2010高教社杯全國大學(xué)生數(shù)學(xué)建模競賽題目A

1、（請先閱讀“全國大學(xué)生數(shù)學(xué)建模競賽論文格式規(guī)范”）A題 儲油罐的變位識別與罐容表標(biāo)定通常加油站都有若干個儲存燃油的地下儲油罐，并且一般都有與之配套的“油位計量管理系統(tǒng)”，采用流量計和油位計來測量進/出油量與罐內(nèi)油位高度等數(shù)據(jù)，通過預(yù)先標(biāo)定的罐容表（即罐內(nèi)油位高度與儲油量的對應(yīng)關(guān)系）進行實時計算，以得到罐內(nèi)油位高度和儲油量的變化情況。許多儲油罐在使用一段時間后，由于地基變形等原因，使罐體的位置會發(fā)生縱向傾斜和橫向偏轉(zhuǎn)等變化（以下稱為變位），從而導(dǎo)致罐容表發(fā)生改變。按照有關(guān)規(guī)定，需要定期對罐容表進行重新標(biāo)定。圖1是一種典型的儲油罐尺寸及形狀示意圖，其主體為圓柱體，兩端為球冠體。圖2是其罐體縱向傾斜

2、變位的示意圖，圖3是罐體橫向偏轉(zhuǎn)變位的截面示意圖。請你們用數(shù)學(xué)建模方法研究解決儲油罐的變位識別與罐容表標(biāo)定的問題。（1）為了掌握罐體變位后對罐容表的影響，利用如圖4的小橢圓型儲油罐（兩端平頭的橢圓柱體），分別對罐體無變位和傾斜角為a0的縱向變位兩種情況做了實驗，實驗數(shù)據(jù)如附件1所示。請建立數(shù)學(xué)模型研究罐體變位后對罐容表的影響，并給出罐體變位后油位高度間隔為1cm的罐容表標(biāo)定值。（2）對于圖1所示的實際儲油罐，試建立罐體變位后標(biāo)定罐容表的數(shù)學(xué)模型，即罐內(nèi)儲油量與油位高度及變位參數(shù)（縱向傾斜角度a和橫向偏轉(zhuǎn)角度b）之間的一般關(guān)系。請利用罐體變位后在進/出油過程中的實際檢測數(shù)據(jù)（附件2），根據(jù)你們所

3、建立的數(shù)學(xué)模型確定變位參數(shù)，并給出罐體變位后油位高度間隔為10cm的罐容表標(biāo)定值。進一步利用附件2中的實際檢測數(shù)據(jù)來分析檢驗?zāi)銈兡Ｐ偷恼_性與方法的可靠性。附件1：小橢圓儲油罐的實驗數(shù)據(jù)附件2：實際儲油罐的檢測數(shù)據(jù)油油浮子出油管油位探測裝置注油口檢查口地平線2m6m1m1m3 m油位高度圖1 儲油罐正面示意圖油位探針油位探針 地平線圖2 儲油罐縱向傾斜變位后示意圖油油浮子出油管油位探測裝置注油口檢查口水平線圖3 儲油罐截面示意圖（b）橫向偏轉(zhuǎn)傾斜后正截面圖地平線垂直線油位探針（a）無偏轉(zhuǎn)傾斜的正截面圖油位探針油位探測裝置3m(b) 小橢圓油罐截面示意圖 油油浮子出油管油位探針注油口水平線cm(

4、a) 小橢圓油罐正面示意圖圖4 小橢圓型油罐形狀及尺寸示意圖問題A附件1：實際采集數(shù)據(jù)表問題A附件2：實際采集數(shù)據(jù)表問題A附件1：實際采集數(shù)據(jù)表(1)罐體無變位進油，罐內(nèi)油量初值262L；(2)C列累加進油量是每次加入一定量油后的累加值；(3)D列是原罐內(nèi)初始油量加入相應(yīng)油量后油位高度值。ABCDE流水號油罐號累加進油量/L油位高度/mm采集時間111502010-08-18 10:32:181211002010-08-18 10:33:181311502010-08-18 10:34:181412002010-08-18 10:35:181512502010-08-18 10:36:1816

5、13002010-08-18 10:37:081713502010-08-18 10:38:081814002010-08-18 10:39:081914502010-08-18 10:40:082015002010-08-18 10:41:082115502010-08-18 10:41:582216002010-08-18 10:42:582316502010-08-18 10:43:582417002010-08-18 10:45:182517502010-08-18 10:46:082618002010-08-18 10:47:082718502010-08-18 10:48:0828

6、19002010-08-18 10:49:082919502010-08-18 10:49:5830110002010-08-18 10:50:5831110502010-08-18 10:51:5832111002010-08-18 10:52:4833111502010-08-18 10:53:4834112002010-08-18 10:54:4835112502010-08-18 10:55:4836113002010-08-18 10:56:3837113502010-08-18 10:57:3838114002010-08-18 10:58:3839114502010-08-18

7、10:59:2840115002010-08-18 11:00:2841115502010-08-18 11:01:1842116002010-08-18 11:02:1843116502010-08-18 11:03:1844117002010-08-18 11:04:0845117502010-08-18 11:05:0846118002010-08-18 11:05:5847118502010-08-18 11:06:5848119002010-08-18 11:07:5849119502010-08-18 11:08:4850120002010-08-18 11:09:48511205

8、02010-08-18 11:10:485212010-08-18 11:11:185312010-08-18 11:12:185412010-08-18 12:36:185512010-08-18 12:37:185612010-08-18 12:38:185712010-08-18 12:39:185812010-08-18 12:40:185912010-08-18 12:41:186012010-08-18 12:42:186112010-08-18 12:50:286212010-08-18 12:51:386312010-08-18 12:53:086412010-08-18 12

9、:54:086512010-08-18 12:54:586612010-08-18 12:56:086712010-08-18 12:57:086812010-08-18 12:58:086912010-08-18 12:59:087012010-08-18 13:00:087112010-08-18 13:01:387212010-08-18 13:02:187312010-08-18 13:03:287412010-08-18 13:04:287512010-08-18 13:05:287612010-08-18 13:06:187712010-08-18 13:07:287812010-

10、08-18 13:08:187912010-08-18 13:09:188012010-08-18 13:10:288112010-08-18 13:11:288212010-08-18 13:12:288312010-08-18 13:13:288412010-08-18 13:14:188512010-08-18 13:15:188612010-08-18 13:16:288712010-08-18 13:17:288812010-08-18 13:18:28問題A附件2：實際采集數(shù)據(jù)表(1)C列進油量；(2)D列出油量是加油機不同時段的出油量vi；(3)E列顯示油高是進/出油vi后對應(yīng)的

11、罐內(nèi)油位顯示高度hi；(4)F列顯示油量容積是進/出油vi后，罐內(nèi)油位顯示高度為hi時系統(tǒng)的顯示儲油量i。ABCDEFG流水號油罐號進油量/L出油量/L顯示油高/mm顯示油量容積/L采集時間2010202632.23 60448.88 2010-08-01 08:00:492020202624.30 60311.43 2010-08-01 08:15:422030202620.67 60248.03 2010-08-01 08:23:412040202610.29 60065.11 2010-08-01 08:38:142050202606.61 59999.69 2010-08-01 08:

12、53:082060202599.59 59874.06 2010-08-01 09:08:012070202587.60 59657.02 2010-08-01 09:32:062080202582.05 59555.51 2010-08-01 09:56:182090202579.57 59509.94 2010-08-01 10:10:092100202575.44 59433.77 2010-08-01 10:26:282110202569.46 59322.85 2010-08-01 10:48:352120202564.12 59223.17 2010-08-01 11:02:482

13、130202559.83 59142.66 2010-08-01 11:36:042140202548.47 58927.69 2010-08-01 13:16:242150202539.63 58758.61 2010-08-01 13:24:252160202528.01 58534.01 2010-08-01 13:37:332170202521.63 58409.58 2010-08-01 14:00:032180202510.23 58185.31 2010-08-01 14:36:022190202508.17 58144.52 2010-08-01 14:52:082200202

14、500.07 57983.36 2010-08-01 15:06:142210202490.06 57782.53 2010-08-01 15:16:432220202485.73 57695.08 2010-08-01 15:48:222230202474.40 57464.67 2010-08-01 16:06:312240202464.77 57267.02 2010-08-01 16:25:542250202454.51 57054.65 2010-08-01 16:41:242260202446.77 56893.24 2010-08-01 17:06:082270202436.85

15、 56684.86 2010-08-01 17:45:542280202431.55 56572.86 2010-08-01 18:03:342290202427.32 56483.12 2010-08-01 18:14:522300202422.20 56374.11 2010-08-01 18:35:242310202414.35 56206.14 2010-08-01 19:12:552320202404.05 55984.22 2010-08-01 20:34:442330202399.15 55878.05 2010-08-01 21:05:572340202393.12 55746

16、.87 2010-08-02 07:18:342350202382.50 55514.45 2010-08-02 07:23:302360202374.35 55334.90 2010-08-02 07:39:212370202362.44 55070.68 2010-08-02 07:48:362380202358.40 54980.57 2010-08-02 08:04:442390202348.13 54750.40 2010-08-02 08:28:322400202339.37 54552.85 2010-08-02 08:33:362410202334.88 54451.17 20

17、10-08-02 08:46:282420202328.13 54297.75 2010-08-02 08:58:392430202322.14 54161.06 2010-08-02 09:03:542440202314.14 53977.71 2010-08-02 09:14:472450202304.14 53747.27 2010-08-02 09:25:552460202301.09 53676.72 2010-08-02 09:35:542470202290.87 53439.37 2010-08-02 09:59:332480202280.46 53196.16 2010-08-

18、02 10:13:322490202274.92 53066.14 2010-08-02 10:18:242500202268.61 52917.56 2010-08-02 10:26:362510202260.89 52735.08 2010-08-02 10:38:332520202251.88 52521.14 2010-08-02 10:46:542530202242.46 52296.37 2010-08-02 10:58:372540202232.88 52066.65 2010-08-02 11:05:342550202226.99 51924.85 2010-08-02 11:

19、26:382560202220.70 51772.96 2010-08-02 11:58:372570202209.13 51492.32 2010-08-02 12:09:462580202201.40 51303.95 2010-08-02 12:36:442590202190.91 51047.20 2010-08-02 12:55:322600202186.14 50930.04 2010-08-02 13:18:342610202177.92 50727.53 2010-08-02 13:26:422620202170.04 50532.69 2010-08-02 13:38:242

20、630202158.40 50243.62 2010-08-02 13:45:372640202155.54 50172.37 2010-08-02 13:55:342650202148.54 49997.62 2010-08-02 14:18:362660202141.32 49816.82 2010-08-02 14:27:332670202138.42 49744.05 2010-08-02 14:48:242680202127.37 49465.96 2010-08-02 14:56:382690202116.53 49191.94 2010-08-02 15:05:142700202

21、110.14 49029.86 2010-08-02 15:16:382710202100.32 48779.99 2010-08-02 15:27:542720202096.84 48691.21 2010-08-02 15:48:342730202088.64 48481.56 2010-08-02 15:56:392740202084.03 48363.42 2010-08-02 16:23:442750202077.58 48197.79 2010-08-02 16:32:362760202067.14 47928.87 2010-08-02 16:54:322770202063.17

22、 47826.34 2010-08-02 17:38:342780202058.14 47696.24 2010-08-02 17:45:262790202051.30 47518.96 2010-08-02 18:08:372800202045.92 47379.23 2010-08-02 19:24:242810202035.94 47119.35 2010-08-02 19:48:542820202024.06 46808.88 2010-08-02 20:08:362830202020.47 46714.83 2010-08-02 20:13:242840202016.11 46600

23、.46 2010-08-02 20:43:342850202007.08 46363.09 2010-08-03 07:01:552860202001.33 46211.59 2010-08-03 07:47:252870201989.59 45901.47 2010-08-03 08:03:512880201977.87 45590.80 2010-08-03 08:15:352890201969.43 45366.43 2010-08-03 08:33:262900201958.83 45083.88 2010-08-03 08:53:452910201952.81 44923.05 20

24、10-08-03 09:04:332920201944.49 44700.35 2010-08-03 09:27:362930201932.64 44382.33 2010-08-03 10:02:122940201925.05 44178.12 2010-08-03 10:57:232950201913.71 43872.31 2010-08-03 11:22:452960201904.51 43623.60 2010-08-03 11:35:362970201897.67 43438.33 2010-08-03 12:31:532980201889.27 43210.41 2010-08-

25、03 13:37:512990201878.40 42914.84 2010-08-03 13:57:253000201874.41 42806.16 2010-08-03 14:21:513010201868.46 42643.93 2010-08-03 14:36:233020201856.54 42318.32 2010-08-03 14:47:553030201850.51 42153.30 2010-08-03 15:14:343040201841.92 41917.87 2010-08-03 15:34:263050201830.91 41615.55 2010-08-03 15:

26、58:503060201818.96 41286.70 2010-08-03 16:17:443070201810.42 41051.26 2010-08-03 17:37:123080201807.34 40966.26 2010-08-03 17:44:563090201804.98 40901.09 2010-08-03 18:07:553100201796.80 40675.04 2010-08-03 18:14:463110201789.13 40462.79 2010-08-03 18:35:433120201777.51 40140.74 2010-08-03 19:07:243

27、130201768.05 39878.12 2010-08-03 20:42:513140201759.42 39638.21 2010-08-04 08:21:223150201752.19 39437.00 2010-08-04 08:32:263160201747.59 39308.87 2010-08-04 08:41:463170201735.97 38984.85 2010-08-04 08:53:323180201728.57 38778.25 2010-08-04 09:21:223190201726.26 38713.71 2010-08-04 09:55:273200201

28、717.30 38463.22 2010-08-04 10:11:283210201710.10 38261.74 2010-08-04 10:34:223220201707.51 38189.22 2010-08-04 10:51:263230201696.61 37883.79 2010-08-04 11:15:523240201691.31 37735.15 2010-08-04 11:31:553250201687.01 37614.49 2010-08-04 11:45:233260201683.87 37526.35 2010-08-04 12:01:223270201678.77

29、 37383.13 2010-08-04 12:17:273280201674.48 37262.60 2010-08-04 12:51:123290201665.96 37023.08 2010-08-04 13:53:263300201663.30 36948.26 2010-08-04 14:11:253310201658.55 36814.61 2010-08-04 15:01:423320201653.73 36678.94 2010-08-04 15:25:283330201642.93 36374.74 2010-08-04 16:44:423340201636.48 36192

30、.94 2010-08-04 17:41:333350201626.92 35923.33 2010-08-04 18:15:443360201618.89 35696.73 2010-08-04 18:31:223370201609.06 35419.17 2010-08-04 19:13:263380201605.92 35330.47 2010-08-04 19:31:453390201594.13 34997.30 2010-08-04 19:44:233400201583.65 34700.98 2010-08-04 19:56:423410201581.14 34629.99 20

31、10-08-04 20:31:213420201574.48 34441.58 2010-08-05 06:55:343430201569.22 34292.75 2010-08-05 07:26:323440201560.92 34057.83 2010-08-05 07:35:143450201556.62 33936.10 2010-08-05 07:50:323460201548.82 33715.25 2010-08-05 08:05:343470201540.79 33487.84 2010-08-05 08:18:323480201532.79 33261.23 2010-08-

32、05 08:30:563490201526.30 33077.38 2010-08-05 08:44:243500201523.95 33010.80 2010-08-05 08:55:343510201516.81 32808.51 2010-08-05 09:06:273520201510.73 32636.23 2010-08-05 09:17:343530201507.65 32548.96 2010-08-05 09:28:283540201501.06 32362.23 2010-08-05 09:40:393550201494.55 32177.83 2010-08-05 09:

33、56:243560201487.03 31964.75 2010-08-05 10:15:563570201476.98 31680.00 2010-08-05 10:25:323580201467.97 31424.74 2010-08-05 10:42:143590201457.25 31121.10 2010-08-05 10:55:543600201454.73 31049.73 2010-08-05 11:06:303610201450.53 30930.79 2010-08-05 11:45:243620201443.93 30743.92 2010-08-05 12:03:313

34、630201432.35 30416.13 2010-08-05 12:15:343640201422.45 30136.01 2010-08-05 12:26:353650201415.93 29951.59 2010-08-05 12:48:223660201410.60 29800.87 2010-08-05 13:15:373670201408.01 29727.64 2010-08-05 13:36:243680201398.60 29461.68 2010-08-05 13:45:553690201391.53 29261.94 2010-08-05 14:02:323700201

35、387.53 29148.98 2010-08-05 14:15:233710201381.26 28971.96 2010-08-05 14:39:003720201377.57 28867.81 2010-08-05 14:55:323730201368.05 28599.24 2010-08-05 15:17:373740201362.37 28439.09 2010-08-05 15:44:333750201350.95 28117.30 2010-08-05 16:05:223760201348.78 28056.19 2010-08-05 16:16:343770201338.49

36、 27766.55 2010-08-05 16:35:383780201330.22 27533.96 2010-08-05 17:06:233790201322.84 27326.55 2010-08-05 17:15:343800201314.33 27087.57 2010-08-05 19:39:253810201305.06 26827.49 2010-08-05 21:05:043820201302.12 26745.05 2010-08-06 07:46:573830201291.34 26443.03 2010-08-06 08:04:343840201289.20 26383

37、.11 2010-08-06 08:26:523850201284.26 26244.87 2010-08-06 08:37:243860201280.46 26138.58 2010-08-06 08:44:473870201269.19 25823.64 2010-08-06 09:06:523880201266.51 25748.82 2010-08-06 09:15:373890201258.70 25530.91 2010-08-06 09:36:593900201250.33 25297.63 2010-08-06 09:59:173910201241.82 25060.73 20

38、10-08-06 10:36:473920201231.17 24764.66 2010-08-06 10:53:433930201228.61 24693.57 2010-08-06 11:15:353940201218.44 24411.40 2010-08-06 11:26:273950201211.15 24209.41 2010-08-06 11:55:533960201202.21 23962.04 2010-08-06 12:16:553970201198.09 23848.16 2010-08-06 12:30:513980201190.65 23642.72 2010-08-

39、06 12:46:223990201181.63 23394.00 2010-08-06 12:58:504000201170.06 23075.57 2010-08-06 13:13:574010201163.62 22898.62 2010-08-06 13:23:214020201160.77 22820.38 2010-08-06 13:34:474030201158.19 22749.60 2010-08-06 13:46:514040201149.90 22522.38 2010-08-06 13:57:214050201139.94 22249.89 2010-08-06 14:

40、06:574060201131.02 22006.33 2010-08-06 14:17:564070201125.57 21857.74 2010-08-06 14:36:334080201114.10 21545.60 2010-08-06 14:47:224090201106.90 21350.06 2010-08-06 14:56:374100201095.36 21037.34 2010-08-06 15:07:564110201092.63 20963.48 2010-08-06 15:16:174120201088.56 20853.45 2010-08-06 15:25:504

41、130201078.81 20590.32 2010-08-06 15:36:384140201067.66 20290.19 2010-08-06 15:49:374150201057.84 20026.55 2010-08-06 15:56:574160201052.88 19893.65 2010-08-06 16:05:594170201049.36 19799.43 2010-08-06 16:16:004180201038.89 19519.72 2010-08-06 16:31:514190201029.04 19257.31 2010-08-06 16:56:114200201

42、024.33 19132.09 2010-08-06 17:01:524210201020.05 19018.44 2010-08-06 17:22:174220201014.84 18880.29 2010-08-06 17:36:504230201004.54 18607.78 2010-08-06 17:58:37424020994.32 18338.22 2010-08-06 18:16:57425020986.62 18135.68 2010-08-06 18:25:30426020978.90 17933.11 2010-08-06 18:36:33427020974.04 178

43、05.83 2010-08-06 20:12:20428020965.05 17570.93 2010-08-06 20:44:53429020955.08 17311.22 2010-08-07 07:10:26430020948.67 17144.71 2010-08-07 08:11:21431020942.21 16977.27 2010-08-07 08:22:16432020935.55 16805.03 2010-08-07 08:40:24433020930.76 16681.41 2010-08-07 08:50:03434020922.00 16455.87 2010-08

44、-07 09:00:26435020910.97 16172.90 2010-08-07 09:12:27436020899.88 15889.56 2010-08-07 09:22:49437020890.41 15648.56 2010-08-07 09:35:28438020885.81 15531.81 2010-08-07 09:50:16439020876.91 15306.54 2010-08-07 10:05:23440020873.59 15222.71 2010-08-07 10:17:47441020870.36 15141.26 2010-08-07 10:30:264

45、42020866.45 15042.81 2010-08-07 10:45:49443020862.99 14955.81 2010-08-07 11:10:06444020855.14 14758.91 2010-08-07 11:30:29445020852.41 14690.59 2010-08-07 12:13:56446020842.18 14435.27 2010-08-07 12:25:22447020832.95 14205.87 2010-08-07 12:37:54448020821.69 13927.29 2010-08-07 12:51:26449020814.77 13