient of thick influence factor; β ₂represent the coefficient of hard rock lithologic proportion coefficient, β ₃represent the coefficient of workplace span, β ₄represent to adopt dark coefficient; x _t1represent that adopting of t group data is thick; x _t2represent the hard rock lithologic proportion coefficient of t group data; x _t3represent the workplace span of t group data; x _t4represent that adopting of t group data is dark; ε _trepresent stochastic error; N represents total group of number of image data;

Step 2-2, the regression model that four factor value substitutions in the historical data gathering are set up, utilize criterion of least squares to calculate the coefficient that obtains each influence factor, complete the foundation of regression model, complete the relation of determining between influence factor and fissure zone height;

Step 3, carry out significance test to calculating the coefficient of each influence factor obtaining:

Step 3-1, suppose that the numerical value of the coefficient of a certain influence factor is 0, formula is as follows:

Suppose:

β _i=0 (2)

Wherein, β _irepresent the coefficient of a certain influence factor, i=1,2 ..., 4;

Step 3-2, calculating hypothesis are deleted factor beta _ithe regression sum of square of the regression model of gained after corresponding influence factor, with the difference P of regression sum of square of the regression model of setting up _i, formula is as follows:

$P_i={{\widehat{\mathrm{\β}}}_i}^2/l^{\mathrm{ii}}---\left(3\right)$

Wherein, P _irepresent sum of squares of partial regression, hypothesis is deleted factor beta _ithe regression sum of square of the regression model of gained after corresponding influence factor, with regression sum of square poor of the regression model of setting up;

represent the least squares estimator of coefficient vector β, $\widehat{\mathrm{\β}}=\left[\begin{array}{c}{\widehat{\mathrm{\β}}}_0\\ {\widehat{\mathrm{\β}}}_1\\ \·\·\·\·\\ {\widehat{\mathrm{\β}}}_4\end{array}\right],$ According to

determine β _icorresponding

l ⁱⁱrepresenting matrix L ^-1i diagonal element, wherein,

represent the data matrix of former data matrix X centralization, wherein $C=\left[\begin{array}{ccccc}1& x_{11}& x_{12}& \·\·\·& x_{14}\\ 1& x_{21}& x_{22}& \·\·\·& x_{24}\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ 1& x_{n1}& x_{n2}& \·\·\·& x_{n4}\end{array}\right],$ $X=\left[\begin{array}{ccccc}& x_{11}& x_{12}& \·\·\·& x_{14}\\ & x_{21}& x_{22}& \·\·\·& x_{24}\\ & \·& \·& & \·\\ & \·& \·& & \·\\ & \·& \·& & \·\\ & x_{n1}& x_{n2}& \·\·\·& x_{n4}\end{array}\right],$ $Y=\left[\begin{array}{c}{y}_1\\ y_2\\ \·\\ \·\\ \·\\ y_n\end{array}\right];$

Step 3-3, the hypothesis obtaining according to calculating are deleted factor beta _ithe difference P of the regression sum of square of the regression sum of square of rear gained regression model and the regression model of foundation _i, matrix of coefficients β residual sum of squares (RSS) Q and image data total group of number, determine the coefficient test statistics of each influence factor;

Test statistics formula is as follows:

$F_i=\frac{P_i}{Q/(n-4-1)}---\left(4\right)$

Wherein, Q represents the residual sum of squares (RSS) of matrix of coefficients β;

The test statistics of each influence factor that step 3-4, judgement calculating obtain is more than or equal to the probability of test statistics setting value, and then acquisition significance probability value, if significance probability value is greater than significance probability setting value, this influence factor is significant for the impact of fissure zone height, needs to retain; Otherwise this influence factor is inapparent for the impact of fissure zone height, need to delete this influence factor;

The regression model after not appreciable impact factor is deleted in step 3-5, acquisition;

Step 4, employing sensitivity analysis method are determined the susceptibility of the rear lingering effect factor of deletion for fissure zone height;

Step 4-1, determine the value of lingering effect factor in mine historical data, and then the variation range of definite lingering effect factor value calculate mean values, reference value using this mean values as corresponding influence factor, and the reference value substitution of each influence factor is deleted in the regression model after not appreciable impact factor, obtain fissure zone altitude datum value;

Step 4-2, in lingering effect factor, choose at random an influence factor, according to deleting the regression model that obtains after not appreciable impact factor and the reference value of other influences factor, determine the impact for fissure zone height of the influence factor chosen;

Delete in the regression model obtaining after not appreciable impact factor by the reference value substitution of other influences factor, the relational expression of the influence factor that acquisition is chosen and fissure zone height, and according to the variation range of the influence factor value of choosing, determine maximal value and the minimum value of fissure zone height value;

Step 4-3, repeating step 4-2 are until complete all lingering effect factors determining for fissure zone effect of altitude;

Step 4-4, according to the reference value, fissure zone height value of calculating the fissure zone height obtaining corresponding maximal value and minimum value in the variation range of influence factor, determine the susceptibility of the each factor of residue;

The susceptibility formula that calculates the each factor of residue is as follows:

${\mathrm{\η}}_{\left(c_j\right)}=\max \left\{\right[(S{\left(c_j\right)}_{\max }-S^{*})/S^{*}],[(S^{*}-S{\left(c_j\right)}_{\min })/S^{*}\left]\right\}---\left(5\right)$

Wherein,

represent influence factor c _jsusceptibility, wherein, c _jrepresent remaining influence factor, j=1,2 ..., m, m represents lingering effect factor number; S ^*represent fissure zone altitude datum value; S (c _j) _maxrepresent influence factor c _jthe maximal value of fissure zone height in its span, S (c _j) _minrepresent influence factor c _jthe minimum value of fissure zone height in its span;

Step 5, according to the lingering effect factor obtaining for the susceptibility of fissure zone height, be optimized deleting the regression model obtaining after not appreciable impact factor;

Step 5-1, set up susceptibility forecast model, formula is as follows:

η _j△(c _j)/c _j ^*=△S(c _j)/S ^* (6)

Wherein, △ S (c _j) be illustrated in influence factor c _jin situation, fissure zone height change value, △ (c _j) expression influence factor c _jchanging value, c _j ^*for influence factor c _jreference value;

Formula (6) is sued for peace, obtains formula as follows:

$S\left(c\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{S}^{*}{\mathrm{\η}}_j(c_j-{c_j}^{*})/{c_j}^{*}+S^{*}---\left(7\right)$

Wherein, S (c) represents the fissure zone height of prediction; η _jrepresent influence factor c _jsusceptibility; c _jrepresent the value of influence factor, c _j ^*for influence factor c _jreference value;

Step 5-2, according to residue each influence factor susceptibility and reference value, substitution obtain susceptibility forecast model, obtain optimize after fissure zone Height Prediction model;

Step 6, gather that adopting of tested mine is thick, hard rock lithologic proportion coefficient, workplace span and adopt deeply, in the fissure zone Height Prediction model after the optimization that substitution obtains, obtain the prediction fissure zone height of tested mine;

Step 7, judge that prediction fissure zone height whether in the safe range of setting, if so, can continue exploitation and produce, adopt thick or carry out filling mining otherwise need to reduce.

2. the fissure zone Height Prediction method based on sensitivity analysis according to claim 1, is characterized in that, the test statistics setting value described in step 3-4, and its span is 0.6～0.8; Described significance probability setting value, its value is 0.95.

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