Calculate top of curve, and the time it takes to get there

[Pengatom]

Hi,

I'm doing a lot of temperature measurement, and I would like to add a function that could estimate how high the temperature would rise and how long it will take to get there.
The calculations would be based on the current temperature relative to the past x measurements.
Anyone have any ideas as to how I should proceed to solve this?
Any help would be highly appreciated!

Pengatom

My example is for temperature, but I guess it could be used for anything really, that's why I posted it under General Math, please feel free to move it if it is under the wrong topic

 

[Buzz Bloom]

Hi Pengatom:

If I understand your problem correctly, you want to extrapolate from experimental data to a range outside the range of the measured data. My personal experience with this kind of problem is somewhat limited, but I will share some general principles that have been useful to me.

If the desired extrapolations are relatively small compared to the range of measurements, and the data is relatively smooth, then a linear extrapolation will give a reasonable value. It is very difficult to get a reasonable extrapolated value to a range somewhat far from the measured range. For a higher order polynomial fit, the error of the extrapolated value will generally grow rapidly with the extent of extrapolation, and the error will also grow more rapidly with a larger exponent in the polynomial.

If you have a theoretical reason for expecting a particular kind of function to fit the quantities being measured over a larger range than the actual measurements, then you can find the best fitting value of set of free parameters for such a function type.

Hope this is helpful.

Regards,
Buzz

 

[Svein]

I did a somewhat similar approximation several years ago, where the object was to describe a population consisting of the (noisy) sum of two gaussian distributions plus something in between. I rapidly found that classical approximation theory did not work, so I did a recursive approximation:

1. Used a low-pass filter to find the approximate value of the first top
2. Used a quadratical regression to find a parabola through the top and several points to each side
3. Used the parabola to find a first gaussian approximation to that part of the data
4. Subtracted the values given by the first approximation from the data.
5. Repeated 1 - 3 in order to find the second top and the second gaussian approximation
6. Subtracted the values given by the second approximation from the data
7. Repeated 1 - 5 in order to find better gaussian approximations to that part of the data
   
8. Repeated 1 - 7 a couple of times until the result seemed stable

Not that my method would help you too much, but you might get an idea. If you have any inkling of what type of curve you would expect, find a method where you can use a try - refine sort of approach.