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zouhy0442

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注册: 2013-09-14
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专业: 能源化工

[求助] 1stopt能进行隐函数非线性拟合吗？谁能帮拟合一下新型液体的粘度混合计算公式

背景，液体的混合粘度通常符合Refutas模型，即：
1：每种组分的混合系数VBNi=a*ln(ln(VisA+b))+c
2: 总混合系数VBNm=A的含量*A的混合系数VBN+B的含量*B的混合系数VBN
3：混合后粘度=exp(exp((VBNm-c)/a))-b,就是根据步骤1的公式反推出来的；
详细理论请参考附件的论文第1页公式2,3。
现在已知：A的粘度，B的粘度，A的含量，B的含量，及实测的混合粘度，需根据上述公式拟合出参数a, b,c 的值。
参数：a, b, c
变量：x1, Vis1,Vis2, Vis_blend
隐函数f=x1*(a*ln(ln(Vis1+b))+c)+(1-x1)*(a*ln(ln(Vis2+b))+c)-(a*ln(ln(Vis_blend+b))+c)
问题：
1：用Origin8 无法进行隐函数的拟合；不知道1stopt是否可以，以前从没接触过。看版上很多人说很强大，但一直没有这个软件。不知哪位大侠可否帮助一下，谢谢啦！

数据如下，请参考附件excel文件：
Vis1 Vis2 x1 1-x1 Vis_blend
4.151 147.4 60.0% 40.0% 15.64
48.43 616.9 9.6% 90.4% 460.3
70.22 616.7 60.0% 40.0% 152.6
70.22 616.9 11.3% 88.7% 461
70.22 616.9 11.3% 88.7% 461
48.43 616.9 22.1% 77.9% 320.3
6.678 616.9 4.6% 95.4% 460.2
4.151 147.4 55.0% 45.0% 18.54
70.22 616.7 80.0% 20.0% 101.9
48.43 616.7 30.0% 70.0% 257.2
31.18 616.9 8.0% 92.1% 460.6
70.22 616.7 75.0% 25.0% 112.3
70.22 616.7 65.0% 35.0% 137.3
70.22 616.7 70.0% 30.0% 124
48.43 616.7 50.0% 50.0% 152.4
70.22 616.7 25.0% 75.0% 330.2
70.22 616.7 35.0% 65.0% 261.9
48.43 616.7 25.0% 75.0% 295.8
70.22 616.7 40.0% 60.0% 233.9
18.74 616.9 6.6% 93.4% 460
48.43 616.7 80.0% 20.0% 75.03
48.43 616.9 35.9% 64.2% 220.1
48.43 616.7 40.0% 60.0% 197.2
70.22 616.7 45.0% 55.0% 209.3
70.22 616.9 42.7% 57.3% 220.2
70.22 616.7 55.0% 45.0% 168.7
6.678 616.9 10.7% 89.4% 318.6
70.22 616.7 30.0% 70.0% 293.3
4.151 147.4 50.0% 50.0% 21.97
48.43 616.7 35.0% 65.0% 225.3
6.678 616.9 17.5% 82.5% 216.3
31.17 616.7 80.0% 20.0% 51.45
70.22 616.7 50.0% 50.0% 187.5
48.43 616.7 45.0% 55.0% 173.5
39.17 147.4 89.4% 10.6% 44.9
48.43 616.7 60.0% 40.0% 119.5
4.151 147.4 65.0% 35.0% 13.2
31.17 616.7 75.0% 25.0% 58.59
48.43 616.7 65.0% 35.0% 106.1
70.22 616.9 26.3% 73.7% 319.4
48.43 616.7 75.0% 25.0% 84.19
31.17 616.7 45.0% 55.0% 135.6
48.43 616.7 70.0% 30.0% 94.44
31.17 616.7 25.0% 75.0% 255.3
31.17 616.7 35.0% 65.0% 184.6
31.18 616.9 18.3% 81.7% 320.8
31.17 616.7 30.0% 70.0% 216.8
31.17 616.7 70.0% 30.0% 67
31.18 616.9 29.6% 70.4% 220
48.43 616.7 55.0% 45.0% 135.4
397.4 1612 89.4% 10.6% 460.7
6.678 616.7 25.0% 75.0% 144.5
31.17 616.7 65.0% 35.0% 76.84
5.966 147.4 80.0% 20.0% 10.88
31.17 616.7 50.0% 50.0% 117.4
4.151 147.4 45.0% 55.0% 26.18
31.17 616.7 60.0% 40.0% 88.3
18.74 616.9 15.1% 84.9% 320.1
31.17 616.7 55.0% 45.0% 101.7
4.151 147.4 35.0% 65.0% 37.15
31.17 616.7 40.0% 60.0% 158.7
8.058 65.87 9.6% 90.4% 51.73
5.966 65.87 8.0% 92.1% 52.29
10.46 65.87 11.3% 88.7% 51.42
4.151 147.4 70.0% 30.0% 11.15
39.16 65.87 61.2% 38.8% 46.9
6.678 616.7 30.0% 70.0% 112
4.151 147.4 40.7% 59.3% 30.46
6.678 616.7 35.0% 65.0% 87.86
4.151 147.4 25.0% 75.0% 53.83
5.966 147.4 75.0% 25.0% 12.64
397.3 616.9 61.2% 38.8% 460.2
4.151 147.4 75.0% 25.0% 9.439
18.74 616.9 24.6% 75.4% 219.9
4.151 147.4 80.0% 20.0% 7.994
6.678 616.7 40.0% 60.0% 69.19
4.151 65.87 6.6% 93.4% 52.33
4.151 147.4 32.4% 67.6% 41.23
10.46 65.87 26.3% 73.7% 37.97
5.966 147.4 70.0% 30.0% 14.72
10.46 65.96 80.0% 20.0% 14.36
4.151 147.4 24.6% 75.5% 55.29
4.151 147.4 40.0% 60.0% 31.58
10.46 65.96 25.0% 75.0% 38.75
5.966 147.4 65.0% 35.0% 17.12
6.678 616.7 45.0% 55.0% 54.98
10.46 65.96 75.0% 25.0% 15.58
8.058 65.87 22.1% 77.9% 38.31
10.46 147.4 80.0% 20.0% 17.3
8.058 147.4 80.0% 20.0% 14.04
10.46 65.96 30.0% 70.0% 35.08
8.058 65.96 25.0% 75.0% 35.88
10.46 65.96 35.0% 65.0% 31.89
8.058 65.96 80.0% 20.0% 11.56
10.46 65.96 70.0% 30.0% 16.93
10.46 65.96 60.0% 40.0% 20.16
10.46 65.96 40.0% 60.0% 28.96
6.678 616.7 50.0% 50.0% 44
10.46 65.96 65.0% 35.0% 18.44
5.966 147.4 60.0% 40.0% 19.98
8.058 65.96 75.0% 25.0% 12.71
10.46 65.87 42.7% 57.3% 27.49
5.966 65.87 18.3% 81.7% 38.94
8.058 147.4 75.0% 25.0% 16.1
5.966 147.4 55.0% 45.0% 23.25
10.46 65.96 45.0% 55.0% 26.33
8.058 65.96 30.0% 70.0% 31.97
10.46 65.96 55.0% 45.0% 21.95
10.46 65.96 50.0% 50.0% 24.01
10.46 147.4 75.0% 25.0% 19.67
8.058 65.96 70.0% 30.0% 13.98
8.058 65.96 35.0% 65.0% 28.65
8.058 65.87 35.9% 64.2% 28.11
5.966 147.4 25.0% 75.0% 60.93
2.059 65.87 4.6% 95.4% 52.89
5.966 147.4 50.0% 50.0% 27.19
5.966 147.4 28.6% 71.4% 53.96
5.966 147.4 47.2% 52.8% 29.65
8.058 65.96 40.0% 60.0% 25.68
8.058 65.96 55.0% 45.0% 18.83
5.966 147.4 40.0% 60.0% 37.2
5.966 147.4 30.0% 70.0% 51.57
8.058 65.96 65.0% 35.0% 15.38
5.966 147.4 45.0% 55.0% 31.79
6.678 616.7 55.0% 45.0% 35.37
8.058 147.4 70.0% 30.0% 18.5
8.058 65.96 45.0% 55.0% 23.1
8.058 65.96 60.0% 40.0% 16.99
5.966 147.4 37.7% 62.3% 40.15
10.46 147.4 25.0% 75.0% 72.27
5.966 147.4 35.0% 65.0% 43.84
10.46 147.4 70.0% 30.0% 22.36
8.058 65.96 50.0% 50.0% 20.77
6.678 616.7 60.0% 40.0% 28.78
8.058 147.4 65.0% 35.0% 21.23
4.151 65.87 15.1% 84.9% 39.33
8.058 147.4 25.0% 75.0% 67.09
5.995 65.96 25.0% 75.0% 32.44
10.46 147.4 65.0% 35.0% 25.37
6.678 616.7 65.0% 35.0% 23.49
2.059 147.4 18.3% 81.7% 56.98
10.46 147.4 30.0% 70.0% 63.23
10.46 147.4 61.6% 38.4% 27.67
8.058 147.4 30.0% 70.0% 57.75
8.058 147.4 60.0% 40.0% 24.44
10.46 147.4 60.0% 40.0% 28.81
5.966 65.87 29.6% 70.4% 28.78
10.46 147.4 35.0% 65.0% 55.25
6.678 616.7 70.0% 30.0% 19.29
5.995 65.96 80.0% 20.0% 8.938
6.678 616.7 80.0% 20.0% 13.23
8.058 147.4 33.2% 66.8% 52.62
10.46 147.4 55.0% 45.0% 32.77
5.995 65.96 30.0% 70.0% 28.43
10.46 147.4 40.0% 60.0% 48.42
8.058 147.4 55.0% 45.0% 28.14
8.058 147.4 54.3% 45.7% 28.67
2.059 147.4 24.1% 75.9% 43.77
10.46 147.4 45.0% 55.0% 42.44
10.46 147.4 50.0% 50.0% 37.28
10.46 147.4 37.7% 62.3% 51.58
8.058 147.4 43.5% 56.5% 38.93
6.678 616.7 75.0% 25.0% 15.86
8.058 147.4 35.0% 65.0% 50.02
8.058 147.4 40.0% 60.0% 43.17
8.058 147.4 45.0% 55.0% 37.37
10.46 147.4 49.4% 50.6% 37.99
8.058 147.4 50.0% 50.0% 32.46
5.995 65.96 75.0% 25.0% 9.926
5.995 65.96 35.0% 65.0% 25.04
6.678 1612 80.0% 20.0% 16.71
5.995 65.96 40.0% 60.0% 22.14
5.995 65.96 70.0% 30.0% 11.05
4.151 65.87 24.6% 75.4% 29.26
5.995 65.96 45.0% 55.0% 19.58
5.995 65.96 60.0% 40.0% 13.83
5.995 65.96 65.0% 35.0% 12.34
2.059 147.4 25.0% 75.0% 41.5
5.995 65.96 50.0% 50.0% 17.4
5.995 65.96 55.0% 45.0% 15.49
70.22 1612 80.0% 20.0% 126.6
2.059 65.87 10.7% 89.4% 40.34
70.22 1612 25.0% 75.0% 690.1
2.059 147.4 30.0% 70.0% 33
2.059 147.4 30.4% 69.6% 32.38
70.22 1612 75.0% 25.0% 147.3
6.678 1612 75.0% 25.0% 21.29
48.43 1612 80.0% 20.0% 93.62
2.059 147.4 35.0% 65.0% 26.48
70.22 1612 30.0% 70.0% 588.2
70.22 1612 70.0% 30.0% 171.4
70.22 1612 35.0% 65.0% 501.1
31.18 1612 80.0% 20.0% 64.36
70.22 1612 65.0% 35.0% 199
2.059 147.4 40.0% 60.0% 21.27
48.43 1612 25.0% 75.0% 619.5
48.43 1612 75.0% 25.0% 110.3
70.22 1612 61.6% 38.4% 220.4
70.22 1612 37.7% 62.3% 461.7
70.22 1612 40.0% 60.0% 428.5
70.22 1612 60.0% 40.0% 231.3
6.678 1612 70.0% 30.0% 27.19
70.22 1612 45.0% 55.0% 366.3
70.22 1612 55.0% 45.0% 269.2
70.22 1612 50.0% 50.0% 314
18.74 1612 80.0% 20.0% 41.79
70.22 1612 49.4% 50.6% 320.7
2.059 147.4 45.0% 55.0% 17.24
48.43 1612 30.0% 70.0% 515.9
31.18 1612 75.0% 25.0% 77.19
48.43 1612 70.0% 30.0% 130.4
2.059 65.87 17.5% 82.5% 29.96
2.059 147.4 50.0% 50.0% 14.05
6.678 1612 18.3% 81.7% 457.3
31.18 1612 25.0% 75.0% 535.2
48.43 1612 33.2% 66.8% 461.5
6.678 1612 65.0% 35.0% 34.66
48.43 1612 65.0% 35.0% 153.8
2.059 147.4 55.0% 45.0% 11.49
48.43 1612 35.0% 65.0% 433.7
2.059 147.4 60.0% 40.0% 9.427
18.74 1612 75.0% 25.0% 51.24
31.18 1612 70.0% 30.0% 93.01
31.18 1612 28.6% 71.4% 461.5
48.43 1612 60.0% 40.0% 182.3
2.059 147.4 80.0% 20.0% 4.34
48.43 1612 40.0% 60.0% 362.9
31.18 1612 30.0% 70.0% 435.1
48.43 1612 43.5% 56.5% 319.8
48.43 1612 45.0% 55.0% 304.4
48.43 1612 54.3% 45.7% 220.8
48.43 1612 55.0% 45.0% 216.1
2.059 147.4 75.0% 25.0% 5.255
2.059 147.4 65.0% 35.0% 7.721
2.059 147.4 70.0% 30.0% 6.374
48.43 1612 50.0% 50.0% 256.6
18.74 1612 25.0% 75.0% 449.2
31.18 1612 65.0% 35.0% 111.9
31.18 1612 35.0% 65.0% 355.5
6.678 1612 25.0% 75.0% 302.3
6.678 1612 60.0% 40.0% 44.89
31.18 1612 37.7% 62.3% 319.4
18.74 1612 70.0% 30.0% 62.93
31.18 1612 40.0% 60.0% 290.2
2.059 65.96 25.0% 75.0% 21.97
18.74 1612 24.6% 75.5% 465.1
31.18 1612 60.0% 40.0% 135.1
6.678 1612 24.1% 75.9% 323.5
31.18 1612 55.0% 45.0% 162.9
6.678 1612 55.0% 45.0% 57.65
6.678 1612 30.4% 69.6% 218.7
6.678 1612 30.0% 70.0% 224.3
31.18 1612 45.0% 55.0% 239.5
31.18 1612 47.2% 52.8% 219.7
18.74 1612 30.0% 70.0% 355.5
31.18 1612 50.0% 50.0% 197.5
6.678 1612 50.0% 50.0% 74.48
18.74 1612 65.0% 35.0% 77.53
2.059 65.96 30.0% 70.0% 18.1
6.678 1612 45.0% 55.0% 96.82
18.74 1612 35.0% 65.0% 281.3
6.678 1612 40.0% 60.0% 126.9
6.678 1612 35.0% 65.0% 168.5
18.74 1612 32.4% 67.6% 320.1
2.059 65.96 80.0% 20.0% 3.524
18.74 1612 60.0% 40.0% 95.71
2.059 65.96 35.0% 65.0% 15.04
18.74 1612 40.7% 59.3% 219.2
18.74 1612 55.0% 45.0% 118
18.74 1612 50.0% 50.0% 145.7
18.74 1612 45.0% 55.0% 181.4
2.059 65.96 40.0% 60.0% 12.51
2.059 65.96 75.0% 25.0% 4.056
18.74 1612 40.0% 60.0% 229.4
2.059 65.96 45.0% 55.0% 10.48
2.059 65.96 70.0% 30.0% 4.716
2.059 65.96 50.0% 50.0% 8.843
2.059 65.96 65.0% 35.0% 5.485
2.059 65.96 60.0% 40.0% 6.384
2.059 65.96 55.0% 45.0% 7.475

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附件 1 : viscosity_blend_test_result.xlsx

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1楼 2013-09-29 11:43:46

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zouhy0442

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4楼: Originally posted by zouhy0442 at 2013-09-29 18:30:59
这个是第一次附件中论文的描述：

新图片.jpg
...

这篇论文的作者竟然还拟合出了参数值。

新图片(1).jpg

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5楼2013-09-29 18:35:43

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dingd

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dbb627: 金币+1, 谢谢指导 2013-09-29 14:39:20

你的隐函数公式：x1*(a*ln(ln(Vis1+b))+c)+(1-x1)*(a*ln(ln(Vis2+b))+c)-(a*ln(ln(Vis_blend+b))+c)=0
好像可以化成显示，用Mathematica试了下，如下：

Vis_blend = -b + E^(Log[b + Vis1]^x1 Log[b + Vis2]^(1 - x1))

只是值剩下一个参数b了，公式没问题吗？

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2楼2013-09-29 13:52:34

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2楼: Originally posted by dingd at 2013-09-29 13:52:34
你的隐函数公式：x1*(a*ln(ln(Vis1+b))+c)+(1-x1)*(a*ln(ln(Vis2+b))+c)-(a*ln(ln(Vis_blend+b))+c)=0
好像可以化成显示，用Mathematica试了下，如下：

Vis_blend = -b + E^(Log^x1 Log^(1 - x1))

只是值剩下 ...

我也很奇怪为何参数b，c可以消去，我看到附件的论文中就是这样的；然后我又查了很多文献，Refutas的数学模型都是这么描述的。我又上传了一个有关粘度混合的论文，您可以看一下，也是这么描述的。在这个论文的第17页也是这么描述的。只是对于石油产品，a=14.534; b=0.8, c=10.975;