How to find the inital formula behind engineering test data ? 2

[FreddyMusic]

Recently, my job seems to work on a mathematic problem.

We did many efforts on engineer test and get a perfect graph curve by discrete data (100 points on EXCEL).
But my customer interest also the inital Formula behind those data. Perhaps it’s a function or calculus.....not clear.

Engineers and physicists distinguish between continuous data and discrete data.

Anyone leads us first step of this cross?
Books, software, method?

 

[melone]

A plot of the raw data looks like a plot of the Tangent function..... it appears to be asymtotic.

 

[m777182]

to GregLocock

A rational function R(x)is a simple method to fit an asymptotic function.You start with a low degree n and can get even better fit by increasing it. With m-n>1 you can fit even multi modal functions easily.
No background, experience only.
m777182

 

[GregLocock]

Yes, but you mentioned "R(x)=P(x)/Q(x) where P(x) is a polinomial of a degree n and Q(x) is a polynomial of degree n+1"

How did you know about the n+1 bit?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[FreddyMusic]

Don't look at me. I am also thinking.

To Denial

There is no argument.
To approach vertical asymptote X=1 is important.
Meanwhile, middle section of curve is the best place, which we can measure precisely in available test environment.

Is that possible to shoot one more co-efficiency off ?

 

[Denial]

FreddyMusic,

I take it you are asking whether the fit could be improved by adding another term into the equation. The answer is almost certainly "yes", but there does come a point when you begin to kid yourself (statistically speaking). Your data is based on physical experiments, and so it will inevitably contain "noise": at some point you begin to overly accommodate this noise.

As someone indirectly pointed out above, if you want an EXACT fit to your 99 data points you could always resort to a polynomial of order 98, but I don't think you'd be any the wiser from the exercise. A statistician would express this in terms of degrees of freedom, and tell you that your 98-order polynomial had zero predictive power because the number of degrees of freedom in your model was zero.

Occam's Razor is never better applied than in the area of curve fitting.

Having said all that, if you really want to "improve" the fit by adding one further term then you have to decide what sort of term to add. Since we already have what I would regard as a good fit, you will have to resort to good old trial&error, guided slightly by your mathematical instincts, and perhaps by any knowledge you (but not the rest of us) might have of the underlying phyical phenomenon.

The first trial I would undertake (since you are insisting on going further) would be to add a quadratic term to the model I used above. Thus:
Y = a + b*X + c*X^2 + d*[sec(pi*X/2)]^e

Happy hunting.

 

[FreddyMusic]

Denial,

No need to go further. Something is wrong in the beginning.

Now I found the correct direction.

Thank you all of you.

Best regards,


FreddyMusic

 

[melone]

So what is the correct direction?

 

[FreddyMusic]

Melone
Perhaps this link interested you. I get from my Math friend

http://www.statsoft.com/textbook/stathome.html

Seems like some company do study for that. They call it DOE (design of Experiment)
Still is not clear, what they can do exactly? How much they want to charge me for software?


Denial

I have a kind of feeling (only feeling), what Greg Locock found e2=1 is a good number.
That seems like predict the vertical asymptote X=1.
Perhaps we can modify the math model to something like
Y = 1/ (X-1) * ………….

Of course, I like Pi. But this physical model doesn’t seem like a period’s function or a period's curve.
Or is sec(x) only a kind “noise "? I don’t know.

I understand, this is big-time-consume job.
Only thinking or searching, No Working !!!
I am great appreciated.


FreddyMusic

 

[FreddyMusic]

To Occam's Razor

Philosopher always speaks paradox, therefore they are always Right
Unfortunately, engineer always works like trial & error, therefore they are always Wrong.


FreddyMusic

 

[FreddyMusic]

Denial,

You curve seems up to down, or perhaps my eyes goes wrong?lol





FreddyMusic

 

[GregLocock]

DoE won't help, if you have described the problem you have, correctly.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[FreddyMusic]

Greglock

I assume, you has understand the "problem" clearly.
I feel, I have no more correctly input....



FreddyMusic

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[Denial]

FreddyMusic,

You are correct. My value for "d" should be positive, not negative. Apologies. [This happened because Excel does not have a sec() function, so I used cos() instead. Then forgot to change the sign when transcribing results into my post. Other values are unaffected.]

 

[FreddyMusic]

Congratulation Denial,

That looks pretty nice.

Your friend




FreddyMusic

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[FreddyMusic]

Congratulation to GregLocock.
Congratulation to electricpete also.

With your guys help, I understand the "problem" and "curve" much better in the last two weeks.

It has been great pleasure for me to meet you all in this forum.







FreddyMusic

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Important information for all new members
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[m777182]

to greglock
yes, you are right. The Q(x) should be in general of degree m and m>n. In the most simple case m=n+1. M and n is got by nonlinear best fit (Solver).
m777182

 

[jplinn]

Fit your data with TableCcurve 2D

http://www.systat.com/products/TableCurve2D

It will give you the best fit, the statics for the fit, residuals, prediction interals and fit intervals with a select confidence level.

Then put the formula into a spread sheet