Can you show me one formula for this points? The Mathcad 15 sheet is in attach!
Thank you!
ACCEPTED SOLUTION
Accepted Solutions
From the very beginning, I was thinking about this Columbian solution, but I expected a more elegant (smoother, with derivatives!).
PS
What is it one Columbian solution&
They say that Columbus during lunch with Cardinal Mendoza suggested that the present grandees solve a simple problem: put an egg upright on the table. No one could do this, except for Columbus himself - he just broke it from one end. All, interrupting each other, began to resent that so can they. “The difference is, gentlemen, that you could do it, but I actually did it,” the navigator replied.
Hi,
The first points are very nearly a straight line, So curve can be broken into two parts. You could possibly get closer to the last eight points with a different function type besides a line.
Thanks to all!
At our university there was a mathematician who by the type of curve immediately determined the formula f(x,a,b,c…). With guess values for a, b, c... But he, alas, retired!
I need the formula for C++! But at first for Mathcad!
From the very beginning, I was thinking about this Columbian solution, but I expected a more elegant (smoother, with derivatives!).
PS
What is it one Columbian solution&
They say that Columbus during lunch with Cardinal Mendoza suggested that the present grandees solve a simple problem: put an egg upright on the table. No one could do this, except for Columbus himself - he just broke it from one end. All, interrupting each other, began to resent that so can they. “The difference is, gentlemen, that you could do it, but I actually did it,” the navigator replied.
Hi Valery.
I guess that Fred make a great job finding a suitable mathematical model for the data, even have some numerical issues with the tail, where it give negative values, but looks very close to the empirical data.
This other uses a more simple model, and shows how to use minerr for get better guesses values for plug them into a minimize solve block.
Maybe some one can join this procedure with the Fred model, which have more complicated math, but an immediate and well know physical interpretation.
Best regards.
Alvaro.
Hi Fred.
@Fred_Kohlhepp wrote:
...But my function form represents a completely different physical event; I only tried to connect the curve shapes of the two events.
If you recognize the shape of the math of some physical model (for example a thermal model), and know how to interpret it in some other physics field (for example, mechanics), then you can try to found the "thermo-mechanical equivalent" or "analog" interpretation. This applies for electrical, hydraulic, pneumatic and other areas. For example, you can use this table, from http://www.dartmouth.edu/~sullivan/22files/System_analogy_all.pdf
or check the wikipedia article: https://en.wikipedia.org/wiki/Analogical_models
So, your control theory model probably have a thermal equivalent which is an easy interpretation.
@Fred_Kohlhepp wrote:
...And not very well1
I'm not sure about that. Valery's data have an exponential and a lineal part, as is pointed before by Werner. One simple model maybe can contain then exponential errors for some values.
But if the point it's only implement some algorithm in Cpp then I guess that this is the shortest way:
Best regards.
Alvaro.
Here's something called Regression Kink Design; seems to be popular in economics. Does a reasonable job. It does undershoot the lowest points if you zoom in. I could only go to 6th order since that's when minerr ran out of variables.
@DJF wrote:
Here's something called Regression Kink Design; seems to be popular in economics. Does a reasonable job. It does undershoot the lowest points if you zoom in. I could only go to 6th order since that's when minerr ran out of variables.
@DJF wrote:
A higher order RKD should help that out some, but I'm not sure how to get there. Someone will probably tell me 15 can do it.
Even Prime can do it, too. But increasing the order doesn't help. After all with n as highest order we have 2*n+2 variables to solve for but still only 14 equations to fulfil.
You may play around with the attached sheet, but I guess this regression will not do whatever Valery has in mind.
Changing the value of the kink point has no big effect, too. Just for fun I added k as an argument of function f and let the solve block optimize k, too, and it came up with k=1.8343.
Worksheet in format P5 attached
