Central Composite Rotatable Design (CCRD) with five factors
Authors: Housam Binous and Ahmed Bellagi
Central Composite Rotatable Design (CCRD) with five factors
Authors: Housam Binous and Ahmed Bellagi
Authors: Housam Binous and Ahmed Bellagi
In[]:=
Clear[x1,x2,x3,x4,x5]
In[]:=
codedvar=Sort[{{16,-1,-1,-1,-1,1},{8,-1,-1,-1,1,-1},{12,-1,-1,1,-1,-1},{4,-1,-1,1,1,1},{14,-1,1,-1,-1,-1},{6,-1,1,-1,1,1},{10,-1,1,1,-1,1},{2,-1,1,1,1,-1},{15,1,-1,-1,-1,-1},{7,1,-1,-1,1,1},{11,1,-1,1,-1,1},{3,1,-1,1,1,-1},{13,1,1,-1,-1,1},{5,1,1,-1,1,-1},{9,1,1,1,-1,-1},{1,1,1,1,1,1},{17,-2,0,0,0,0},{18,2,0,0,0,0},{19,0,-2,0,0,0},{20,0,2,0,0,0},{21,0,0,-2,0,0},{22,0,0,2,0,0},{23,0,0,0,-2,0},{24,0,0,0,2,0},{25,0,0,0,0,-2},{26,0,0,0,0,2},{27,0,0,0,0,0},{28,0,0,0,0,0},{29,0,0,0,0,0},{30,0,0,0,0,0},{31,0,0,0,0,0},{32,0,0,0,0,0}},#1[[1]]<#2[[1]]&]
Out[]=
{{1,1,1,1,1,1},{2,-1,1,1,1,-1},{3,1,-1,1,1,-1},{4,-1,-1,1,1,1},{5,1,1,-1,1,-1},{6,-1,1,-1,1,1},{7,1,-1,-1,1,1},{8,-1,-1,-1,1,-1},{9,1,1,1,-1,-1},{10,-1,1,1,-1,1},{11,1,-1,1,-1,1},{12,-1,-1,1,-1,-1},{13,1,1,-1,-1,1},{14,-1,1,-1,-1,-1},{15,1,-1,-1,-1,-1},{16,-1,-1,-1,-1,1},{17,-2,0,0,0,0},{18,2,0,0,0,0},{19,0,-2,0,0,0},{20,0,2,0,0,0},{21,0,0,-2,0,0},{22,0,0,2,0,0},{23,0,0,0,-2,0},{24,0,0,0,2,0},{25,0,0,0,0,-2},{26,0,0,0,0,2},{27,0,0,0,0,0},{28,0,0,0,0,0},{29,0,0,0,0,0},{30,0,0,0,0,0},{31,0,0,0,0,0},{32,0,0,0,0,0}}
In[]:=
Dimensions[codedvar]
Out[]=
{32,6}
In[]:=
codedvar//TableForm
Out[]//TableForm=
1 | 1 | 1 | 1 | 1 | 1 |
2 | -1 | 1 | 1 | 1 | -1 |
3 | 1 | -1 | 1 | 1 | -1 |
4 | -1 | -1 | 1 | 1 | 1 |
5 | 1 | 1 | -1 | 1 | -1 |
6 | -1 | 1 | -1 | 1 | 1 |
7 | 1 | -1 | -1 | 1 | 1 |
8 | -1 | -1 | -1 | 1 | -1 |
9 | 1 | 1 | 1 | -1 | -1 |
10 | -1 | 1 | 1 | -1 | 1 |
11 | 1 | -1 | 1 | -1 | 1 |
12 | -1 | -1 | 1 | -1 | -1 |
13 | 1 | 1 | -1 | -1 | 1 |
14 | -1 | 1 | -1 | -1 | -1 |
15 | 1 | -1 | -1 | -1 | -1 |
16 | -1 | -1 | -1 | -1 | 1 |
17 | -2 | 0 | 0 | 0 | 0 |
18 | 2 | 0 | 0 | 0 | 0 |
19 | 0 | -2 | 0 | 0 | 0 |
20 | 0 | 2 | 0 | 0 | 0 |
21 | 0 | 0 | -2 | 0 | 0 |
22 | 0 | 0 | 2 | 0 | 0 |
23 | 0 | 0 | 0 | -2 | 0 |
24 | 0 | 0 | 0 | 2 | 0 |
25 | 0 | 0 | 0 | 0 | -2 |
26 | 0 | 0 | 0 | 0 | 2 |
27 | 0 | 0 | 0 | 0 | 0 |
28 | 0 | 0 | 0 | 0 | 0 |
29 | 0 | 0 | 0 | 0 | 0 |
30 | 0 | 0 | 0 | 0 | 0 |
31 | 0 | 0 | 0 | 0 | 0 |
32 | 0 | 0 | 0 | 0 | 0 |
In[]:=
M=codedvar;
In[]:=
x1=Transpose[M][[2]]
Out[]=
{1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
In[]:=
Dimensions[x1]
Out[]=
{32}
In[]:=
x2=Transpose[M][[3]]
Out[]=
{1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0}
In[]:=
x3=Transpose[M][[4]]
Out[]=
{1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0}
In[]:=
x4=Transpose[M][[5]]
Out[]=
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0}
In[]:=
x5=Transpose[M][[6]]
Out[]=
{1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0}
In[]:=
MD=Transpose[{Table[1.0,{i,1,32}],x1,x2,x3,x4,x5,x1x1,x2x2,x3x3,x4x4,x5x5,x1x2,x1x3,x1x4,x1x5,x2x3,x2x4,x2x5,x3x4,x3x5,x4x5}];
In[]:=
Dimensions[MD]
Out[]=
{32,21}
In[]:=
Grid[MD,Frame->All]
Out[]=
1. | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1. | -1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 |
1. | 1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 |
1. | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 |
1. | 1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 |
1. | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 |
1. | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 |
1. | -1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 |
1. | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 |
1. | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
1. | 1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 |
1. | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 |
1. | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 |
1. | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 |
1. | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 |
1. | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 |
1. | -2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | -2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
In[]:=
yexp={31.1,30.8,27.1,29.1,21.6,20.8,24.8,17.8,27.2,29.4,31.1,30.8,23.4,22.2,23.4,22.3,23.0,31.7,28.3,26.8,18.8,35.8,25.2,27.0,23.2,28.5,28.3,32.1,28.0,29.4,34.5,35.1};
Contour plots and optimization