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        基于Matlab的概率積分法開采沉陷預(yù)計(jì)參數(shù)解算

        2015-03-20 06:59:22徐良驥秦長才
        金屬礦山 2015年9期
        關(guān)鍵詞:積分法監(jiān)測(cè)點(diǎn)反演

        沈 震 徐良驥 劉 哲 秦長才

        (安徽理工大學(xué)測(cè)繪學(xué)院,安徽 淮南 232000)

        基于Matlab的概率積分法開采沉陷預(yù)計(jì)參數(shù)解算

        沈 震 徐良驥 劉 哲 秦長才

        (安徽理工大學(xué)測(cè)繪學(xué)院,安徽 淮南 232000)

        通過在開采工作面地表建立觀測(cè)站獲取地表變形數(shù)據(jù)解算概率積分法開采沉陷預(yù)計(jì)參數(shù),從而預(yù)計(jì)工作面周邊或相似開采條件下工作面的開采沉陷并評(píng)估和指導(dǎo)開采作業(yè),其前提是精確獲取概率積分法開采沉陷預(yù)計(jì)參數(shù)。為此,基于Matlab軟件,采用最小二乘法擬合觀測(cè)點(diǎn)變形數(shù)據(jù)解算概率積分法開采沉陷預(yù)計(jì)參數(shù),并結(jié)合Matlab軟件繪圖工具開發(fā)了集數(shù)據(jù)載入、坐標(biāo)轉(zhuǎn)換、參數(shù)解算、結(jié)果輸出、開采沉陷預(yù)計(jì)及反演為一體的可視化開采沉陷預(yù)計(jì)系統(tǒng)。以淮南謝橋煤礦11316工作面為例,根據(jù)地表移動(dòng)觀測(cè)點(diǎn)位移數(shù)據(jù)解算開采沉陷預(yù)計(jì)參數(shù)并與實(shí)測(cè)值進(jìn)行對(duì)比分析,結(jié)果表明,該系統(tǒng)解算出的開采沉陷預(yù)計(jì)參數(shù)符合兩淮礦區(qū)開采沉陷的基本規(guī)律,反演結(jié)果與實(shí)測(cè)值基本吻合,該系統(tǒng)對(duì)于實(shí)現(xiàn)礦區(qū)開采沉陷高精度預(yù)計(jì)和反演具有一定的參考價(jià)值。

        開采沉陷 概率積分法 開采沉陷預(yù)計(jì)系統(tǒng) 最小二乘法 Matlab

        開采沉陷會(huì)改變礦區(qū)原始地表狀態(tài),對(duì)礦區(qū)環(huán)境及周邊居民生產(chǎn)生活造成影響,因此有必要對(duì)開采沉陷進(jìn)行精確預(yù)計(jì)以便有計(jì)劃地進(jìn)行開采作業(yè)[1-3]。開采沉陷的預(yù)計(jì)方法有概率積分法、負(fù)指數(shù)函數(shù)法,典型曲線法等,其中概率積分法應(yīng)用較廣泛[4-6]。本研究借助Matlab軟件豐富的內(nèi)置函數(shù)與強(qiáng)大的數(shù)據(jù)處理功能,實(shí)現(xiàn)根據(jù)任意點(diǎn)變形量解算概率積分法開采沉陷預(yù)計(jì)參數(shù),并結(jié)合該軟件的繪圖工具開發(fā)出可視化開采沉陷預(yù)計(jì)系統(tǒng)。

        1 系統(tǒng)主要功能

        1.1 概率積分法模型

        以自定義函數(shù)的形式建立概率積分法模型,并保存在單獨(dú)的M文件中,該模型程序代碼如下:

        Function Wz= probability_integration_method (data2,xy)

        l=data1 (1)-data2 (3)-data2 (4);

        L=data1 (2)-data2 (5)-data2 (6))*sin (data2 (7) +data1 (3))/sin (data2 (7));

        CX=1/2*(erf(pi^(1/2)*xy(:,1)*data2(2)/data1(4))-erf(pi^(1/2)*(xy(:,1)-l)*data2(2)/data1(4)));

        CY=1/2*(erf(pi^(1/2)*xy(:,2)*data2(2)/data1(5))-erf(pi^(1/2)*(xy(:,2)-L)*data2(2)/data1(6)))

        Wmax=data1 (7)*data2 (1)*cos (data1 (3));

        WZ=Wmax*CX.*CY.

        (1)已知參數(shù)。包括L0、L1、a、H0、H1、H2和M。L0、L1分別為走向和傾向線長度,m;a為煤層傾角,(°);H0為平均開采深度,m;H1、H2分別為下山及上山方向開采深度,m;M為煤層開采厚度,m。已知參數(shù)以向量的形式保存于“data1”中,調(diào)用時(shí)按順序記為data1(n)。

        (2)預(yù)計(jì)參數(shù)。包括q、tanβ、S1、S2、S3、S4和θ0。q為下沉系數(shù);tanβ為主要影響角正切值;S1、S2為走向線兩端拐點(diǎn)偏距,m;S3、S4為傾向線下山和上山方向拐點(diǎn)偏距,m;θ0為影響傳播角,(°)[7]。待求參數(shù)以向量形式保存于“data2”中。

        (3)點(diǎn)坐標(biāo)。地表觀測(cè)點(diǎn)在工作面坐標(biāo)系中的坐標(biāo)為(x,y)。

        1.2 數(shù)據(jù)載入和坐標(biāo)轉(zhuǎn)換

        將所有觀測(cè)點(diǎn)的坐標(biāo)值、下沉量和水平移動(dòng)量按一定格式保存于Excel或.txt文檔中,通過“xlsread”、“textread”等命令讀取數(shù)據(jù)。Matlab軟件可將所有數(shù)據(jù)保存在一個(gè)矩陣中,按需要從該矩陣中提取坐標(biāo)值、下沉量和平移量等信息,并保存在相應(yīng)的數(shù)據(jù)矩陣中,便于調(diào)用[8]。

        概率積分法通常采用獨(dú)立坐標(biāo)系(工作面坐標(biāo)系)預(yù)計(jì)開采沉陷。開采工作面多為矩形,以工作面的西南端點(diǎn)為原點(diǎn),X軸沿工作面走向線方向,Y軸沿工作面傾向線方向并與X軸垂直,建立工作面坐標(biāo)系,見圖1。圖1中,矩形ABCD為開采工作面,XOY為測(cè)量坐標(biāo)系,X′O′Y′為工作面坐標(biāo)系[9-10]。

        圖1 工作面坐標(biāo)系

        坐標(biāo)轉(zhuǎn)換時(shí)將點(diǎn)D在XOY坐標(biāo)系中的坐標(biāo)作為平移參數(shù),在CAD軟件中量取工作面的傾斜角度作為旋轉(zhuǎn)參數(shù)(如無特殊要求可不考慮尺度參數(shù))。當(dāng)工作面范圍較大時(shí),也可根據(jù)2個(gè)或2個(gè)以上公共點(diǎn)在2套坐標(biāo)系中的坐標(biāo),采用最小二乘法求解坐標(biāo)轉(zhuǎn)換參數(shù),坐標(biāo)轉(zhuǎn)換模型為[11-12]

        (1)

        式中,(x′,y′)、(x,y)分別為點(diǎn)E在XOY測(cè)量坐標(biāo)系和X′O′Y′工作面坐標(biāo)系中的坐標(biāo);α為旋轉(zhuǎn)角度,(°);x0、y0為平移參數(shù),m。

        將獲取的坐標(biāo)轉(zhuǎn)換參數(shù)以向量形式保存于“p1”中,定義坐標(biāo)轉(zhuǎn)換函數(shù),程序代碼如下:

        Function x1=coordinate_transformation (p1,X0)

        for k=1:length(X0);

        X1(k,:) = (X0(k,:)-[p1 (1),p1 (2)]) ;

        X1(k,:) = [cos (p1 (3)),sin (p1 (3));-sin (p1 (3)),cos (p1 (3))]*X1(k,:)′.

        end

        調(diào)用函數(shù)“coordinate_transformation”可完成由測(cè)量坐標(biāo)系至工作面坐標(biāo)系的轉(zhuǎn)換。

        1.3 解算概率積分法預(yù)計(jì)參數(shù)

        監(jiān)測(cè)點(diǎn)在工作面坐標(biāo)系中的坐標(biāo)為(x,y),實(shí)際下沉量為z,采用最小二乘法進(jìn)行曲面擬合,經(jīng)過多次迭代求取1組參數(shù),使得擬合曲面與實(shí)測(cè)結(jié)果偏差的平方和最小,數(shù)學(xué)模型為[13-14]

        (2)

        式中,V1為各監(jiān)測(cè)點(diǎn)實(shí)測(cè)下沉量與最小二乘擬合值的偏差,m;V2為各監(jiān)測(cè)點(diǎn)實(shí)測(cè)水平變形量與最小二乘擬合值的偏差,m;k為監(jiān)測(cè)點(diǎn)數(shù)目;Wzk、Uk分別為各監(jiān)測(cè)點(diǎn)實(shí)測(cè)下沉和水平變形量,m;W(x,y),U(x,y)分別為各監(jiān)測(cè)點(diǎn)實(shí)測(cè)下沉和水平變形量的最小二乘擬合值,m,可調(diào)用Matlab軟件中的“l(fā)sqcurvefit”函數(shù)[15]進(jìn)行擬合得到。程序代碼如下:

        X1=coordinate_transformation (p1,X0);

        ff=optimset; ff.MaxFunEvals=2^12; ff.TolFun=1e-10; ff.TolX=1e-10;

        [data2,resnorm,residual]=lsqcurvefit (@probability_integration_method,data0,X1,Wz).

        程序中,“X1”、“Wz”為監(jiān)測(cè)點(diǎn)在工作面坐標(biāo)系下的坐標(biāo)和對(duì)應(yīng)的下沉量;“data0”為參數(shù)迭代初始值包含了7個(gè)變量,其格式與“data2”一致,初值的選取直接影響預(yù)計(jì)參數(shù)的解算精度,可參考開采工作面地質(zhì)及技術(shù)資料確定[16]。函數(shù)返回值包括預(yù)計(jì)參數(shù)的擬合最佳值(data2)、監(jiān)測(cè)點(diǎn)擬合殘差(residual)、監(jiān)測(cè)點(diǎn)擬合殘差的平方和(resnorm),將解算所得參數(shù)作為已知值,根據(jù)水平移動(dòng)量可解算監(jiān)測(cè)點(diǎn)水平移動(dòng)參數(shù)。

        1.4 開采沉陷反演及預(yù)計(jì)

        解算出開采沉陷預(yù)計(jì)參數(shù)后,將已知參數(shù)和預(yù)計(jì)參數(shù)代入概率積分法模型計(jì)算開采沉陷區(qū)域內(nèi)的地表變形量,并采用Matlab軟件中的“ezmesh”、“ezcontour”函數(shù)繪制下沉曲面及下沉等值線圖,從而預(yù)計(jì)或反演地表變形結(jié)果,程序代碼如下[17-21]:

        syms x; syms y;

        xy=[x,y]

        ezmesh (coordinate_transformation(data2,x,y),[min_x,max_x],[ min_y,max_y]);

        ezcontour (coordinate_transformation(data2,x,y),[min_x,max_x],[ min_y,max_y]);

        程序中,“min_x”、“max_y”分別為X、Y軸上的繪圖邊界,繪圖結(jié)果見圖2、圖3。

        圖2 預(yù)計(jì)下沉曲面

        2 應(yīng)用實(shí)例

        2.1 開采沉陷預(yù)計(jì)參數(shù)解算

        以淮南礦區(qū)謝橋礦11316工作面為例,工作面走向長1 980 m,傾向長240 m,煤層傾角15°,平均采深718.3 m,煤層開采厚度3.9 m。地表移動(dòng)觀測(cè)站共設(shè)置2條觀測(cè)線,計(jì)87個(gè)測(cè)點(diǎn),選取其中30個(gè)有較高精度并能反映工作面地表變形特點(diǎn)的監(jiān)測(cè)點(diǎn)實(shí)測(cè)數(shù)據(jù)作為解算數(shù)據(jù),見表1。根據(jù)礦區(qū)預(yù)計(jì)參數(shù)經(jīng)驗(yàn)值,取迭代初始值data0=[0.7;2;25;25;10;5; 1.31]進(jìn)行最小二乘擬合,可得q=0.798,tanβ= 1.755,S1=35.97,S2=35.47,S3=9.996、S4=4.996,θ0=1.133。

        圖3 地表下沉等值線

        表1 11316工作面部分觀測(cè)點(diǎn)實(shí)測(cè)數(shù)據(jù)

        Table1 Part of measured date at observation points of 11316 working face m

        點(diǎn) 號(hào)XY下沉量ml01-14.41130.850.793ml0217.00139.570.885ml0347.85135.891.010ml0476.58136.241.131ml08225.37132.861.642ml10346.98135.541.670ml11377.39128.581.661ml17555.05126.511.457ml18585.66128.761.695ml21675.94120.781.717ml23826.03137.071.637ml24856.07134.051.661ml291215.86136.741.689ml301245.91139.921.702ml311275.38133.611.716ml331335.98137.941.638ml351396.63123.481.923ml371456.57138.791.668ml401577.31133.361.613ml411606.03126.611.648ml461876.96122.240.984ml471906.16131.590.817ml491965.44134.130.619ms03939.2621.011.519ms04944.1843.191.445ms07947.51102.591.614ms10950.25162.651.550ms11938.92183.511.583ms13954.14221.461.501ms14941.84242.971.411

        2.2 預(yù)計(jì)參數(shù)驗(yàn)證及地表移動(dòng)變形規(guī)律反演

        將開采沉陷預(yù)計(jì)參數(shù)代入概率積分法模型計(jì)算上述30個(gè)監(jiān)測(cè)點(diǎn)的地表變形量的最小二乘擬合值,并與實(shí)測(cè)數(shù)據(jù)進(jìn)行對(duì)比,計(jì)算擬合殘差,結(jié)果見表2。

        表2 觀測(cè)點(diǎn)擬合殘差

        Table.2 Fitting residual of observation points m

        點(diǎn)號(hào)殘差點(diǎn)號(hào)殘差點(diǎn)號(hào)殘差ml01-0.01ml230.04ml46-0.01ml020.02ml240.02ml470.03ml030.02ml29-0.01ml49-0.01ml040.01ml30-0.02ms03-0.13ml08-0.10ml31-0.03ms040.05ml10-0.02ml330.04ms070.05ml110.01ml35-0.24ms100.10ml170.23ml370.01ms110.02ml18-0.01ml400.03ms13-0.04ml21-0.03ml41-0.02ms14-0.05

        根據(jù)擬合值和擬合殘差計(jì)算擬合決定系數(shù),公式為

        (3)

        式中,SSR為擬合值平方和,m2;SSE為殘差平方和,m2。

        將相關(guān)數(shù)值代入式(3),計(jì)算得R2=0.997 5,擬合程度較好,擬合值與實(shí)測(cè)值(表1)較為接近。

        采用概率積分法對(duì)11316工作面開采沉陷進(jìn)行反演,并將反演結(jié)果與實(shí)測(cè)值進(jìn)行對(duì)比,結(jié)果見表3。

        表3 概率積分法反演結(jié)果與實(shí)測(cè)值比較

        由表3可知,由反演得到的最大下沉值與實(shí)測(cè)值的誤差僅為0.242 m,其余變形參數(shù)反演值和實(shí)測(cè)值也較為接近。對(duì)原始觀測(cè)數(shù)據(jù)進(jìn)行分析可知,達(dá)到充分下沉的下沉盆地內(nèi)監(jiān)測(cè)點(diǎn)實(shí)測(cè)下沉量為1.60~1.72 m,最大下沉值(1.923 m)對(duì)應(yīng)的是ml35點(diǎn),為異常點(diǎn)。據(jù)此可認(rèn)為,本研究開發(fā)的開采沉陷預(yù)計(jì)系統(tǒng)能夠滿足礦區(qū)地表沉陷預(yù)計(jì)的精度要求。

        3 結(jié) 語

        基于Matlab軟件,開發(fā)了開采沉陷預(yù)計(jì)系統(tǒng),該系統(tǒng)采用最小二乘法擬合觀測(cè)點(diǎn)變形數(shù)據(jù)解算概率積分法開采沉陷預(yù)計(jì)參數(shù)?;茨现x橋煤礦11316工作面試驗(yàn)結(jié)果表明,該系統(tǒng)對(duì)于礦區(qū)地表沉陷的預(yù)計(jì)精度較高。

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        (責(zé)任編輯 王小兵)

        Calculating on the Prediction Parameters of Mining Subsidence with Probability Integral Method Based on Matlab

        Shen Zhen Xu Liangji Liu Zhe Qin Changcai

        (SchoolofGeodesyandGeomatics,AnhuiUniversityofScience&Technology,Huainan232000,China)

        The prediction parameters of mining subsidence are calculated by the probability integral method of the surface deformation data obtained by the observation stations established on the surface of mining working face,and the mining subsidence of the surrounding area of mining working face or the mining working face under the similar mining conditions are predicted to conduct evaluation and guidance on the mining operation.Therefore,obtaining the prediction parameters of mining subsidence with high precision is the precondition of prediction and inversion of mining subsidence prediction.Based on Matlab software,the deformation data of observation points are fitted by the least square method to calculate the prediction parameters of mining subsidence with probability integral method.Combing with the drawing tools of Matlab software,the mining subsidence visualization system with the functions of data loading,coordinate transformation,calculation parameters,the output of calculation results,prediction and inversion of mining subsidence is developed.Taking the 11316 working face of Xieqiao coal mine,Huainan city as the research example,according to the deformation data of the observation points of the surface observation stations,the prediction parameters of mining subsidence are calculated,and comparison between predicted parameters and measured parameters is conducted.The results show that the predicted parameters calculated by the mining subsidence visualization system is consistent with the basic rules of the mining subsidence in Huainan & Huaibei mining area,and the inversion results of the mining subsidence visualization system is identical to the measured parameters.The mining subsidence visualization system can provide reference for realizing the prediction and inversion of mining subsidence with high precision.

        Mining subsidence,Probability integral method,Mining subsidence prediction system,Least square method,Matlab

        2015-06-04

        安徽省對(duì)外科技合作計(jì)劃項(xiàng)目(編號(hào):1503062020),國家自然科學(xué)基金項(xiàng)目(編號(hào):41472323)。

        沈 震(1990—),男,碩士研究生。通訊作者 徐良驥(1978—),男,副教授,博士,碩士研究生導(dǎo)師。

        TD325

        A

        1001-1250(2015)-09-170-05

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