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MathGroup Archive 2000

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Fit and InverseLaplaceTransform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23564] Fit and InverseLaplaceTransform
  • From: "SANCHEZ DE LEON, Guillermo" <gsl at fab.enusa.es>
  • Date: Sat, 20 May 2000 03:10:37 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear friend, I have the LaplaceTransform: 

In[1]:= Cout[s_] = (3*(7876.7668/(10.41635 + s) - 7891.21/(12.09768 + s))*
     (off*(PS + s*Tu) + s*(PS + (on + s)*Tu)))/
   (off*(3*PS + 3*s*Tu + PS*s*Tu + p*s*(PS + s*Tu)) + 
     s*(3*PS + 3*on*Tu + on*PS*Tu + 3*s*Tu + PS*s*Tu + p*s*(PS + (on +
s)*Tu)));

Where  "off", "Tu", "PS", "on", "PS"  are coeffs. to be calculated. I have
the experimental "data" of Cout[t]. For this reason I need to fit data to a
model given by " InverseLaplaceTransform[Cout[s], s, t] ". The experimental
Cout[t] data are:

In[2]:=data = {{0.03, 27.5}, {0.08, 48.61}, {0.28, 133.39}, 
    {0.33, 106.18}, {0.38, 92.11}, {0.48, 60.47}, 
    {0.55, 56.54}, {0.65, 27.73}, {0.75, 23.25}, {0.85, 15.83}, 
    {0.95, 13.82}, {1.05, 10.58}, {1.15, 7.83}, 
    {1.25, 7.35}, {1.35, 6.08}, {1.45, 5.21}, 
    {1.6, 4.18}, {1.8, 3.48}, {2., 2.86}, 
    {2.2, 2.42}, {2.40, 2.11}, 
    {2.6, 2.00}, {2.78, 1.7}, {3., 1.58}, 
    {3.40, 1.58}, {3.75, 1.44}, {4.25, 1.35}, 
    {4.75, 1.3}, {5.25, 1.29}, {6.75, 0.81}, {7.25, 0.78}, 
    {7.75, 0.73}, {8.25, 0.75}, {11., 0.68}};

Any suggestions. I am testing with the follow method:

In[3]:=sse2[Tu_?NumberQ, off_?NumberQ, on_?NumberQ, p_?NumberQ, PS_?NumberQ]
:= 
  Block[{sol, q2}, sol = Chop[InverseLaplaceTransform[Simplify[N[Cout[s]]],
s, t], 10^(-8)]; 
    Plus @@ Apply[(q2[#1] - #2)^2 & , data, {1}] /. q2 -> sol];

In[4]:=FindMinimum[sse2[Tu, off, on, p,  PS], {Tu, 10, 20}, 
  {off, 0.1, 0.3},  {on, 0.4, 0.7}, {p, 1, 2},  {PS, 4, 5}, MaxIterations ->
50]


But some think is wrong

Guillermo Sanchez
guillerm at gugu.usal.es
gsl at fab.enusa.es


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