储油罐的变位识别与罐容表标定.docx

1、储油罐的变位识别与罐容表标定储油罐的变位识别与罐容表标定摘要：本论文主要针对储油罐的变位识别与罐容表标定进行研究和讨论的。储油罐在我们的现实生活中非常的重要，特别是它的安全存储非常的重要，所以这是一个很好很实际的研究课题。首先采用了统计方法对数据进行了分析，将数据按无变位和有变位综合分析体积与油品液面度的函数关系,并通过测量油罐实际参数,使该函数具体化,给出了该函数的计算机程序,用maTLAB软件，通过拟合法，得出了油品体积与油品液面高度对照表,提高了油品体积的测量精度,减少了实际测量中的工作量。模型一：本模型的建立是研究在无变位情况下，油面高度h与油的体积v之间的函数关系。通过大量的数据录入

2、，得出十分逼近的拟合图像和函数。注意的是录入的数据越多，拟合出的图像与真实的图像就越接近，误差就越小。模型二：它主要是研究油罐在变位情况下，在模型一的基础上，建立油位高度与油的体积之间的函数关系。对模型进行了充分的验证和合理的理论推导，所求出的结果都在理论的误差值范围内。然后借助MATLAB软件的拟合方法进行分析，对附件中的数据进行了筛选，去除异常的数据，对残缺数据进行适当的补充。结果显示，理论结果跟模拟数据结果基本吻合模型三：它是建立在前两个模型基础上的。通过对前两个模型的研究，来讨论更加复杂的情况。在有三个变化量的情况下，如何研究呢？首先我求出在没有变为下，应用积分学的知识求出油面高度与油

3、的体积之间的一般函数关系式（见模型三内的(9)）然后再用MATLAB的拟合方法帮助我们拟合出在横向与纵向都变化的情况下，h与v之间的函数关系关键词：卧式储油罐油品体积变位识别 标定 MATLAB 数据的拟合 统计学一、问题重述现实生活中，许多储油罐在使用一段时间后，由于地基变形等原因，使罐体的位置会发生纵向倾斜和横向偏转等变化（以下称为变位），从而导致罐容表发生改变。按照有关规定，需要定期对罐容表进行重新标定。图1是一种典型的储油罐尺寸及形状示意图，其主体为圆柱体，两端为球冠体。图2是其罐体纵向倾斜变位的示意图，图3是罐体横向偏转变位的截面示意图。（1）为了掌握罐体变位后对罐容表的影响，利用如

4、图4的小椭圆型储油罐（两端平头的椭圆柱体），分别对罐体无变位和倾斜角为=4.10的纵向变位两种情况做了实验，实验数据如附件1所示。请建立数学模型研究罐体变位后对罐容表的影响，并给出罐体变位后油位高度间隔为1cm的罐容表标定值。（2）对于图1所示的实际储油罐，试建立罐体变位后标定罐容表的数学模型，即罐内储油量与油位高度及变位参数（纵向倾斜角度和横向偏转角度 ）之间的一般关系。请利用罐体变位后在进/出油过程中的实际检测数据（附件2），根据你们所建立的数学模型确定变位参数，并给出罐体变位后油位高度间隔为10cm的罐容表标定值。进一步利用附件2中的实际检测数据来分析检验你们模型的正确性与方法的可靠性。

5、二、问题的分析在石油的产地和加工厂，为了储存原油，经常使用大量的储油罐，油罐的外形由三部分组成，中间是一个平放圆柱体，两边是由一个椭球体沿对称轴一分为二的两个半椭球体焊接在圆柱体两端组合成的，上端有住有孔，由于经常油和取油，很难知道注入油和取出油的数量，这给注油和取油数量带来很大麻烦。因此，要给油桶上安装一个精细的刻度计，工人根据刻度计就能知道每次注入和取出油的量的多少。如何设计刻度计呢？这是一个很实际的问题。下面我将用maTLAB和积分的方法解决这个问题。三、模型的假定1假设所给油罐都是完好的，没有破损； 2. 假设题目中所给的数据真实可靠；3. 假设当测量罐体的直径时，罐体的内外经长度相同

6、；（见模型三中的（9）4. 假设油位刻度的变化只与有关的体积和油罐的倾斜度有关，与温度、气压等因素无关；5. 假设每次油量的注入或抽出不会引起油罐随着油量的变化而发生倾斜；6. 假设油罐的焊接处都是圆滑的，圆柱体是标准的，两边的椭球体也是标准的。 四、模型的建立与求解4.1 模型一：若油罐的高为h时，此时油罐的出油量为v，那么问题就归结为求出函数h=h（V） （1）油罐的高度和油量的函数关系如下：由MATLAB的拟合法，通过已经给出的数据在MATLAB中进行你和运算体位无变化时：x=159.02,176.14,192.59,208.50,223.93,238.97,253.66,268.04,

7、282.16,296.03,309.69,323.15,336.44,349.57,362.56,375.42,388.16,400.97,413.32,425.76,438.12,450.40,462.62,474.78,486.89,498.95,510.97,522.95,534.90,546.82,558.72,570.61,582.48,594.35,606.22,618.09,629.96,641.85,653.75,665.67,677.63,678.54,690.53,690.82,702.85,714.91,727.03,739.19,751.42,763.70,764.16

8、,776.53,788.99,801.54,814.19,826.95,839.83,852.84,866.00,879.32,892.82,892.84,906.53,920.45,934.61,949.05,963.80,978.91,994.43,1010.43,1026.99,1044.25,1062.37,1081.59,1102.33,1125.32,1152.36,1193.49;y=312,362,412,462,512,562,612,662,712,762,812,862,912,962,1012,1062,1112,1162,1212,1262,1312,1362,141

9、2,1462,1512,1562,1612,1662,1712,1762,1812,1862,1912,1962,2012,2062,2112,2162,2212,2262,2312,2315.83,2365.83,2367.06,2417.06,2467.06,2517.06,2567.06,2617.06,2666.98,2668.83,2718.83,2768.83,2818.83,2868.83,2918.83,2968.83,3018.83,3068.83,3118.83,3168.83,3168.91,3218.91,3268.91,3318.91,3368.91,3418.91,

10、3468.91,3518.91,3568.91,3618.91,3668.91,3718.91,3768.91,3818.91,3868.91,3918.91,3968.91;p=polyfit(x,y,3)p =-0.00000240774433 0.00431658990406 1.66987172334547 -49.329得到三次拟合多项式 ：-0.00000240774433x+0.00431658990406+1.66987172334547x-49.329xi=159.02:100:1193.49;yi=polyval(p,xi); plot(x,y,.,xi,yi);我们得到拟

11、合之后油位高度h与储油量v的函数图：（关系图像如图1）（图1）即h=h（v）=-0.0000024x3+0.0043x2+1.6699x-49.1864;4.2模型二：倾斜4.1时，油罐上的刻度h与储油量之间的函数关系倾斜变位时：x=411.29,423.45,438.33,450.54,463.90,477.74,489.37,502.56,514.69,526.84,538.88,551.96,564.40,576.56,588.74,599.56,611.62,623.44,635.58,646.28,658.59,670.22,680.63,693.03,704.67,716.45,7

12、27.66,739.39,750.90,761.55,773.43,785.39,796.04,808.27,820.80,832.80,844.47,856.29,867.60,880.06,892.92,904.34,917.34,929.90,941.42,954.60,968.09,980.14,992.41,1006.34,1019.07,1034.24,1035.36;y=962.86,1012.86,1062.86,1112.86,1162.86,1212.86,1262.86,1312.79,1362.79,1412.73,1462.73,1512.73,1562.73,161

13、2.73,1662.73,1712.73,1762.73,1812.73,1862.73,1912.73,1962.73,2012.73,2062.73,2112.73,2162.73,2212.73,2262.73,2312.73,2362.73,2412.73,2462.73,2512.73,2562.73,2612.73,2662.73,2712.73,2762.73,2812.73,2862.73,2912.73,2962.73,3012.73,3062.73,3112.73,3162.73,3212.73,3262.73,3312.73,3362.73,3412.73,3462.73

14、,3512.73,3514.74;h=polyfit(x,y,3)h =-0.00000249721671 0.00539373083922 0.44909628838092 42.10407086898768得到三次拟合多项式 -0.0000025x3+0.0054x2+0.449096x+42.104071；我们得到拟合之后油位高度h与储油量v的函数图：（图2）（图2）将在无变位情况下油位高度与罐内储油量关系与4.1倾斜变位后比较无变位与倾斜变位（4.1）油位高度比较罐内储油量实际无变位油位高度函数计算值（无变位）计算与给出数据的差值函数计算值（倾斜变位）实际倾斜与计算出来结果的差值312

15、159.02157.50460961.515390431217.710670160.20606054362176.14174.07268872.067311258233.863109359.79042058412192.59190.32977812.260221877249.773298759.4435206462208.5206.28568492.214315109265.447729659.16204469512223.93221.95021621.979783774280.892893158.94267691562238.97237.33317931.636820693296.11528

16、0658.78210133612253.66252.44438131.215618685311.121383358.67700203662268.04267.29362940.746370569325.917692558.62406307712282.16281.89073080.269269167340.510699458.61996852762296.03296.2454927-0.215492702354.906895258.66140246812309.69310.3677222-0.677722218369.112771258.74504895862323.15324.2672266

17、-1.117226561383.134818658.86759206912336.44337.9538129-1.513812911396.979528859.02571587962349.57351.4372884-1.867288447410.653392959.216104441012362.56364.7274604-2.167460351424.162902259.435441841062375.42377.8341358-2.414135802437.514547959.680412151112388.16390.767122-2.607121979450.714821459.94

18、7699421162400.79403.5362261-2.746226063463.770213860.233987751212413.32416.1512552-2.831255234476.687216460.535961181262425.76428.6220167-2.862016673489.472320560.85030381312438.12440.9583176-2.838317558502.132017261.173699671362450.4453.1699651-2.769965069514.672797961.502832861412462.62465.2667664

19、-2.646766388527.101153861.834387451462474.78477.2585287-2.478528694539.423576262.16504751512486.89489.1550592-2.265059166551.646556262.491497081562498.95500.966165-2.016164986563.776585362.810420271612510.97512.7016533-1.731653332575.820154563.118501131662522.95524.3713314-1.421331386587.783755163.4

20、12423731712534.9535.9850063-1.085006326599.673878563.688872141762546.82547.5524853-0.732485333611.497015863.944530441812558.72559.0835756-0.363575587623.259658364.176082691862570.61570.58808430.021915732634.968297264.380212971912582.48582.07581860.404181444646.629423964.553605341962594.35593.5565856

21、0.79341437658.249529564.692943872012606.22605.04019271.179807328669.835105364.794912632062618.09616.53644691.55355314681.392642664.85619572112629.96628.05515541.904844624692.928632564.873477142162641.85639.60612542.243874602704.449566464.843441022212653.75651.19916412.550835893715.961935564.76277142

22、2262665.67662.84407872.825921317727.472231164.62815242312677.63674.55067633.079323694738.986944364.436268032315.83678.54675.4502253.089774974739.869338864.419113782365.83690.53687.23419343.295806585751.396064364.161870882367.06690.82687.52507293.294927124751.679820764.154747822417.06702.85699.393231

23、93.456768106763.224965763.831733812467.06714.91711.3534883.556512015774.794659163.441171082517.06727.03723.41564833.61435167786.395392162.979743722567.06739.19735.58952013.600479892798.033655962.444135792617.06751.42747.88491053.535089501809.715941961.831031362666.98763.7760.29163383.408366172821.42

24、9924961.138291082668.83764.16760.75406113.405938868821.865088761.11102762718.83776.53773.32708613.20291387833.657029660.329943472768.83788.99786.05139852.938601544845.512696159.461297662818.83801.54798.93680532.603194711857.438579558.501774252868.83814.19811.99311382.19688619869.441171157.4480573129

25、18.83826.95825.23013121.719868801881.526962156.296830912968.83839.83838.65766461.172335365893.702443755.044779113018.83852.84852.28552130.554478701905.974107353.688585993068.83866866.1235084-0.123508371918.34844452.224935623118.83879.32880.181433-0.86143303930.831945150.650512063168.83892.82894.4691

26、025-1.649102457943.431101948.961999393168.91892.84894.4921521-1.652152061943.451356648.959204583218.91906.53909.0197646-2.489764578956.172860947.153096373268.91920.45923.7967519-3.346751913969.023013845.226261873318.91934.61938.8329212-4.222921248982.008306443.175385173368.91949.05954.1380798-5.0880

27、79761995.135230140.997150333418.91963.8969.7220346-5.9220346341008.41027638.688241423468.91978.91985.594593-6.6845930461021.83993636.245342513518.91994.431001.765562-7.3355621781035.430733.665137673568.911010.431018.244749-7.8147492081049.1890630.944310973618.911026.991035.041961-8.0519613181063.121

28、50828.079546493668.911044.251052.167006-7.9170056871077.23453425.067528293718.911062.371069.629689-7.2596894951091.5346321.904940443768.911081.591087.43982-5.8498199221106.02828718.588467013818.911102.331105.607204-3.2772041481120.72199615.114792073868.911125.321124.1416491.1783506461135.62224911.480599693918.911152.361143.0529639.3070372821150.7355377.682573953968.911193.491162.35095131.139048581166.068353.717398907平均值-0.00232617353.88973544