Given table of data, how to create formula so I can get a desired Y value?

[hemnath]

Hi all,
I have Y vectors = (0, 5, 10, 15, 20)
At Condition1, x Vectors = (-0.0056, 5.0000, 10.0057, 15.0057, 20.0000)
At Condition2, x vectors = (-0.0028, 5.0028, 10.0085, 15.0085, 20.0028)
At Condition3, x vectors = ( 0.0000, 5.0056, 10.0113, 15.0113, 20.0056)

There can happen many conditions between condition1 and condition2 or between condition2 and condition3.

I calculated the co-efficients for conditon2.

When I apply x = 10.0057 for condition1, I get y = 9.99720
When I apply x = 10.0085 for condition2, I get y = 10.0000
When I apply x = 10.0113 for condition3, I get y = 10.002798

To get y = 10.0000 for any condition, Do I have to calculate co-efficients individually? Or is there any mathematical model?

Thanks in advance.

 

[FvM]

You forgot to tell what's the underlying problem, respectively the meaning of the "vectors" and "conditions". We shouldn't need to guess about it.

 

[hemnath]

Condition1 : At 0°C
Condition2 : At 25°C
Condition3 : At 50°C

 

[andre_luis]

To get y = 10.0000 for any condition, Do I have to calculate co-efficients individually? Or is there any mathematical model?

At first, you should calculate their ( poynomial ? ) coefficients individually, but if the outputs are somewhat linearly correlated you could simlify that by just one coefficient vector. What is the permissible tolerance of the error ?

 

[_Eduardo_]

At least 0.0028
What seem to be the resolution of the daq system.

 

[andre_luis]

At least 0.0028

Taking another look at the vectors above, the values seems like not matching a physical measurement using an equipment properly calibrated, due to be not repeating the same offset added to all values at each condition.

At Condition1, x Vectors = (-0.0056, 5.0000, 10.0057, 15.0057, 20.0000)
At Condition2, x vectors = (-0.0028, 5.0028, 10.0085, 15.0085, 20.0028)
At Condition3, x vectors = ( 0.0000, 5.0056, 10.0113, 15.0113, 20.0056)

 

[_Eduardo_]

Temperature only shift .0028 every 25°

y = [0, 5, 10, 15, 20] + .0056*[-1, 0, 1, 1, 0] + .0028*T/25)

But the vector error e = [-1,0,1,1,0] is too coarse ==> very few and bad measurements for the desired accuracy (4 decimals exact LOL)

 

[Warpspeed]

Depending on the resolution and accuracy required, perhaps a simple lookup table and interpolation may be sufficient for many practical purposes.

From there, generating a suitable polynomial and number crunching is about the only other way. That can be quite slow and software intensive.

 

[vGoodtimes]

If you don't have temperature as an input, you probably can't do too much.

A way to generate the model coefficients is by minimizing the l2 or l_inf norm of the error values. The model is probably a line or a parabola. There isn't much difference in the difficulty of either problem.