全國大學生數(shù)學建模競賽論文選之煤礦瓦斯和煤塵的監(jiān)測與控制

D題：煤礦瓦斯和煤塵的監(jiān)測與控制摘要近年來，煤礦安全事故頻發(fā)，煤礦安全生產(chǎn)是我國目前亟待解決的問題之一，做好井下瓦斯和煤塵的監(jiān)測與控制是實現(xiàn)安全生產(chǎn)的關(guān)鍵環(huán)節(jié)，同時對瓦斯和煤塵監(jiān)測數(shù)據(jù)進行科學處理顯得更加重要。第一問的求解，我們根據(jù)《煤礦安全規(guī)程》，由風速和瓦斯檢測數(shù)據(jù)求出礦井最大絕對瓦斯涌出量max=10.9452和最大相對瓦斯涌出量或max=/=25.3991，可以看出最大相對瓦斯涌出量max10成立，因此該礦為高瓦斯礦井。將危險性100%的標準設(shè)定為甲烷傳感器的斷電濃度或達到煤塵的爆炸下限濃度，（1）、由公式，得出升序排列的值和總監(jiān)測次數(shù)N的折線圖，以此設(shè)定瓦斯極限安全系數(shù)=0.5（當時發(fā)生爆炸）并統(tǒng)計的個數(shù)=235，可得瓦斯發(fā)生爆炸事故的概率=0.4352；（2）、用最小二乘法對數(shù)據(jù)進行3次多項式擬合，求出瓦斯?jié)舛扰c煤塵爆炸下限濃度最小值的關(guān)系，即擬合的3次多項式，根據(jù)此多項式和的值計算出相對應(yīng)的值（即的值），然后根據(jù)公式，得出升序排列值和總監(jiān)測次數(shù)N的折線圖，以此設(shè)定煤塵極限安全系數(shù)=0.4（當時發(fā)生爆炸），統(tǒng)計的個數(shù)=232，由公式計算出煤塵發(fā)生爆炸事故的概率=0.4296；（3）、計算該煤礦發(fā)生爆炸事故的概率，假設(shè)與是相互獨立的，由公式求得該煤礦發(fā)生爆炸事故的概率67.78%。根據(jù)公式，求得工作面和工作面所需要的風量為399.83和534.94，局部通風機的額定風量是183.575，該煤礦所需要的最佳（總）通風量是1342.014。關(guān)鍵詞瓦斯通風量最小二乘法不安全程度問題重述煤礦安全生產(chǎn)是我國目前亟待解決的問題之一，做好井下瓦斯和煤塵的監(jiān)測與控制是實現(xiàn)安全生產(chǎn)的關(guān)鍵環(huán)節(jié)。瓦斯是一種無毒、無色、無味的可燃氣體，其主要成分是甲烷，在礦井中它通常從煤巖裂縫中涌出。瓦斯爆炸需要三個條件：空氣中瓦斯達到一定的濃度；足夠的氧氣；一定溫度的引火源。煤塵是在煤炭開采過程中產(chǎn)生的可燃性粉塵。煤塵爆炸必須具備三個條件:煤塵本身具有爆炸性；煤塵懸浮于空氣中并達到一定的濃度；存在引爆的高溫熱源。試驗表明，一般情況下煤塵的爆炸濃度是30～2000g/m3，而當?shù)V井空氣中瓦斯?jié)舛仍黾訒r，會使煤塵爆炸下限降低，結(jié)果如表1所示。表1:瓦斯?jié)舛扰c煤塵爆炸下限濃度關(guān)系空氣中瓦斯?jié)舛?%)00.51.01.52.02.53.03.54煤塵爆炸下限濃度(g/m3)30~5022.5~37.515~2510.5~17.56.5~12.54.5~7.53~52.5~3.51.5~2.5國家《煤礦安全規(guī)程》給出了煤礦預防瓦斯爆炸的措施和操作規(guī)程，以及相應(yīng)的專業(yè)標準。規(guī)程要求煤礦必須安裝完善的通風系統(tǒng)和瓦斯自動監(jiān)控系統(tǒng)，所有的采煤工作面、掘進面和回風巷都要安裝甲烷傳感器，每個傳感器都與地面控制中心相連，當井下瓦斯?jié)舛瘸瑯藭r，控制中心將自動切斷電源，停止采煤作業(yè)，人員撤離采煤現(xiàn)場。圖1是有兩個采煤工作面和一個掘進工作面的礦井通風系統(tǒng)示意圖，結(jié)合表2的監(jiān)測數(shù)據(jù)，按照煤礦開采的實際情況研究下列問題：（1）根據(jù)《煤礦安全規(guī)程》第一百三十三條的分類標準，鑒別該礦是屬于“低瓦斯礦井”還是“高瓦斯礦井”。（2）根據(jù)《煤礦安全規(guī)程》第一百六十八條的規(guī)定，并參照表1，判斷該煤礦不安全的程度（即發(fā)生爆炸事故的可能性）為多大。（3）為了保障安全生產(chǎn)，利用兩個可控風門調(diào)節(jié)各采煤工作面的風量，通過一個局部通風機和風筒實現(xiàn)掘進巷的通風。根據(jù)圖1所示各井巷風量的分流情況、對各井巷中風速的要求（見《煤礦安全規(guī)程》第一百零一條），以及瓦斯和煤塵等因素的影響，確定該煤礦所需要的最佳（總）通風量，以及兩個采煤工作面所需要的風量和局部通風機的額定風量（實際中，井巷可能會出現(xiàn)漏風現(xiàn)象）。表2:各監(jiān)測點的風速,瓦斯和煤塵的監(jiān)測數(shù)據(jù)表（表格格式示例）監(jiān)測日期點與班次工作面Ⅰ工作面Ⅱ掘進工作面回風巷Ⅰ回風巷Ⅱ總回風巷日產(chǎn)量（t/d）風速瓦斯煤塵風速瓦斯煤塵風速瓦斯煤塵風速瓦斯煤塵風速瓦斯煤塵風速瓦斯煤塵1早班2.40.7182.070.947.672.220.267.442.130.767.522.090.977.05597中班2.560.628.42.080.857.512.290.267.452.270.667.932.10.897.275.360.67.28晚班2.240.667.612.090.827.512.40.297.622.090.77.075.310.636.8…早班………………中班…………………晚班………………[注]瓦斯的濃度：%，即體積百分比；煤塵的單位：g/m3；風速的單位：m/s；日產(chǎn)量的單位：t/d。采煤工作面Ⅱ掘進工作面局部通風機風筒待采煤層總回風巷回風巷II主巷道進風巷II采煤工作面Ⅱ掘進工作面局部通風機風筒待采煤層總回風巷回風巷II主巷道進風巷II掘進巷道放大示意圖待采煤層待采煤層回風巷I圖例局部通風機風量調(diào)節(jié)風門新鮮風流（進風）乏風流（回風）掘進工作面采煤工作面Ⅰ出風口進風口總進風巷待掘進的巷道進風巷I掘進巷道放大示意圖待采煤層待采煤層回風巷I圖例局部通風機風量調(diào)節(jié)風門新鮮風流（進風）乏風流（回風）掘進工作面采煤工作面Ⅰ出風口進風口總進風巷待掘進的巷道進風巷I圖1某煤礦的通風系統(tǒng)示意圖附圖:某煤礦通風系統(tǒng)示意圖圖注:主巷道斷面大約為5m2，其他各采煤區(qū)的進風巷、回風巷和掘進巷的斷面大約為4m2，掘進巷道中的風筒直徑為400mm。附圖:某煤礦通風系統(tǒng)示意圖符號說明--絕對瓦斯涌出量，或；--風量，；--瓦斯的濃度，%；--相對瓦斯涌出量，；--日產(chǎn)量，其中＝1,2,，30，；--甲烷傳感器的斷電濃度的最小值，%；--瓦斯?jié)舛扔绊懴碌拿簤m爆炸下限的最小值，；--檢測數(shù)據(jù)表（表2）中第天第班次第個監(jiān)測點檢測的瓦斯數(shù)據(jù)，其中=1,2,3，…，30；=1，2，3（早班，中班，晚班），=1，2，3，4，5，6（工作面，工作面，掘進工作面，回風巷，回風巷和總回風巷）%；--檢測數(shù)據(jù)表（表2）中第天第班次第個監(jiān)測點檢測的煤塵數(shù)據(jù)，其中=1,2,3，…，30；=1，2，3（早班，中班，晚班），=1，2，3，4，5，6（工作面，工作面，掘進工作面，回風巷，回風巷和總回風巷），；--檢測數(shù)據(jù)表（表2）中第天第班次第個監(jiān)測點檢測的風速數(shù)據(jù)，其中=1,2,3，…，30；=1，2，3（早班，中班，晚班），=1，2，3，4，5，6（工作面，工作面，掘進工作面，回風巷，回風巷和總回風巷），；--第個監(jiān)測點的斷面面積，其中=1，2，3，4，5，6（工作面，工作面，掘進工作面，回風巷，回風巷和總回風巷），；--第天第班次第個監(jiān)測點瓦斯發(fā)生爆炸事故的概率；--第天第班次第個監(jiān)測點煤塵發(fā)生爆炸事故的概率；--第個采煤工作面需要風量，；--第個采煤工作面瓦斯平均涌出量，；--第個采煤工作面因瓦斯涌出不均勻的備用風量系數(shù)；--掘進工作面的需風量，；--掘進工作面平均絕對瓦斯涌出量，；--掘進工作面瓦斯涌出不均勻的備用風量系數(shù)；模型假設(shè)瓦斯的主要成分是甲烷（），瓦斯的濃度即為甲烷的濃度。表2所測數(shù)據(jù)為準確數(shù)據(jù)，不考慮測量誤差。煤礦發(fā)生爆炸事故的原因只與瓦斯和煤塵的爆炸濃度有關(guān)，不考慮其他自然因素如溫度和水分及人為因素的影響。煤礦甲烷傳感器與地面控制中心相連，當井下瓦斯?jié)舛瘸瑯藭r，控制中心將自動切斷電源，停止采煤作業(yè)，人員撤離采煤現(xiàn)場，因此將甲烷傳感器的斷電濃度設(shè)為危險性100%；將煤塵的爆炸下限濃度設(shè)為危險性100%。模型建立鑒別該礦是屬于“低瓦斯礦井”還是“高瓦斯礦井”的問題根據(jù)《煤礦安全規(guī)程》第一百三十三條的分類標準，礦井相對瓦斯涌出量小于或等于10m3/t且礦井絕對瓦斯涌出量小于或等于40m3/min的為低瓦斯礦井，礦井相對瓦斯涌出量大于10m3/t或礦井絕對瓦斯涌出量大于40m3/min的為高瓦斯礦井。絕對瓦斯涌出量是指單位時間涌出的瓦斯體積，單位為或，其計算公式為：相對瓦斯涌出量是指平均日產(chǎn)一噸煤同期所涌出的瓦斯量，單位為，其計算公式為：或（取決于絕對瓦斯涌出量的單位）根據(jù)分類標準：若條件（1）同時成立，則該礦為低瓦斯礦井。若條件（2）中任一條件成立，則該礦為高瓦斯礦井。判斷該煤礦不安全的程度（即發(fā)生爆炸事故的可能性）的問題根據(jù)《煤礦安全規(guī)程》第一百六十八條的規(guī)定，并參照表1和假設(shè)3、4，煤礦發(fā)生爆炸事故只與瓦斯和煤塵的爆炸濃度有關(guān)，并且將甲烷傳感器的斷電濃度設(shè)為危險性100%；或者將煤塵的爆炸下限濃度設(shè)為危險性100%。從圖1和表2得出，該礦的數(shù)據(jù)來源僅限于工作面、工作面、掘進工作面、回風巷、回風巷和總回風巷，因此從原附件2中《煤礦安全規(guī)程》第一百六十八條中選取部分數(shù)據(jù)為表3，作為瓦斯?jié)舛任ｋU性的參照標準。表3甲烷傳感器的報警濃度、斷電濃度、復電濃度和斷電范圍（部分）甲烷傳感器設(shè)置地點報警濃度斷電濃度復電濃度斷電范圍低瓦斯和高瓦斯礦井的采煤工作面≥1.0%CH4≥1.5%CH4＜1.0%CH4工作面及其回風巷內(nèi)全部非本質(zhì)安全型電氣設(shè)備本規(guī)程第一百三十六條所規(guī)定的裝有礦井安全監(jiān)控系統(tǒng)的采煤工作面回風巷≥1.5%CH4≥1.5%CH4＜1.5%CH4工作面及其回風巷內(nèi)全部非本質(zhì)安全型電氣設(shè)備采用串聯(lián)通風的被串掘進工作面局部通風機前≥0.5%CH4≥0.5%CH4＜0.5%CH4被串掘進巷道內(nèi)全部非本質(zhì)安全型電氣設(shè)備（1）瓦斯發(fā)生爆炸事故的概率根據(jù)以上分析，第天第班次第個監(jiān)測點瓦斯發(fā)生爆炸事故的概率，其中：為已知監(jiān)測數(shù)據(jù)；由表3，當=1，2，4，5，6時，=1.5；當=3時，=0.5。經(jīng)過計算整理，數(shù)據(jù)組成一個新的數(shù)據(jù)表表4，用Excel軟件進行升序排列并作出關(guān)于和總監(jiān)測次數(shù)N（共540次）的折線圖2，依據(jù)圖2設(shè)定瓦斯極限安全系數(shù)（當時發(fā)生爆炸），統(tǒng)計表4中的個數(shù)，由下面公式計算出瓦斯發(fā)生爆炸事故的概率，其中（2）煤塵發(fā)生爆炸事故的概率分析同上，第天第班次第個監(jiān)測點煤塵發(fā)生爆炸事故的概率，其中：為已知監(jiān)測數(shù)據(jù)，因此關(guān)鍵是求出(瓦斯?jié)舛扔绊懴碌拿簤m爆炸下限的最小值),對表1進行處理取最小值得到表5：瓦斯?jié)舛扰c煤塵爆炸下限濃度最小值的關(guān)系。表5:瓦斯?jié)舛扰c煤塵爆炸下限濃度最小值關(guān)系空氣中瓦斯?jié)舛?%)00.51.01.52.02.53.03.54煤塵爆炸下限濃度最小值(g/m3)3022.51532.51.5以表5為依據(jù)，在Matlab中用最小二乘法對數(shù)據(jù)進行3次多項式擬合，求出瓦斯?jié)舛扰c煤塵爆炸下限濃度最小值的關(guān)系，即擬合的3次多項式，根據(jù)此多項式和表1中的的值計算出相對應(yīng)的系列的值（即的值），然后根據(jù)概率公式計算整理，數(shù)據(jù)組成一個新的數(shù)據(jù)表表6，用Excel軟件進行升序排列并作出關(guān)于和總監(jiān)測次數(shù)N（共540次）的折線圖3，依據(jù)圖3設(shè)定煤塵極限安全系數(shù)（當時發(fā)生爆炸），統(tǒng)計表6中的個數(shù)，由下面公式計算出煤塵發(fā)生爆炸事故的概率，其中（3）該煤礦發(fā)生爆炸事故的概率假設(shè)該煤礦中瓦斯發(fā)生爆炸事故的概率與煤塵發(fā)生爆炸事故的概率是相互獨立的，由相互獨立事件概率計算公式可求得該煤礦發(fā)生爆炸事故的概率。（三）確定該煤礦所需要的最佳（總）通風量，以及兩個采煤工作面所需要的風量和局部通風機的額定風量的問題根據(jù)中華人民共和國煤炭工業(yè)部1996年12月30日批準的《煤礦礦井風量計算方法》，風量計算原則是按該地區(qū)各個實際用風地點，分別計算出各個用風地點的實際最大需風量，從而求出該地區(qū)的風量總和，再考慮一定的備用風量系數(shù)后，作為該地區(qū)的供風量。（1）采煤工作面需風量的計算采煤工作面需風量應(yīng)按瓦斯涌出量、工作面進風流溫度及使用炸藥量等因素分別計算，最后取其最大值。由于本題除瓦斯涌出量外未給出其他條件，因此采煤工作面需風量只按瓦斯涌出量進行計算，公式為：其中：（2）掘進工作面需風量計算掘進工作面需風量計算應(yīng)按瓦斯涌出量、炸藥量及工作人員數(shù)量等因素分別計算，最后取其最大值。由于本題除瓦斯涌出量外未給出其他條件，因此掘進工作面需風量只按瓦斯涌出量進行計算，公式為：其中：（3）礦井總需風量計算礦井所需總風量是礦井井下各個用風地點需風量之和，并考慮漏風和配風不均勻等的備用風量系數(shù)，按下式進行計算：，其中為礦井內(nèi)部漏風和配風不均勻等的備用風量系數(shù)，通?？扇?.15~1.25。模型求解（一）該礦是屬于“高瓦斯礦井”依據(jù)表１中的監(jiān)測數(shù)據(jù)、和，根據(jù)絕對瓦斯涌出量計算公式和相對瓦斯涌出量計算公式，最終計算出絕對瓦斯涌出量和相對瓦斯涌出量。絕對瓦斯涌出量，其中：，。相對瓦斯涌出量由上面的計算最終得出表7：各檢測點的絕對瓦斯涌出量和相對瓦斯涌出量表7：各檢測點的絕對瓦斯涌出量和相對瓦斯涌出量日期與班次工作面Ⅰ工作面Ⅱ掘進工作面回風巷Ⅰ回風巷Ⅱ總回風巷絕對相對絕對相對絕對相對絕對相對絕對相對絕對相對1早班4.08969.20374.6699210.4731.385283.60573.885128.95884.9156811.22310.351524.1491中班3.809284.24321.428963.595684.48569.648晚班3.548164.113121.67043.661684.557610.03592早班3.377768.62994.243210.711.219923.07613.344648.57134.557611.4589.25223.5184中班3.643924.703041.428963.639365.0803210.3488晚班3.80164.48561.209123.765844.731849.89523早班4.249448.75844.485610.3781.483922.81764.063688.52914.810811.16410.587622.8275中班3.782884.614721.441443.848644.9120810.257晚班3.627364.715040.82563.442085.138889.54454早班3.714488.8244.815369.96971.644242.85233.595448.56915.08810.50610.546822.4546中班4.038483.594240.962163.958083.8168.9436晚班3.57124.38481.054083.443524.57929.32645早班3.425768.59074.2537610.4691.525443.14653.294728.19644.5710411.0469.534322.5731中班3.732484.10881.359363.593524.250889.3438晚班3.759124.942081.113843.5285.215929.80856早班3.957129.34984.888812.1961.08962.77543.566648.66025.1897612.91710.058424.9972中班3.671044.962721.15923.442085.1631210.2204晚班3.825365.0881.151043.65.4698410.34287早班3.96489.793.9362410.5731.219922.97983.711849.21034.2508811.2559.34224.0277中班3.97444.213441.264083.587524.477449.6348晚班3.93124.669921.128963.868084.9183210.15688早班3.824648.95914.0060810.0671.525443.11253.606728.4744.2508810.7119.451822.5847中班3.871924.01281.385283.529684.23369.3186晚班3.595684.669921.012323.544325.0169.69579早班3.384249.21364.9934410.6870.860162.32923.271688.98345.241611.3989.461123.3607中班3.867844.58640.934323.874.83369.9792晚班3.977043.444481.044243.806883.8169.030610早班3.68168.72624.4265610.0841.743362.96863.574088.4264.600810.79910.10122.6117中班3.794884.34521.230963.680644.725129.7278晚班3.794884.253760.860163.62884.62249.37811早班3.84728.8644.173129.66181.129922.91423.747368.60094.4642410.3459.48622.3642中班3.60364.062961.255683.492484.355049.4611晚班3.924724.163281.354323.7984.456329.753612早班3.640328.73174.414089.37361.012322.57533.30968.48844.658889.98459.10821.3655中班3.68164.08240.889443.62884.375688.9262晚班3.738243.37681.360323.81363.612489.028813早班3.922569.40564.8052810.5421.2843.00293.954729.20085.13611.33910.526423.9953中班4.038484.464241.112643.8524.81089.9696晚班4.031044.172161.432083.924244.5100810.09814早班3.49928.89723.8750410.8351.078562.8723.348488.52044.1632811.5968.772323.3544中班3.908165.541121.10883.711845.9188810.8054晚班3.825364.26361.438563.696724.55769.907215早班3.810249.38883.98169.80580.82442.9583.606729.05494.2628810.5938.77822.7564中班3.81364.26361.278723.6364.57929.5046晚班3.955683.848641.545123.924964.223049.783616早班3.987369.11674.07049.82531.524243.12653.92168.84154.4169610.6359.98422.9589中班3.765844.464241.18683.64.83369.867晚班3.81363.93121.255683.6964.242969.278117早班3.659049.04624.939211.7551.23843.15043.731768.65985.342412.49310.485624.803中班3.867845.117041.367283.574085.3157610.5晚班3.875044.760161.365123.609125.08810.276518早班3.79089.32724.586411.1570.906242.90883.676329.08714.9075211.9559.68424.2797中班3.817444.253761.2843.71284.60089.828晚班3.68164.664881.330563.610084.962729.876619早班4.072569.06994.731849.62971.5662.96863.7628.57175.0332810.2610.60822.2452中班3.659043.676321.154163.594244.01288.892晚班3.908163.949921.08963.644164.121289.04820早班3.68648.61854.7827210.0021.445043.45323.676328.46955.0846410.56610.454422.8847中班3.706563.676321.68483.646083.793929.2748晚班3.595684.293121.272963.476164.592649.448821早班3.908169.18344.2134410.9111.379042.93043.661688.70564.4265611.4819.597623.4382中班3.93124.861441.181283.7445.06410.0584晚班3.659044.58641.10883.49444.884489.690622早班3.655688.72734.6588810.5821.4222.71193.5528.50054.9819211.23510.041622.7688中班3.84724.18321.359363.812164.375689.6624晚班3.69724.73760.698883.54485.060889.51623早班3.68649.51284.7095211.8420.962883.03833.394569.27464.9120812.6669.469525.3991中班4.0864.958641.275123.91685.2876810.6692晚班3.88084.83841.483924.055.3164810.975224早班3.738248.45814.6147210.3091.70282.85943.54488.12724.838410.86110.291222.1198中班3.511684.664881.0083.410884.88889.393晚班3.76324.143361.012323.626644.414089.117625早班3.613689.06864.2537611.2411.08962.66983.443528.55544.5196811.8558.960423.27中班3.81364.73761.219683.4564.935369.5976晚班3.870725.013361.016883.759125.314810.432526早班3.706568.74924.121289.73831.29722.79933.368.39264.4582410.5019.41422.355中班3.851524.38481.01523.8344.73769.882晚班3.706564.0321.291683.611524.32489.48627早班3.88089.12084.03210.3491.278722.86973.6728.76014.324811.0459.369622.9401中班3.851524.986240.9723.81845.314810.0992晚班3.991684.2841.438083.769924.557610.018828早班4.04889.08584.5283210.5091.00322.22293.749288.72514.8278411.219.657922.4935中班3.784.564560.786243.6484.83369.342晚班3.623044.152481.012323.64.468329.351329早班3.91689.68434.96810.0561.489443.45463.731769.12645.342410.93710.86323.9679中班3.80643.459841.093683.6663.81848.6832晚班4.099683.848641.63443.7444.191849.714630早班3.437288.64614.939210.3711.07042.84693.541448.5495.2653610.96310.198523.017中班3.583444.152481.290243.476164.396329.414晚班4.14724.30441.316644.02484.4985610.1178max4.249449.795.5411212.1961.743363.60574.063689.27465.9188812.91710.975225.3991由表7得出：該礦絕對瓦斯涌出量的最大值=10.9452該礦相對瓦斯涌出量的最大值=25.3991根據(jù)分類標準的條件，得：，滿足條件（2），因此，該礦是屬于“高瓦斯礦井”。（二）該煤礦不安全的程度（即發(fā)生爆炸事故的可能性）為67.7846%（1）瓦斯發(fā)生爆炸事故的概率第天第班次第個監(jiān)測點瓦斯發(fā)生爆炸事故的概率，其中：為已知監(jiān)測數(shù)據(jù)；由表3，當=1，2，4，5，6時，=1.5；當=3時，=0.5。計算整理后，數(shù)據(jù)組成一個新的數(shù)據(jù)表表4：各監(jiān)測點瓦斯發(fā)生爆炸事故的概率，用Excel進行升序排列并作出關(guān)于和總監(jiān)測次數(shù)N（共540次）的折線圖2。表4各監(jiān)測點瓦斯發(fā)生爆炸事故的概率監(jiān)測工作面Ⅰ工作面Ⅱ掘進工作面回風巷Ⅰ回風巷Ⅱ總回風巷日期點與班次1早班0.47330.62670.52000.50670.65330.4467中班0.41330.56670.52000.44000.59330.4000晚班0.44000.54670.58000.48670.60000.42002早班0.41330.56670.46000.44670.60000.4000中班0.42000.61330.52000.45330.65330.4267晚班0.44000.59330.44000.47330.62000.41333早班0.52000.59330.54000.55330.63330.4533中班0.47330.61330.52000.50670.64670.4333晚班0.44000.62670.32000.47330.67330.42004早班0.44670.64000.62000.47330.66670.4533中班0.47330.48000.38000.50670.50000.3867晚班0.41330.58000.36000.45330.60000.38675早班0.40670.56000.56000.44000.59330.4067中班0.42670.53330.48000.46000.54670.3867晚班0.46000.66000.42000.50000.68670.43336早班0.48000.64670.40000.51330.68000.4400中班0.42670.65330.46000.47330.67330.4533晚班0.46000.66670.44000.50000.71330.45337早班0.46670.51330.46000.49330.54670.4000中班0.46000.56000.46000.49330.58670.4133晚班0.43330.62670.42000.47330.66000.42678早班0.42670.52000.56000.45330.54670.3933中班0.48670.53330.52000.51330.56000.4133晚班0.44000.62670.38000.47330.66670.42009早班0.39330.67330.32000.42670.70000.4067中班0.45330.60670.34000.50000.63330.4200晚班0.48670.46000.38000.51330.50000.386710早班0.43330.58000.64000.48670.60000.4333中班0.44670.56670.46000.48000.61330.4133晚班0.44670.56000.32000.48000.60000.400011早班0.46670.56000.44000.49330.59330.4133中班0.43330.54000.48000.45330.57330.4067晚班0.46000.55330.54000.50000.58670.426712早班0.42670.58670.38000.46670.61330.4000中班0.43330.54000.34000.48000.57330.3867晚班0.44000.44670.52000.46670.47330.380013早班0.48000.62670.50000.51330.66670.4533中班0.47330.59330.38000.50000.63330.4133晚班0.50670.54670.54000.55330.58000.440014早班0.40000.52000.42000.42670.55330.3800中班0.46000.74000.40000.49330.78670.4600晚班0.46000.56670.54000.48670.60000.426715早班0.42000.52670.30000.45330.55330.3667中班0.46670.56670.48000.50000.60000.4133晚班0.44670.50670.58000.49330.55330.413316早班0.47330.53330.58000.50670.57330.4267中班0.47330.59330.46000.50000.63330.4333晚班0.46670.52000.48000.51330.55330.406717早班0.44000.65330.48000.48670.70000.4533中班0.45330.68670.54000.48670.71330.4667晚班0.46000.62670.48000.48670.66670.433318早班0.43330.60670.32000.46000.64000.4000中班0.44000.56000.50000.46670.60000.4200晚班0.43330.62000.48000.46000.65330.413319早班0.47330.62000.58000.50000.65330.4533中班0.44000.49330.42000.48000.53330.3800晚班0.46000.52000.40000.48670.54000.386720早班0.42670.62670.54000.46000.66000.4400中班0.44000.49330.60000.48000.50670.3933晚班0.44000.57330.48000.47330.61330.413321早班0.46000.56000.52000.48670.58000.4133中班0.46670.64000.46000.50000.66670.4400晚班0.44000.60670.40000.46670.64000.413322早班0.45330.61330.50000.49330.64670.4267中班0.46670.55330.48000.50670.57330.4067晚班0.43330.62670.26000.46670.66000.406723早班0.40000.62000.34000.42670.64670.3933中班0.50000.64670.46000.53330.68000.4533晚班0.46670.64000.54000.50000.69330.453324早班0.44000.61330.66000.46670.64000.4467中班0.41330.62000.40000.45330.64670.4133晚班0.42670.55330.38000.46000.58670.386725早班0.42000.56000.40000.45330.58670.3800中班0.46670.62670.44000.48000.64670.4133晚班0.42670.66000.38000.46000.68670.433326早班0.44000.54000.46000.46670.57330.4000中班0.45330.58000.36000.47330.62670.4067晚班0.44000.53330.46000.48000.56670.400027早班0.46670.53330.48000.50000.56670.4067中班0.45330.65330.36000.49330.68670.4267晚班0.48000.56670.56000.51330.60000.440028早班0.46670.59330.40000.48670.62670.4200中班0.46670.60670.28000.50670.63330.4000晚班0.45330.54670.38000.50000.58000.406729早班0.45330.66670.58000.48670.70670.4733中班0.40670.45330.42000.43330.49330.3600晚班0.48670.50670.60000.52000.54670.420030早班0.41330.65330.40000.45330.68670.4333中班0.42000.54670.48000.45330.57330.4000晚班0.48000.56670.52000.52000.58670.4400圖2:關(guān)于瓦斯爆炸的概率和總監(jiān)測次數(shù)N（共540次）的折線圖依據(jù)圖2可以看出瓦斯引起爆炸的概率主要集中在之間，也就可視為該煤礦發(fā)生爆炸的可能性之間。設(shè)定瓦斯極限安全系數(shù)（當時發(fā)生爆炸），統(tǒng)計表4中的個數(shù)為=235，由下面公式計算出瓦斯發(fā)生爆炸事故的概率，其中（2）煤塵發(fā)生爆炸事故的概率分析同上，第天第班次第個監(jiān)測點煤塵發(fā)生爆炸事故的概率，其中：為已知監(jiān)測數(shù)據(jù)，因此關(guān)鍵是求出(瓦斯?jié)舛扔绊懴碌拿簤m爆炸下限的最小值),對表1進行處理去最小值得到表5瓦斯?jié)舛扰c煤塵爆炸下限濃度最小值的關(guān)系。表5:瓦斯?jié)舛扰c煤塵爆炸下限濃度最小值關(guān)系空氣中瓦斯?jié)舛?%)00.51.01.52.02.53.03.54煤塵爆炸下限濃度最小值(g/m3)3022.51532.51.5以表5為依據(jù)，在Matlab中用最小二乘法對數(shù)據(jù)進行3次多項式擬合，求出瓦斯?jié)舛扰c煤塵爆炸下限濃度最小值的關(guān)系，即擬合的3次多項式。在Matlab中輸入命令如下：>>X=[0,0.5,1,1.5,2,2.5,3,3.5,4];>>y=[30,22.5,15,10.5,6.5,4.5,3,2.5,1.5];用三次多項式進行曲線擬合時，用命令>>n=3;>>p=polyfit(x,y,n)即可得到p=-0.33004.2655-18.929130.2929這表明擬合的三次多項式為根據(jù)此多項式和表1中的的值計算出相對應(yīng)的系列的值（即的值），然后根據(jù)概率公式計算整理，數(shù)據(jù)組成一個新的數(shù)據(jù)表表6為各監(jiān)測點煤塵發(fā)生爆炸事故的概率。表6：各監(jiān)測點煤塵發(fā)生爆炸事故的概率監(jiān)測工作面1工作面2掘進工作面回風巷1回風巷2總回風巷日期點與班次爆炸下限爆炸概率爆炸下限爆炸概率爆炸下限爆炸概率爆炸下限爆炸概率爆炸下限爆炸概率爆炸下限爆炸概率1早班18.88540.423616.54260.463725.66550.289922.03230.341315.52840.465619.42590.3629中班20.11790.417517.48770.429425.66550.290321.08820.376016.59210.438220.39970.3569晚班19.56290.389017.82110.421425.17020.302721.74460.328416.47120.429219.97800.34042早班20.11790.382217.48770.440326.16890.279321.18070.346116.47120.440220.39970.3461中班19.97800.399916.74540.462225.66550.291121.27360.363415.52840.473319.83890.3639晚班19.56290.402317.05730.460226.33850.287021.55490.339116.11260.459920.11790.34943早班17.96670.431417.05730.449725.49950.291022.71830.324015.87690.461019.28970.3644中班18.88540.408316.74540.451525.66550.291422.03230.329115.64390.464119.70050.3518晚班19.56290.392616.54260.454027.37480.262321.55490.332615.18570.470819.97800.34744早班19.42590.394816.34400.461924.84460.293021.55490.338715.29930.470619.28970.3603中班18.88540.417818.99840.399026.85260.261422.03230.336818.35620.386220.68450.3360晚班20.11790.397217.27040.440627.02580.285321.27360.347416.47120.440220.68450.33795早班20.25840.386517.59780.441525.33440.294521.08820.350916.59210.440620.25840.3455中班19.83890.408318.04850.425026.00020.290421.36700.361317.45720.417020.68450.3433晚班19.15420.398916.05390.476526.50900.276921.93600.329614.96060.474619.70050.35336早班18.75200.416516.24630.477026.68030.280422.12900.336215.07280.483019.56290.3588中班19.83890.401216.14960.466926.16890.276721.55490.354415.18570.469519.28970.3660晚班19.15420.403615.95930.467426.33850.272221.93600.333214.51810.489019.28970.35987早班19.01940.410618.39720.416426.16890.280921.84010.342017.45720.424520.39970.3466中班19.15420.415117.59780.433626.16890.288121.84010.342016.71360.433220.11790.3539晚班19.70050.417816.54260.471526.50900.284821.55490.368815.41350.479419.83890.37458早班19.83890.412818.27990.425625.33440.294121.27360.371417.45720.423320.54180.3593中班18.61940.407618.04850.426625.66550.280922.12900.323117.20660.429520.11790.3450晚班19.56290.392116.54260.464326.85260.274521.55490.334515.29930.487019.97800.35099早班20.54180.380715.86570.482827.37480.263020.90450.357814.73800.496720.25840.3549中班19.28970.418916.84840.449327.19980.274621.93600.331915.87690.460419.97800.3519晚班18.61940.410919.37100.387726.85260.273322.12900.331718.35620.394420.68450.335510早班19.70050.403517.27040.436624.68320.302221.74460.344016.47120.434119.70050.3548中班19.42590.404117.48770.448926.16890.282421.64960.331216.23150.451620.11790.3514晚班19.42590.404617.59780.430227.37480.274321.64960.345516.47120.438320.39970.351011早班19.01940.414317.59780.426826.33850.275621.84010.340716.59210.429120.11790.3430中班19.70050.392917.93430.437726.00020.278521.27360.339416.95870.442220.25840.3455晚班19.15420.422917.70890.429725.49950.274121.93600.351916.71360.422419.83890.358412早班19.83890.396217.16340.445726.85260.268521.46070.343016.23150.435620.39970.3412中班19.70050.395917.93430.426027.19980.269521.64960.344616.95870.428720.68450.3408晚班19.56290.399219.62440.391325.66550.280521.46070.353718.88540.380220.82810.344713早班18.75200.416016.54260.464325.83240.273722.12900.332615.29930.487619.28970.3727中班18.88540.411417.05730.450826.85260.288221.93600.331915.87690.456620.11790.3504晚班18.22570.416417.82110.433225.49950.287522.71830.323516.83580.431219.56290.361414早班20.39970.390218.27990.409226.50900.276520.90450.365517.33160.412520.82810.3409中班19.15420.417714.98840.511126.68030.289721.84010.348413.35360.543719.15420.3733晚班19.15420.404617.48770.431725.49950.287821.74460.341216.47120.440219.83890.356415早班19.97800.404418.16370.427827.55060.275521.27360.364817.33160.426421.11730.3386中班19.01940.407517.48770.440926.00020.279221.93600.334616.47120.448120.11790.3509晚班19.42590.420618.51540.413725.17020.284521.84010.355817.33160.422920.11790.358916早班18.88540.418318.04850.425525.17020.284522.03230.342216.95870.428719.83890.3528中班18.88540.400317.05730.445626.16890.278221.93600.332815.87690.463619.70050.3548晚班19.01940.401718.27990.419026.00020.268522.12900.326317.33160.417720.25840.346017早班19.56290.399216.14960.480526.00020.276921.74460.345814.73800.505519.28970.3660中班19.28970.414715.68180.478325.49950.277721.74460.357814.51810.486319.01940.3770晚班19.15420.414516.54260.460626.00020.295021.74460.353215.29930.464119.70050.352318早班19.70050.406116.84840.457627.37480.279821.36700.352415.76010.467620.39970.3446中班19.56290.411517.59780.431325.83240.275621.46070.361616.47120.445019.97800.3644晚班19.70050.400016.64350.450626.00020.283821.36700.351015.52840.457920.11790.348419早班18.88540.418316.64350.466825.17020.286421.93600.339615.52840.464319.28970.3655中班19.56290.400218.75490.407926.50900.282521.64960.349717.71060.424020.82810.3462晚班19.15420.415118.27990.408126.68030.281121.74460.357817.58350.412320.68450.354920早班19.83890.397216.54260.454625.49950.282821.36700.349615.41350.464519.56290.3588中班19.56290.401318.75490.397225.00700.294721.64960.343718.22570.391220.54180.3359晚班19.56290.389517.37850.442526.00020.275421.55490.348416.23150.444220.11790.348921早班19.15420.396317.59780.436425.66550.286421.74460.337116.83580.427120.11790.3460中班19.01940.412716.34400.468126.16890.268621.93600.340515.29930.468019.56290.3619晚班19.56290.392116.84840.449326.68030.282221.46070.343415.76010.447320.11790.346022早班19.28970.389816.74540.461025.83240.295421.84010.335215.64390.471719.83890.3523中班19.01940.412217.70890.429226.00020.296222.03230.342716.95870.425720.25840.3441晚班19.70050.405116.54260.460027.90490.268121.46070.361115.41350.459320.25840.353423早班20.39970.404916.64350.453627.19980.277620.90450.383215.64390.459620.54180.3529中班18.35620.419516.24630.474626.16890.289722.42180.330915.07280.483019.28970.3665晚班19.01940.415416.34400.465025.49950.292221.93600.335114.84900.488919.28970.358724早班19.56290.402316.74540.457424.52270.289121.46070.349515.76010.461319.42590.3691中班20.11790.395716.64350.449426.68030.267621.27360.362015.64390.451920.11790.3504晚班19.83890.410317.70890.426926.85260.271521.36700.352916.71360.417020.68450.336525早班19.97800.385417.59780.431326.68030.269921.27360.345516.71360.432620.82810.3327中班19.01940.408516.54260.461826.33850.282521.64960.340415.64390.461520.11790.3435晚班19.83890.409316.05390.478426.85260.271921.36700.363214.96060.479919.70050.369026早班19.56290.408917.93430.423226.16890.280521.46070.346216.95870.422220.39970.3480中班19.28970.399717.27040.440127.02580.284221.55490.329915.99440.455820.25840.3411晚班19.56290.395118.04850.417826.16890.285821.64960.334917.08230.406920.39970.337327早班19.01940.420118.04850.431126.00020.275021.93600.339617.08230.427920.25840.3485中班19.28970.409516.14960.468127.02580.267921.84010.342014.96060.481919.83890.3549晚班18.75200.421317.48770.434025.33440.285022.12900.339416.47120.446219.56290.364028早班19.01940.419617.05730.454326.68030.267221.74460.345415.99440.466419.97800.3594中班19.01940.411216.84840.458227.72730.274522.03230.343615.87690.457320.39970.3431晚班19.28970.393017.82110.431526.85260.265521.93600.327816.83580.437820.25840.343129早班19.28970.423515.95930.474325.17020.283721.74460.344914.62770.494318.88540.3675中班20.25840.415619.49720.397026.50900.267120.99620.387718.48740.392221.26300.3452