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ahamer

Germany
6 Posts
Posted - 08/18/2014 :  11:40:22 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Origin Ver. and Service Release (Select Help-->About Origin): 9.1
Operating System: win 7 32
Hello could anyone help me please modifying the built-in function in originlab:

Equation: ExpAssoc
y=y_0+A_1(1-e^{-x/t_1})+A_2(1-e^{-x/t_2})

Data:
I have two columns Time(x) vs Work_of_adhesion(y)

Model

y=y_0+A_1(1-e^{-x/t_1})+A_2(1-e^{-x/t_2})


y0 is the y value when x (time) is zero.

I need also more parameters in the output report (table) which are K_fast, K_slow, Hf and Hs

K_fast=1/t_1
K_slow=1/t_2
K_fast should be > K_slow

Half-time_fast(Hf): Hf=ln(2)/K_fast
Half-time_slow (Hs): Hs=ln(2)/K_slow

greg

USA
1378 Posts
Posted - 08/19/2014 :  09:48:54 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Several points:
1. Math operators can never be implied, so
A_1(1 ...
must be A_1*(1 ...
2. We only support parentheses so replace { and }
3. We do not recommend using "_" in variable names
4. There is no "e" defined in Origin

Here is the equation:
y=y0+A1*(1-exp(-x/t1))+A2*(1-exp(-x/t2))

Also, derived parameters cannot be defined using other derived parameters. This just requires some substitution:
Kfast = 1/t1;
Kslow = 1/t2;
Hf = t1*ln(2);
Hs = t2*ln(2);

Finally, you cannot use derived parameters as constraints so you cannot say
Kfast > Kslow
but you could say
t2>t1

Your function is over-parameterized (two of its terms are essentially identical) and as such, which term is 'fast' and which term is 'slow' is completely arbitrary, or forced to be one or the other by some constraint. While the constraint of t2>t1 will ensure the 'correctness' of fast vs slow, it is unlikely to differentiate the two terms sufficiently to produce the best fit. You will probably need to provide some additional bounds on your parameters or even fix some (at least during the fit).
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