Power function model fit, multiple independent values

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Power function model fit, multiple independent values

mismichael
Hi All,

Recently I have approached new challenge that I have difficulties to work
around.
I have number of curves describing material behaviour during plastic forming
and would like to place the data into elegant power law equation.
The material is temperature and strain rate sensitive so I have few curves
for various temperatures and strain rates.
The curves are in form of stress-strain curves.
In language of mathematics:
f(x,y,z)=A*B^x*C^y*D^z.
I have number of curves describing f(x) for variation of y and variation of
z.

Everything I have tried up till now is regarding linear functions or single
independent variable.
Can you assist me in writing the code finding y and z?
Thank you



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Re: Power function model fit, multiple independent values

Doug Stewart-4


On Thu, Jun 27, 2019 at 10:29 AM mismichael <[hidden email]> wrote:
Hi All,

Recently I have approached new challenge that I have difficulties to work
around.
I have number of curves describing material behaviour during plastic forming
and would like to place the data into elegant power law equation.
The material is temperature and strain rate sensitive so I have few curves
for various temperatures and strain rates.
The curves are in form of stress-strain curves.
In language of mathematics:
f(x,y,z)=A*B^x*C^y*D^z.
I have number of curves describing f(x) for variation of y and variation of
z.

Everything I have tried up till now is regarding linear functions or single
independent variable.
Can you assist me in writing the code finding y and z?
Thank you



--
Sent from: http://octave.1599824.n4.nabble.com/Octave-General-f1599825.html


did you read

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RE: Power function model fit, multiple independent values

Windhorn, Allen E [ACIM/LSA/MKT]
In reply to this post by mismichael
> -----Original Message-----
> From: Help-octave  On Behalf Of mismichael
>
> Recently I have approached new challenge that I have difficulties to work
> around.  I have number of curves describing material behaviour during
> plastic forming and would like to place the data into elegant power law
> equation.
> The material is temperature and strain rate sensitive so I have few curves
> for various temperatures and strain rates.  The curves are in form of
> stress-strain curves.  In language of mathematics:
> f(x,y,z)=A*B^x*C^y*D^z.
> I have number of curves describing f(x) for variation of y and variation of
> z.
>
> Everything I have tried up till now is regarding linear functions or single
> independent variable.
> Can you assist me in writing the code finding y and z?

Some example data would be helpful.

If you take the logarithm of your equation you will have a linear curve-
fitting problem that will be easy to solve.  The answers will not be the
same as for the original problem, but they should be close, and may be
more useful if you want to minimize the percent error rather than the
absolute error.  (ln(A*B^x*C^y*D^z) = ln(A)+x*ln(B)+y*ln(C)+z*ln(D).)
At least this would get you values for starting a nonlinear solution.

The optim package has a bunch of functions that look useful for this.

Regards,
Allen