某隧道監(jiān)控量測數(shù)據(jù)回歸分析方法

量測數(shù)據(jù)的處理與回歸分析,,,,,,,,,,,,,,,,,,,,,,,,,,

一、建立位移（U）隨時間（T）發(fā)展的時態(tài)函數(shù)，根據(jù)量測數(shù)據(jù)分別進行下列函數(shù)：,,,,,,,,,,,,,,,,,,,,,,,,,,

1、對數(shù)函數(shù)U=a+b/lg（1+T）；2、指數(shù)函數(shù)U=a*e-（b/T）；3、雙曲函數(shù)U=T/（a+bT）的回歸計算。,,,,,,,,,,,,,,,,,,,,,,,,,,

時間T,實測收斂值U,回歸值U,U-U,1、對數(shù)函數(shù)U=,20.397,-,4.490,/lg（1+T）,,,,,,,,,,,,,,,,,,

,,,,,,,r=,3.287,-1/lg(1+t),∑U,b,(-1/lg(1+t))*(-1/lg(1+t)),a,,1/t,lnU,(1/t)2,(1/t)*lnU,b,a,1/T,1/U,(1/t)*(1/t),(1/U)*(1/t),b,a

第01天,7.73,7,0.44,2、指數(shù)函數(shù)U=,17.499,e(,-0.956,/T),-3.321928095,218.53,4.490108057,11.03520627,20.39698592,-25.66521646,1,2.044591264,1,2.044591264,-0.955804668,17.4990317,1,0.129433083,1,0.129433083,0.054697096,0.082586491

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第02天,9.81,10,-0.61,,,,r=,-0.919,-2.095903274,,53.05945244,4.392810535,,-20.56500293,0.5,2.283606126,0.25,1.141803063,,4.180353438,0.5,0.101916021,0.25,0.050958011,,0.016752923

,,,,3、雙曲函數(shù)U=,T/(,0.083,0.055,*T),,,,,,,,,,,,,,,,,,

第03天,11.11,12,-1.05,,,,,,-1.660964047,,108.5287817,2.758801567,,-18.44998864,0.333333333,2.407665569,0.111111111,0.80255519,,5.214856941,0.333333333,0.090025207,0.111111111,0.030008402,,0.010386875

,,,,,,,r=,0.964,,,,,,,,,,,,,,,,,,

第04天,12.08,13,-1.19,"以上三種回歸方程,函數(shù)",,3,"的相關(guān)系數(shù)r的絕對值最靠近1,",,-1.430676558,,147.9048625,2.046835414,,-17.27971147,0.25,2.491385616,0.0625,0.622846404,,5.796853494,0.25,0.082795165,0.0625,0.020698791,,0.008104538

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第05天,12.87,14,-1.17,回歸精度較高.故選用該回歸方程來預測,,,D1K39+320××隧道,,-1.285097209,,176.1594308,1.651474836,,-16.54434147,0.2,2.555209774,0.04,0.511041955,,6.207002287,0.2,0.077675936,0.04,0.015535187,,0.006855039

,,,,的最終收斂情況.,,,,,,,,,,,,,,,,,,,,,,

第06天,13.66,15,-0.95,,,,,,-1.183294662,,197.1807136,1.400186258,,-16.15907191,0.166666667,2.614178985,0.027777778,0.435696498,,6.529096987,0.166666667,0.073227885,0.027777778,0.012204648,,0.006033551

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第07天,14.36,15,-0.68,,,,,,-1.107309365,,213.3570708,1.22613403,,-15.90096248,0.142857143,2.664446564,0.020408163,0.380635223,,6.833931768,0.142857143,0.069637883,0.020408163,0.009948269,,0.005362323

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第08天,15.06,15,-0.32,,,,,,-1.047951637,,226.1621124,1.098202634,,-15.77795985,0.125,2.711776583,0.015625,0.338972073,,7.09927549,0.125,0.066418704,0.015625,0.008302338,,0.004849435

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第09天,15.84,16,0.18,,,,,,-1,,236.5378422,1,,-15.836,0.111111111,2.762285829,0.012345679,0.306920648,,7.353732235,0.111111111,0.063147259,0.012345679,0.007016362,,0.004411444

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第10天,16.42,16,0.54,,,,,,-0.960252568,,245.1095905,0.922084994,,-15.76926767,0.1,2.798621899,0.01,0.27986219,,7.630223002,0.1,0.060893923,0.01,0.006089392,,0.003987576

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第11天,17.00,16,0.92,,,,,,-0.926628408,,252.3069807,0.858640207,,-15.75268294,0.090909091,2.833213344,0.008264463,0.257564849,,7.832284535,0.090909091,0.058823529,0.008264463,0.005347594,,0.00370807

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第12天,17.54,16,1.30,備注,,,,,-0.897711718,,258.4342022,0.805886328,,-15.74945437,0.083333333,2.864712011,0.006944444,0.238726001,,8.027097853,0.083333333,0.056999544,0.006944444,0.004749962,,0.003460208

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第13天,18.01,16,1.63,平均值:,U=,14.37,,,-0.87250287,,263.7123429,0.761261257,,-15.71377668,0.076923077,2.890927159,0.00591716,0.222379012,,8.206574907,0.076923077,0.055524708,0.00591716,0.004271131,,0.003248948

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第14天,18.40,17,1.90,標準差:,S=√∑(U-U)2/n=,,0.29,,-0.850274154,,268.3057912,0.722966136,,-15.64674498,0.071428571,2.912459354,0.005102041,0.208032811,,8.35745984,0.071428571,0.054341919,0.005102041,0.003881566,,0.003082993

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第15天,18.64,17,2.03,變異系數(shù),:Sr=S/U*100％=,,2.03,％,-0.830482024,,272.3392334,0.689700392,,-15.48350685,0.066666667,2.925524379,0.004444444,0.195034959,,8.482419491,0.066666667,0.053636559,0.004444444,0.003575771,,0.002953044

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∑（U-U）2=,,,19.210,里程樁號:,D1K39+320××隧道,,圍巖類別:,Ⅴ,-19.47097659,,275.9089109,31.37019086,,-256.2936887,3.318228993,39.76060446,1.580440283,7.98666214,,8.558692889,3.318228993,1.094497326,1.580440283,0.312020507,,0.00287688

二、根據(jù)量測數(shù)據(jù)和選取的回歸方程繪制：位移量（U）與時間（T）的變化關(guān)系圖,,,,,,,,,,,,,,,,,,,,,,,,,,

,,,,,,,,,,,3195.007318,,,,,,,,,106.3098552,,,,,,0.086073848

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時間T,收斂值U（mm）,收斂率U/Umax*100％,時間T,收斂值U（mm）,收斂率U/Umax*100％,時間T,收斂值U（mm）,收斂率U/Umax*100％,,,,,,,,,,,,,,,,,,

5,14.04,76.81,20,17.00,92.98,40,17.62,96.36,,,,,,,,,,,,,,,,,,

三、量測數(shù)據(jù)處理結(jié)果,,,,,,,,,,,,,,,,,,,,,,,,,,

1、推算出最終位移量：,,Umax=,18.28,mm,,,,,,,,,,,,,,,,,,,,,,

2、推算出基本穩(wěn)定時間：第,,,40,天以后，開挖面距該量測斷面,,,,m，,,,,,,,,,,,,,,,,,,

圍巖收