高教社杯全国大学生数学建模竞赛题目A.docx
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高教社杯全国大学生数学建模竞赛题目A
2010高教社杯全国大学生数学建模竞赛题目（A）
（请先阅读“全国大学生数学建模竞赛论文格式规范”）
A题储油罐的变位识别与罐容表标定
通常加油站都有若干个储存燃油的地下储油罐，并且一般都有与之配套的“油位计量管理系统”，采用流量计和油位计来测量进/出油量与罐内油位高度等数据，通过预先标定的罐容表（即罐内油位高度与储油量的对应关系）进行实时计算，以得到罐内油位高度和储油量的变化情况。
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。
请你们用数学建模方法研究解决储油罐的变位识别与罐容表标定的问题。
（1）为了掌握罐体变位后对罐容表的影响，利用如图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。
附件1：
小椭圆储油罐的实验数据
附件2：
实际储油罐的检测数据
问题A附件1：
实际采集数据表
问题A附件2：
实际采集数据表
问题A附件1：
实际采集数据表
（1）罐体无变位进油，罐内油量初值262L；
（2）C列累加进油量是每次加入一定量油后的累加值；
（3）D列是原罐内初始油量加入相应油量后油位高度值。
A
B
C
D
E
流水号
油罐号
累加进油量/L
油位高度/mm
采集时间
11
1
50
159.02
2010-08-1810:
32:
18
12
1
100
176.14
2010-08-1810:
33:
18
13
1
150
192.59
2010-08-1810:
34:
18
14
1
200
208.50
2010-08-1810:
35:
18
15
1
250
223.93
2010-08-1810:
36:
18
16
1
300
238.97
2010-08-1810:
37:
08
17
1
350
253.66
2010-08-1810:
38:
08
18
1
400
268.04
2010-08-1810:
39:
08
19
1
450
282.16
2010-08-1810:
40:
08
20
1
500
296.03
2010-08-1810:
41:
08
21
1
550
309.69
2010-08-1810:
41:
58
22
1
600
323.15
2010-08-1810:
42:
58
23
1
650
336.44
2010-08-1810:
43:
58
24
1
700
349.57
2010-08-1810:
45:
18
25
1
750
362.56
2010-08-1810:
46:
08
26
1
800
375.42
2010-08-1810:
47:
08
27
1
850
388.16
2010-08-1810:
48:
08
28
1
900
400.79
2010-08-1810:
49:
08
29
1
950
413.32
2010-08-1810:
49:
58
30
1
1000
425.76
2010-08-1810:
50:
58
31
1
1050
438.12
2010-08-1810:
51:
58
32
1
1100
450.40
2010-08-1810:
52:
48
33
1
1150
462.62
2010-08-1810:
53:
48
34
1
1200
474.78
2010-08-1810:
54:
48
35
1
1250
486.89
2010-08-1810:
55:
48
36
1
1300
498.95
2010-08-1810:
56:
38
37
1
1350
510.97
2010-08-1810:
57:
38
38
1
1400
522.95
2010-08-1810:
58:
38
39
1
1450
534.90
2010-08-1810:
59:
28
40
1
1500
546.82
2010-08-1811:
00:
28
41
1
1550
558.72
2010-08-1811:
01:
18
42
1
1600
570.61
2010-08-1811:
02:
18
43
1
1650
582.48
2010-08-1811:
03:
18
44
1
1700
594.35
2010-08-1811:
04:
08
45
1
1750
606.22
2010-08-1811:
05:
08
46
1
1800
618.09
2010-08-1811:
05:
58
47
1
1850
629.96
2010-08-1811:
06:
58
48
1
1900
641.85
2010-08-1811:
07:
58
49
1
1950
653.75
2010-08-1811:
08:
48
50
1
2000
665.67
2010-08-1811:
09:
48
51
1
2050
677.63
2010-08-1811:
10:
48
52
1
2053.83
678.54
2010-08-1811:
11:
18
53
1
2103.83
690.53
2010-08-1811:
12:
18
54
1
2105.06
690.82
2010-08-1812:
36:
18
55
1
2155.06
702.85
2010-08-1812:
37:
18
56
1
2205.06
714.91
2010-08-1812:
38:
18
57
1
2255.06
727.03
2010-08-1812:
39:
18
58
1
2305.06
739.19
2010-08-1812:
40:
18
59
1
2355.06
751.42
2010-08-1812:
41:
18
60
1
2404.98
763.70
2010-08-1812:
42:
18
61
1
2406.83
764.16
2010-08-1812:
50:
28
62
1
2456.83
776.53
2010-08-1812:
51:
38
63
1
2506.83
788.99
2010-08-1812:
53:
08
64
1
2556.83
801.54
2010-08-1812:
54:
08
65
1
2606.83
814.19
2010-08-1812:
54:
58
66
1
2656.83
826.95
2010-08-1812:
56:
08
67
1
2706.83
839.83
2010-08-1812:
57:
08
68
1
2756.83
852.84
2010-08-1812:
58:
08
69
1
2806.83
866.00
2010-08-1812:
59:
08
70
1
2856.83
879.32
2010-08-1813:
00:
08
71
1
2906.83
892.82
2010-08-1813:
01:
38
72
1
2906.91
892.84
2010-08-1813:
02:
18
73
1
2956.91
906.53
2010-08-1813:
03:
28
74
1
3006.91
920.45
2010-08-1813:
04:
28
75
1
3056.91
934.61
2010-08-1813:
05:
28
76
1
3106.91
949.05
2010-08-1813:
06:
18
77
1
3156.91
963.80
2010-08-1813:
07:
28
78
1
3206.91
978.91
2010-08-1813:
08:
18
79
1
3256.91
994.43
2010-08-1813:
09:
18
80
1
3306.91
1010.43
2010-08-1813:
10:
28
81
1
3356.91
1026.99
2010-08-1813:
11:
28
82
1
3406.91
1044.25
2010-08-1813:
12:
28
83
1
3456.91
1062.37
2010-08-1813:
13:
28
84
1
3506.91
1081.59
2010-08-1813:
14:
18
85
1
3556.91
1102.33
2010-08-1813:
15:
18
86
1
3606.91
1125.32
2010-08-1813:
16:
28
87
1
3656.91
1152.36
2010-08-1813:
17:
28
88
1
3706.91
1193.49
2010-08-1813:
18:
28
问题A附件2：
实际采集数据表
（1）C列进油量；
（2）D列出油量是加油机不同时段的出油量vi；
（3）E列显示油高是进/出油vi后对应的罐内
油位显示高度hi；
（4）F列显示油量容积是进/出油vi后，罐内
油位显示高度为hi时系统的显示储油量Ｖi。
A
B
C
D
E
F
G
流水号
油罐号
进油量/L
出油量/L
显示油高/mm
显示油量容积/L
采集时间
201
02
0
60.00
2632.23
60448.88
2010-08-0108:
00:
49
202
02
0
149.09
2624.30
60311.43
2010-08-0108:
15:
42
203
02
0
68.45
2620.67
60248.03
2010-08-0108:
23:
41
204
02
0
199.27
2610.29
60065.11
2010-08-0108:
38:
14
205
02
0
70.05
2606.61
59999.69
2010-08-0108:
53:
08
206
02
0
136.36
2599.59
59874.06
2010-08-0109:
08:
01
207
02
0
232.74
2587.60
59657.02
2010-08-0109:
32:
06
208
02
0
107.97
2582.05
59555.51
2010-08-0109:
56:
18
209
02
0
49.24
2579.57
59509.94
2010-08-0110:
10:
09
210
02
0
80.65
2575.44
59433.77
2010-08-0110:
26:
28
211
02
0
120.29
2569.46
59322.85
2010-08-0110:
48:
35
212
02
0
108.24
2564.12
59223.17
2010-08-0111:
02:
48
213
02
0
83.46
2559.83
59142.66
2010-08-0111:
36:
04
214
02
0
229.93
2548.47
58927.69
2010-08-0113:
16:
24
215
02
0
181.70
2539.63
58758.61
2010-08-0113:
24:
25
216
02
0
238.52
2528.01
58534.01
2010-08-0113:
37:
33
217
02
0
131.79
2521.63
58409.58
2010-08-0114:
00:
03
218
02
0
238.33
2510.23
58185.31
2010-08-0114:
36:
02
219
02
0
42.92
2508.17
58144.52
2010-08-0114:
52:
08
220
02
0
171.34
2500.07
57983.36
2010-08-0115:
06:
14
221
02
0
212.34
2490.06
57782.53
2010-08-0115:
16:
43
222
02
0
92.38
2485.73
57695.08
2010-08-0115:
48:
22
223
02
0
243.85
2474.40
57464.67
2010-08-0116:
06:
31
224
02
0
206.69
2464.77
57267.02
2010-08-0116:
25:
54
225
02
0
224.50
2454.51
57054.65
2010-08-0116:
41:
24
226
02
0
169.26
2446.77
56893.24
2010-08-0117:
06:
08
227
02
0
220.09
2436.85
56684.86
2010-08-0117:
45:
54
228
02
0
117.54
2431.55
56572.86
2010-08-0118:
03:
34
229
02
0
93.44
2427.32
56483.12
2010-08-0118:
14:
52
230
02
0
114.46
2422.20
56374.11
2010-08-0118:
35:
24
231
02
0
174.69
2414.35
56206.14
2010-08-0119:
12:
55
232
02
0
232.77
2404.05
55984.22
2010-08-0120:
34:
44
233
02
0
110.86
2399.15
55878.05
2010-08-0121:
05:
57
234
02
0
138.59
2393.12
55746.87
2010-08-0207:
18:
34
235
02
0
242.21
2382.50
55514.45
2010-08-0207:
23:
30
236
02
0
186.43
2374.35
55334.90
2010-08-0207:
39:
21
237
02
0
275.38
2362.44
55070.68
2010-08-0207:
48:
36
238
02
0
92.65
2358.40
54980.57
2010-08-0208:
04:
44
239
02
0
239.28
2348.13
54750.40
2010-08-0208:
28:
32
240
02
0
206.68
2339.37
54552.85
2010-08-0208:
33:
36
241
02
0
104.63
2334.88
54451.17
2010-08-0208:
46:
28
242
02
0
158.80
2328.13
54297.75
2010-08-0208:
58:
39
243
02
0
142.43
2322.14
54161.06
2010-08-0209:
03:
54
244
02
0
189.17
2314.14
53977.71
2010-08-0209:
14:
47
245
02
0
238.95
2304.14
53747.27
2010-08-0209:
25:
55
246
02
0
73.58
2301.09
53676.72
2010-08-0209:
35:
54
247
02
0
245.27
2290.87
53439.37
2010-08-0209:
59:
33
248
02
0
251.78
2280.46
53196.16
2010-08-0210:
13:
32
249
02
0
134.59
2274.92
53066.14
2010-08-0210:
18:
24
250
02
0
153.02
2268.61
52917.56
2010-08-0210:
26:
36
251
02
0
188.26
2260.89
52735.08
2010-08-0210:
38:
33
252
02
0
220.97
2251.88
52521.14
2010-08-0210:
46:
54
253
02
0
229.97
2242.46
52296.37
2010-08-0210:
58:
37
254
02
0
237.73
2232.88
52066.65
2010-08-0211:
05:
34
255
02
0
144.04
2226.99
51924.85
2010-08-0211:
26:
38
256
02
0
158.25
2220.70
51772.96
2010-08-0211:
58:
37
257
02
0
287.87
2209.13
51492.32
2010-08-0212:
09:
46
258
02
0
192.77
2201.40
51303.95
2010-08-0212:
36:
44
259
02
0
262.67
2190.91
51047.20
2010-08-0212:
55:
32
260
02
0
121.96
2186.14
50930.04
2010-08-0213:
18:
34
261
02
0
208.47
2177.92
50727.53
2010-08-0213:
26:
42
262
02
0
198.58
2170.04
50532.69
2010-08-0213:
38:
24
263
02
0
297.29
2158.40
50243.62
2010-08-0213:
45:
37
264
02
0
72.41
2155.54
50172.37
2010-08-0213:
55:
34
265
02
0
178.40
2148.54
49997.62
2010-08-0214:
18:
36
266
02
0
184.06
2141.32
49816.82
2010-08-0214:
27:
33
267
02
0
74.38
2138.42
49744.05
2010-08-0214:
48:
24
268
02
0
285.23
2127.37
49465.96
2010-08-0214:
56:
38
269
02
0
279.15
2116.53
49191.94
2010-08-0215:
05:
14
270
02
0
166.23
2110.14
49029.86
2010-08-0215:
16:
38
271
02
0
254.41
2100.32
48779.99
2010-08-0215:
27:
54
272
02
0
89.64
2096.84
48691.21
2010-08-0215:
48:
34
273
02
0
214.75
2088.64
48481.56
2010-08-0215:
56:
39
274
02
0
120.77
2084.03
48363.42
2010-08-0216:
23:
44
275
02
0
168.81
2077.58
48197.79
2010-08-0216:
32:
36
276
02
0
272.92
2067.14
47928.87
2010-08-0216:
54:
32
277
02
0
103.92
2063.17
47826.34
2010-08-0217:
38:
34
278
02
0
131.94
2058.14
47696.24
2010-08-0217:
45:
26
279
02
0
181.74
2051.30
47518.96
2010-08-0218:
08:
37
280
02
0
142.11
2045.92
47379.23
2010-08-0219:
24:
24
281
02
0
264.62
2035.94
47119.35
2010-08-0219:
48:
54
282
02
0
313.84
2024.06
46808.88
2010-08-0220:
08:
36
283
02
0
96.66
2020.47
46714.83
2010-08-0220:
13:
24
284
02
0
116.16
2016.11
46600.46
2010-08-0220:
43:
34
285
02
0
239.12
2007.08
46363.09
2010-08-0307:
01:
55
286
02
0
154.50
2001.33
46211.59
2010-08-0307:
47:
25
287
02
0
314.56
1989.59
45901.47
2010-08-0308:
03:
51
288
02
0
316.03
1977.87
45590.80
2010-08-
升级会员 