RE: Fit and InverseLaplaceTransform. Improvement

• To: mathgroup at smc.vnet.net
• Subject: [mg23565] RE: Fit and InverseLaplaceTransform. Improvement
• From: "SANCHEZ DE LEON, Guillermo" <gsl at fab.enusa.es>
• Date: Sat, 20 May 2000 03:10:38 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```[Sorry I sent this question a few minutes ago, but I have yet found a a
solution. I will apreciate any suggestion to improve my method]

> 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}};
>
> I have found the following method.
>
> In[3]:=sse2[(Tu_)?NumberQ, (off_)?NumberQ, (on_)?NumberQ,
(p_)?NumberQ, (PS_)?NumberQ] := Block[{sol, q2},
q2[t_] = InverseLaplaceTransform[ Cout[s], s, t];
Plus @@ Apply[(q2[#1] - #2)^2 & , data, {1}]]

> 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]
>
out[4]:0{605.6289546197199,
{Tu -> 6.467180826261866,
off -> 0.0968608641750308,
on -> 0.6629560337902439,
p -> 0.971307914603113,
PS -> 2.709414690357603}}

Any suggestion to improve it

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

```

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