Back Analysis of Rock Hydraulic Fracturing by Coupling Numerical Model and Computational Intelligent Technology

Algorithm 1

The code of MSVM.

Sub MSVM()

Dim N As Integer                The number of training samples

Dim Dim As Integer     The dimension of input variables

Dim Dim As Integer     The number of output variables

Dim C As Double               Pentalty factor of SVM

Dim epsilon As Double

Dim sigma As Double

Dim input() As Double         The input of training samples

Dim output() As Double       The output of traning samples

The one sample

Dim     As Double

Dim     As Double

The weights of MSVM

Dim As Double

Dim As Double

Dim As Double

Dim As Double

Dim As Double

Dim As Double

the error of each sample

Dim As Double

Dim As Double

Dim As Double

Dim new() As Double

The coefficient of matrix for computing and

Dim As Double

Dim BB() As Double

Dim lastrow() As Double

Dim lastrow() As Double

The Descending direction

Dim () As Double

Dim () As Double

Dim () As Double

Dim () As Double

Dim 1() As Double

Dim kf() As Double

Dim As Integer

Dim As Integer

Dim As Integer

The step size eta

Dim eta As Double

The control parameters of algorithm convergence                      

Dim delta As Double

Dim As Integer

The value of the numbers of parameters of training samples                  

= Range().Cells.Value

Dim = Range(Dim).Cells.Value

Dim = Range(Dim).Cells.Value

The parameters of SVM

= Range().Cells.Value

epsilon = Range(epsilon).Cells.Value

sigma = Range(sigma).Cells.Value

ReDim input(1 To , 1 To Dim) As Double

ReDim output(1 To , 1 To Dim) As Double

ReDim (1 To Dim) As Double

ReDim (1 To Dim) As Double

ReDim (1 To Dim, 1 To ) As Double

ReDim (1 To Dim) As Double

ReDim (1 To Dim, 1 To ) As Double

ReDim (1 To Dim) As Double

ReDim (1 To Dim, 1 To ) As Double

ReDim (1 To Dim) As Double

ReDim (1 To ) As Double

ReDim (1 To ) As Double

ReDim (1 To Dim) As Double

ReDim new(1 To ) As Double

ReDim (1 To , 1 To ) As Double

ReDim (1 To , 1 To Dim) As Double

ReDim BB(1 To , 1 To Dim) As Double

ReDim lastrow(1 To ) As Double

ReDim lastrow(1 To Dim) As Double

ReDim (1 To Dim, 1 To ) As Double

ReDim (1 To Dim) As Double

ReDim (1 To , 1 To ) As Double

ReDim (1 To , 1 To ) As Double

ReDim 1(1 To , 1 To ) As Double

ReDim (1 To ) As Double

Read the input of training samples

For To

For To Dim

input = Range().Cells

Next

Next

Read the output of training samples

For To

For To Dim

output = Range().Cells.Value

Next

Next

The initial value of and

For To Dim

For To

Next

Next

delta = 1

The iteration process of algorithm

While (delta > 0.001 And )

Replace the value of and by the New and

For To Dim

For To

Next

Next

Compute the value of and

For To

For To Dim

= input

Next

For ii = 1 To

For To Dim

= input(ii, j)

Next

(ii) = kernelfun

Next

For ii = 1 To Dim

(ii) = (ii)

For To

(ii) = (ii) +

Next

Next

For To Dim

Next

= Sqr

If (u(I) < epsilon) Then = 0

If Then ai(I) =

Next

compute the Matrix and Da

For To

For To

For To Dimx

input

input

Next

= kernelfun

If Then Else = 0

Next

Next

For To

For To

If Then Else                

Next

Next

Compute Transpose(a)

For To

lastrow

For To

lastrowlastrow

Next

Next

For To

lastrow

Next

For To Dim

lastrow

For To

lastrowlastrowoutput

Next

Next

For To

For To Dim

BBoutput

Next

Next

For To Dim

BB = lastrow

Next

Compute and

With Application.WorksheetFunction                        

  =  .MMult(.MInverse(), BB)

End With

For To Dim

For To

=

Next

=

Next

Compute the descending direction

For To Dim

For To

=

Next

Next

eta = 1

Dim deltaLp As Double

Dim Lpk1 As Double

Dim Lpk As Double

deltaLp = 1

Update the solution of and

While (delta)

For To Dim

For To

Next

Next

For To

new

For To Dim

= input

Next

For To

For To Dim

= input

Next

kf(ii) = kernelfun

Next

For To Dim

For To

Next

Next

For To Dim

newnewoutput

Next

new =

If (new() < epsilon) Then

If (new >= epsilon) Then newnew()

delta = delta + new()

Next

For To Dim

For To

1 = 1 +

= + 2/2

Next

Next

For To

If new >= epsilon Then 1 = 1 + newnew)

If Then =

Next

delta = 1 -

eta = 0.5 eta

Wend

delta

For To

delta = delta + new()

Next

delta = delta

Wend

For To

For To Dim

Range().Cells =

Next

Next

For To Dim

Range(bi).Cells

Next

End Sub

Kernel function of RBF

Function kernelfun(xx, yy, sigma2) As Double                      

Dim temp As Double

Dim temp1 As Double

Dim Dim As Integer

Dim = Range(Dim).Cells.Value

temp = 0

For To Dim

temp = temp +

temp = temp +

Next I

temp1 = Sqr(temp)/()

kernelfun =

End Function

Compoute the performance    function value using the MSVM

Sub Perffunc()

Dim As Integer

Dim As Integer

Dim As Integer

Dim As Integer

Dim As Integer

Dim As Integer

Dim sigma As Double

Dim As Double

Dim As Double

Dim As Double

Dim As Double

Dim As Double

Dim As Double

= Range().Cells.Value

= Range().Cells.Value

Dim = Range(Dim).Cells.Value                          

Dim = Range(Dim).Cells.Value

sigma = Range(sigma).Cells.Value

ReDim (1 To Dim) As Double

ReDim (1 To Dimx) As Double

ReDim (1 To Dim, 1 To ) As Double

ReDim (1 To Dim) As Double

ReDim (1 To , 1 To Dim) As Double

ReDim kf(1 To ) As Double

For To Dim

For To

= Range().Cells

Next

= Range().Cells

Next

For To

For To Dim

= Range(input).Cells

Next

For To

For To Dim

= Range().Cells

Next

kf = kernelfun

Next

For To Dim

For To

Next

Next

Next

For To

For To Dim

Range(output).Cells

Next

Next

End Sub