计算机在化工中的应用实验报告

1、计算机在化学化工中的应用实验报告学院： 化学与化工学院 班级：12级硕勋励志班 姓名: 徐凯杰 学号： 120702028实验一 传热实验中多变量的曲线的拟合一、实验目的1） 熟悉VB编程平台2） 掌握多变量曲线拟合的算法3） 编拟合所给的传热实验模型的VB程序4） 通过实验数据求出模型数据、并掌握解线性方程组的克拉默法则二、运行环境1） Microsoft Windows XP2） VB6.0三、实验原理略四、vb代码Private Sub Command1_Click()Dim m As Integer'm=inputbox(“实验次数”)m = 7Dim x10, x20, y0

2、Dim i, j, k As IntegerDim a(1 To 10, 1 To 10), y(1 To 10), y1(1 To 10), a0, a1, a2Dim s, S1, S2, S3, b(1 To 10, 1 To 10), xxDim x1(1 To 10), x2(1 To 10), YY, sd'open"dem.dat"for input as#1'for i=1 to m' input#1,xx,YY' x1(i)=xx' x2(i0=xx2' y(i)=YY'next i'clos

3、e#1'7组努塞尔准数、雷诺数及普兰德准数，数据最大时应采用直接从文件读取方法x10 = Array(0, 100, 200, 300, 500, 100, 700, 800) '注意下标的起点处理（加0)x20 = Array(0, 2, 4, 1, 0.3, 5, 3, 4) '注意下标的起点处理（加0)y0 = Array(0, 1.127, 2.416, 2.205, 2.312, 1.484, 6.038, 7.325) '注意下标的起点处理（加0)For i = 1 To m x1(i) = Log(x10(i) x2(i) = Log(x20(i)

4、 y(i) = Log(y0(i)Next i'求解法方程系数矩阵a(1, 1) = ma(1, 2) = 0For i = 1 To m a(1, 2) = a(1, 2) + x1(i)Next ia(2, 1) = a(1, 2)a(1, 3) = 0For i = 1 To m a(1, 3) = a(1, 3) + x2(i)Next ia(3, 1) = a(1, 3)a(2, 2) = 0For i = 1 To m a(2, 2) = a(2, 2) + x1(i) * x1(i)Next ia(3, 3) = 0For i = 1 To m a(3, 3) = a(3

5、, 3) + x2(i) * x2(i)Next ia(2, 3) = 0For i = 1 To m a(2, 3) = a(2, 3) + x1(i) * x2(i)Next ia(3, 2) = a(2, 3)'求解法方程常数向量y1(1) = 0 For i = 1 To m y1(1) = y1(1) + y(i) Next iy1(2) = 0 For i = 1 To m y1(2) = y1(2) + x1(i) * y(i) Next iy1(3) = 0 For i = 1 To m y1(3) = y1(3) + x2(i) * y(i) Next i'(

6、利用克拉默法则解法方程/线性非常组)s = a(1, 1) * a(2, 2) * a(3, 3) + a(1, 2) * a(2, 3) * a(3, 1) + a(1, 3) * a(2, 1) * a(3, 2)s = s - a(1, 1) * a(2, 3) * a(3, 2) - a(1, 2) * a(2, 1) * a(3, 3) - a(1, 3) * a(2, 2) * a(3, 1)For j = 1 To 3 b(j, 1) = a(j, 1) a(j, 1) = y1(j)Next jS1 = a(1, 1) * a(2, 2) * a(3, 3) + a(1, 2)

7、 * a(2, 3) * a(3, 1) + a(1, 3) * a(2, 1) * a(3, 2)S1 = S1 - a(1, 1) * a(2, 3) * a(3, 2) - a(1, 2) * a(2, 1) * a(3, 3) - a(1, 3) * a(2, 2) * a(3, 1)For j = 1 To 3 a(j, 1) = b(j, 1)Next jFor j = 1 To 3 b(j, 2) = a(j, 2) a(j, 2) = y1(j) Next jS2 = a(1, 1) * a(2, 2) * a(3, 3) + a(1, 2) * a(2, 3) * a(3,

8、1) + a(1, 3) * a(2, 1) * a(3, 2)S2 = S2 - a(1, 1) * a(2, 3) * a(3, 2) - a(1, 2) * a(2, 1) * a(3, 3) - a(1, 3) * a(2, 2) * a(3, 1)For j = 1 To 3 a(j, 2) = b(j, 2) Next jFor j = 1 To 3 b(j, 3) = a(j, 3) a(j, 3) = y1(j)Next jS3 = a(1, 1) * a(2, 2) * a(3, 3) + a(1, 2) * a(2, 3) * a(3, 1) + a(1, 3) * a(2

9、, 1) * a(3, 2)S3 = S3 - a(1, 1) * a(2, 3) * a(3, 2) - a(1, 2) * a(2, 1) * a(3, 3) - a(1, 3) * a(2, 2) * a(3, 1)a0 = S1 / sa1 = S2 / sa2 = S3 / sText1.Text = Int(1000 * Exp(a0) + 0.5) / 1000 '四舍五入保留三位Text2.Text = Int(1000 * a1 + 0.5) / 1000Text3.Text = Int(1000 * a2 + 0.5) / 1000sd = 0For i = 1 T

10、o m sd = sd + Abs(a0 + a1 * x1(i) + a2 * x2(i) - y(i) '求 Nextsd = sd / mText4.Text = sd 'Int(1000 * sd + 0.5) / 1000Print Tab(50); "序号", "模型计算值", "实验值"For i = 1 To mPrintPrint Tab(45); i; (Text1.Text) * (x10(i) (Text2.Text) * (x20(i) (Text3.Text); 0.023 * (x10(i

11、) 0.8) * (x20(i) 0.3)NextEnd Sub五、实验结果截图六、实验后思考。 VB编程是一种简单，并且效率高的可视化的、面向对象和采用事件驱动方式的结构化高级程序设计语言。通过对本实验的实际操作，我掌握了多变量曲线拟合的基本算法，了解了解线性方程组的克拉默法则。并且，同时在以后的工作中，可以通过这个实验来解决大部分实验数据及模型参数的拟合问题。实验二 梯度法拟合蒸汽压与温度关系模型一 、实验目的1) 掌握梯度法拟合的基本算法以及理解其普适性2) 编写梯度法拟合蒸汽压与温度的关系的VB程序3) 通过实对程序进行验证，并注意比较初值对运行速度和结果的影响二 、运行环境1） Mi

12、crosoft Windows XP2） VB6.0三 、实验原理略四、 实验VB程序代码Private Sub Command1_Click(Index As Integer)Dim m, n As Integerm = 6Dim i, j, k As IntegerDim A, B, C, F, ee, P(1 To 10), T(1 To 10)Dim A1, B1, C1, TA, TB, TC, TT, f1, f2, f3Dim sd, W, S, EY, XX, YY'(由dem.dat输入实验数据XX = Array(-23.7, -10, 0, 10, 20, 30,

13、 40) '注意下标的起点处理（加0)YY = Array(0.101, 0.174, 0.254, 0.359, 0.495, 0.662, 0.88) '注意下标的起点处理（加0)Print "直接读数据文件后计算"For i = 1 To m T(i) = XX(i) T(i) = 273.15 + T(i) P(i) = YY(i) * 7600 Print T(i), P(i)Next iClose i A = Val(InputBox("A") '指定初值 B = Val(InputBox("B")

14、 '指定初值 C = Val(InputBox("C") '指定初值1000 F = 0For i = 1 To m ee = FNP(A, B, C, T(i), P(i) ee = ee 2 F = F + eeNext if1 = 0A1 = A + 0.000001 * A'print"A,A1="A,A1For i = 1 To m ee = FNP(A1, B, C, T(i), P(i) ee = ee 2 f1 = f1 + eeNext iTA = (f1 - F) / (0.000001 * A)'pr

15、int f1,F,TA'A=val(inputbox("A")f2 = 0B1 = B + 0.00001 * BFor i = 1 To m ee = FNP(A, B1, C, T(i), P(i) ee = ee 2 f2 = f2 + eeNext iTB = (f2 - F) / (0.00001 * B)f3 = 0C1 = C + 0.00001 * CFor i = 1 To m ee = FNP(A, B, C1, T(i), P(i) ee = ee 2 f3 = f3 + eeNext iTC = (f3 - F) / (0.00001 * C

16、)TT = TA 2 + TB 2 + TC 2TT = Sqr(TT)If TT > 0.001 ThenA = A - 0.005 * TAB = B - 1.5 * TBC = C - 0.001 * TCGoTo 1000ElseEnd IfPrintsd = 0For i = 1 To m '/计算绝对平均相对误差sd = sd + Abs(FNSD(A, B, C, T(i), P(i) / P(i)Print FNSD(A, B, C, T(i), P(i)Next isd = sd / mPrintPrint "A,B,C=" A, B, CP

17、rint "sd=" sd '/打印绝对平均相对误差End SubPublic Function FNP(A, B, C, T, P)FNP = (A - B / (T + C) - Log(P)End FunctionPublic Function FNSD(A, B, C, T, P)FNSD = Exp(A - B / (T + C) - PEnd Function五 、实验结果截图六 、实验后思考。本实验是基于最小二乘原理，函数拟合的目标是使拟合函数和实际测量值之间的差的平方和最小。对于最小值的问题，梯度法是用负梯度方向作为优化搜索方向。而梯度法是一个简单的

18、迭代优化计算方法。注意的是，负梯度的最速下降性是一个局部的性质。在计算的前期使用此法，当接近极小点时，在改用其他的算法，如共轭梯度法。 实验三 二分法求解化工中的非线性方程一、实验目的1） 掌握二分法解非线性方程组的基本算法2） 编写二分法邱珏非线性方程组的VB程序3） 通过实例的程序进行调试，并学习输出数据格式化二、 运行环境1） Microsoft WindowsXP2） VB6.0三 、实验原理略四 、实验VB代码Private Sub Command1_Click()Dim ax As SingleDim bx As SingleDim cx As SingleDim ay As Si

19、ngleDim by As SingleDim cy As SingleDim e As SingleDim num As Integer '累计次数变量Dim st As StringDim ch As StringDim sp As Stringch = Chr(13) + Chr(10)sp = Space(10)st = "二分法解方程" + chst = st + "求2,3-二甲基苯胺沸点（当 P=101325 时 解 lnP=59.7622-8013.69/T-5.081lnT)" + chax = 200bx = 500e = 0

20、.01st = st + "区间左端点初始值 ax=" + Str(ax) + chst = st + "区间右端点初始值 bx=" + Str(bx) + chst = st + "精度控制限 e=" + Str(e) + chst = st + "num" + sp + "ax" + Space(14) + "bx" + Space(14) + "|ax-bx|" + chay = F(ax)by = F(bx)num = 1Do While Abs(

21、ax - bx) > e cx = (ax + bx) / 2 cy = F(cx) If cy = 0 Then Exit Do '如果已得解，则退出循环 If cy * ay > 0 Then ax = cx ay = cy Else bx = cx by = cy End If st = st + Format(num, "000") + sp + Format(ax, "000.00") + sp + Format(bx, "000.00") + sp + Format(Abs(ax - bx), &quo

22、t;0.0000") + ch num = num + 1Loopst = st + ch + "2,3-二甲基苯胺沸点:" + Format(cx, "#00.00") + "K" + ch + chst = st + "*时间:" + Str(Time) + Space(3) + "日期:" + Str(Date) + chText1.Text = ""Text1.Text = stEnd Sub'二分法求2,3-二甲基苯胺沸点所用函数Private F

23、unction F(ByVal u As Single)F = Log(101325) - 59.7622 + 8013.69 / u + 5.081 * Log(u) '注意对数运算End Function五、实验结果截图六 、实验后思考。 通过应用微积分中的介值定理，是是用二分法的前提条件。如果我们所要求解的方程从物理意义上来讲确实存在实根，但又不满足f(a)f(b)<0,这时候，我们必须通过改变a和b的值来满足二分法的应用条件。实验四 主元最大高斯消元法解化工中的线性方程组一、实验目的1） 掌握主元最大高斯消元法2） 编写最大高斯消元法求解线性方程组的VB程序3） 通过实例

24、对程序进行调试，并比较一般的高斯消去法比较二 、运行环境1） Microsoft WIndowsXP_2） VB6.0三 、实验原理略四 、实验程序代码Private Sub Command1_Click()Dim m, n As IntegerDim a(), z(), x(), w, aa(), s, t, k, ln = 4ReDim a(n + 2, 2 + n), z(n + 2, 2 + n), x(n + 1), aa(n + 2, 2 + n)Dim i, j, k1, k2, stDim ch As StringDim sp As Stringch = Chr(13) + C

25、hr(10)sp = Space(5)a(1, 1) = 6# / 123.1a(1, 2) = 6# / 93.13a(1, 3) = 3# / 73.1a(1, 4) = 2# / 43.07a(2, 1) = 5# / 123.1a(2, 2) = 7# / 93.13a(2, 3) = 7# / 73.1a(2, 4) = 6# / 43.07a(3, 1) = 1# / 123.1a(3, 2) = 1# / 93.13a(3, 3) = 1# / 73.1a(3, 4) = 0# / 43.07a(4, 1) = 2# / 123.1a(4, 2) = 0# / 93.13a(4,

26、 3) = 1# / 73.1a(4, 4) = 1# / 43.07a(1, 5) = 57.78 / 12.01a(2, 5) = 7.92 / 1.008a(3, 5) = 11.23 / 14.01a(4, 5) = 23.09 / 16st = st + "主元最大高斯消去法解线性方程组" + chst = st + "设有一混合物由硝基苯、苯胺、氨基丙酮、乙醇组成;" + chst = st + "对该混合物进行元素分析结果以百分数表示如下" + chst = st + "C%=57.78%;H%=7.92%;N

27、%=11.23%;O%=23.09%" + chst = st + "原子量：A(C)=12.01;A(H)=1.008;A(N)=14.01;A(O)=16.00" + chst = st + "分子量：硝基苯 123.1;苯胺 93.13;氨基丙酮 73.10;乙醇 43.07" + chst = st + "硝基苯分子C-6;H-5;N-1;O-2" + chst = st + "苯胺分子C-6;H-7;N-1;O-0" + chst = st + "氨基丙酮分子C-3;H-7;N-1;O

28、-1" + chst = st + "乙醇分子C-2;H-6;N-0;O-1" + chst = st + "确定上面四种化合物在混合物中所占的百分比" + ch + ch'寻找主元For i = 1 To n If i = n Then GoTo 200 For t = i + 1 To n If Abs(a(i, i) < Abs(a(t, i) Then For s = i To n + 1 aa(t, s) = a(i, s) a(i, s) = a(t, s) a(t, s) = aa(t, s) Next s Else

29、 End If Next t200'消去w = a(i, i) For j = 1 To n + 1 a(i, j) = a(i, j) / w Next jIf i = n Then GoTo 100For j = i + 1 To n For k = i + 1 To n + 1 z(i, k) = a(i, k) * a(j, i) a(j, k) = a(j, k) - z(i, k) Next kNext jNext i100'回代x(n + 1) = 0 For k = n To 1 Step -1 s = 0 For j = k + 1 To n s = s +

30、a(k, j) * x(j) Next j x(k) = a(k, n + 1) - s 'st=st+"x("+str(i)+")="+format(x(i),"00.00")+"%"+ch 'print"x("k;")="x(k) Next kFor i = 1 To n '输出结果 st = st + "x(" + Str(i) + ")=" + Format(x(i), "00.00"

31、) + "%" + chNext ist = st + chst = st + "*时间:" + Str(Time) + Space(3) + "日期:" + Str(Date) + chText1.Text = ""Text1.Text = stEnd Sub五 、实验结果截图六、 实验后思考高斯消去法不需要方程组的初值，也不需要重复迭代计算。只通过“消去”和“回代”2个过程就可以直接求出方程组的解。然后若是在消去的过程中，若碰到主元为0，则无法计算。所以，发展了“主元最大高斯消去法”。就是在主元所在的列中，寻找

32、到最大的元素，进行行与行之间的调换，并将该最大的元素作为主元，保证主元不为0。实验五 松弛迭代法求解化工中的线性方程组一、实验目的1） 掌握松弛迭代法的基本算法及和紧凑迭代的细微区别2） 编写松弛迭代法求救线性方程组的VB代码，注意学习从文件读取数据3） 通过实例的程序进行验证，并观察松弛迭代因子对结果的影响二、运行环境1） Microsoft WIndowse XP2） VB6.0三、实验原理略四、实验程序代码Private Sub Command1_Click()Dim n As IntegerDim i, j, ff, t, k, l, hDim st As StringDim a()

33、As SingleDim y() As SingleDim b() As SingleDim g() As SingleDim x1() As SingleDim x2() As SingleDim jk() As IntegerDim ch As StringDim sp As Stringch = Chr(13) + Chr(10)sp = Space(5)CommonDialog1.CancelError = True'on error goto errhandlerCommonDialog1.Filter = "数据文件（*.txt）|*.txt|拉图文件（*.bmp

34、）|*.bmp|AllFiles(*.*)|*.*" '文件过滤CommonDialog1.FilterIndex = 0CommonDialog1.DialogTitle = "加载增广矩阵数据文件"CommonDialog1.ShowOpen'*数据文件的行数就是方程的个数Open CommonDialog1.FileName For Input As #1Do While Not EOF(1) Line Input #1, st n = n + 1LoopClose #1'*数据文件的行数就是方程的个数ReDim a(1 To n,

35、1 To n) As SingleReDim b(1 To n, 1 To n) As SingleReDim x1(1 To n) As SingleReDim x2(1 To n) As SingleReDim g(1 To n) As SingleReDim y(1 To n) As Single'*读数据Open CommonDialog1.FileName For Input As #1For i = 1 To n For j = 1 To n Input #1, a(i, j) '方程等号左端数据 Next j Input #1, y(i) '方程等号右端数

36、据Next iClose #q'*读数据st = "松弛迭代法解线性方程" + chst = st + Space(5) + "数据来源于" + CommonDialog1.FileName + ch + chst = st + "增广矩阵如下（对二甲苯-间二甲苯-邻二甲苯-乙苯-（混合物）：" + ch + chst = st + Space(5) + "第一行为12.5nm波长处摩尔吸收系数-混合物吸收" + chst = st + Space(5) + "第一行为13.0nm波长处摩尔吸收系

37、数-混合物吸收" + chst = st + Space(5) + "第一行为13.4nm波长处摩尔吸收系数-混合物吸收" + chst = st + Space(5) + "第一行为14.3nm波长处摩尔吸收系数-混合物吸收" + ch + ch'*输出原始数据 For i = 1 To n For j = 1 To n If a(i, j) >= 0 Then st = st + Space(5) + Format(a(i, j), "0.00000") Else st = st + Space(4) +

38、Format(a(i, j), "0.00000") End If Next j If y(i) >= 0 Then st = st + Space(5) + Format(y(i), "0.00000") + ch Else st = st + Space(4) + Format(y(i), "0.00000") + ch End If Next i'*输出原始数据'-For i = 1 To n x1(i) = 0 x2(i) = 0Next i'for i = 1 to n' for j =

39、 1 to n' a(i,j) = InputBox("a("&i&","&j&")")' Print a(i,j),' next j'y(i) = InputBox("y("&i&")")'print" ",y(i)'Next i'产生迭代矩阵For i = 1 To n g(i) = y(i) / a(i, i) For j = 1 To n If j = i Then

40、 b(i, j) = 0 Else b(i, j) = -a(i, j) / a(i, i) End If Next j Next i e = InputBox("输入松弛因子") '开始松弛迭代Do If k >= 1 Then For i = 1 To n x1(i) = x2(i) Next i End If For i = 1 To n s = g(i) For j = 1 To n s = s + b(i, j) * x2(j) Next j x2(i) = (1 - e) * x1(i) + e * s '注意 Next i eer = 0

41、 For i = 1 To n eer = cer + Abs(x1(i) - x2(i) '计算误差 Next i k = k + 1 '累计次数Loop While (k < 100 And eer >= 0.001) Print kst = st + ch + "方程组的解为：" + ch + chFor i = 1 To n st = st + "x(" + Str(i) + ")=" + Format(x2(i), "0.00000") + ch Next ist = st +

42、 ch + "迭代次数为：" + Str(k) + ch 'format(k,"000")st = st + ch + "松弛因子为：" + Format(e, "0.0000") + chst = st + ch + "误差为：" + Format(eer, "0.000000") + chst = st + chst = st + "*时间：" + Str(Time) + Space(3) + "日期：" + Str(Dat

43、e) + chText1.Text = ""Text1.Text = st End Sub五、实验结果截图六、 实验后思考。松弛迭代法是数值计算中解线性代数方程组的一类迭代法。逐次超松弛迭代过程中，已知迭代方程及其系数矩阵，对任意的初始值，确定超松弛因子，用迭代矩阵来进行计算确定谱半径，然后其绝对值小于一解出来超松弛因子。而紧凑迭代是当松弛因子为1的时候，叫做紧凑迭代。两者的区别在于松弛因子的不同。实验六 龙格库塔法求解化工过程中的常微分方程一、实验目的1） 掌握龙格库塔法的基本原理2） 编写龙格库塔法解决常微分方程的VB程序3） 通过实例的程序进行调试和验证，并观察初值对

44、计算过程及结果的影响4） 掌握VB绘制二维曲线图的方法和绘图参数的设置二、 运行环境1） Microsoft WindowsXP2） VB6.0三 、实验原理略四、 实验程序截图Private Sub Command1_Click()Const eps = 0.00001Dim t() As SingleDim x() As SingleDim y() As SingleDim z() As SingleDim J1, J2 As SingleDim K1, K2, K3, K4 As SingleDim Q1, Q2, Q3, Q4 As SingleDim S1, S2, S3, S4 A

45、s SingleDim h As SingleDim i As IntegerDim n As Integerh = 0.01J1 = 1J2 = 1.1n = Int(10 / h)ReDim t(n + 1), x(n + 1), y(n + 1), z(n + 1) As Singlet(0) = 0x(0) = 0y(0) = 0'z(0) = 0For i = 0 To n - 1K1 = -J1 * x(i)Q1 = J1 * x(i) - J2 * y(i)S1 = h * (J2 * y(i)K2 = -J1 * (x(i) + h * K1 / 2)Q2 = J1 *

46、 (x(i) + h * K1 / 2) - J2 * (y(i) + h * Q1 / 2)S2 = h * (J2 * (y(i) + Q1 / 2)K3 = -J1 * (x(i) + h * K2 / 2)Q3 = J1 * (x(i) + h * K2 / 2) - J2 * (y(i) + h * Q2 / 2)S3 = h * (J2 * (y(i) + Q2 / 2)K4 = -J1 * (x(i) + h * K3)Q4 = J1 * (x(i) + h * K3) - J2 * (y(i) + h * Q3)S4 = h * (J2 * (y(i) + Q3)x(i + 1

47、) = x(i) + h * (K1 + 2 * K2 + 2 * K3 + K4) / 6 '计算A物质的浓度y(i + 1) = y(i) + h * (Q1 + 2 * Q2 + 2 * Q3 + Q4) / 6z(i + 1) = z(i) + (S1 + 2 * Q2 + 2 * Q3 + Q4) / 6z(i) = x(0) - x(i) - y(i)t(i + 1) = t(i) + h '计算反应时间tNext iDim axisname1 As String, axisname2 As Stringaxisname1 = "t"axisna

48、me2 = ""xy_axis picture1, t(), x(), axisname1, axisname2For i = 0 To n - 1 picture1.PSet (t(i), x(i)Next i'xy_axis picture1,t(),y(),axisname1,axisname2For i = 0 To n - 1 Picture.PSet (t(i), y(i) Next i 'xy_axis picture1,t(),z(),axisname1,axisname2 For i = 0 To n - 1 Picture.PSet (t

49、(i), z(i)Next iEnd Sub模块代码Sub xy_axis(pic As PictureBox, x1() As Single, y1() As Single, axisname1 As String, axisname2 As String)On Error GoTo problemx:Dim maxnumber As Single, minnumber As SingleDim leftx As Single, topy As SingleDim rightx As Single, bottomy As SingleDim n As Integern = UBound(x1)pic.Font