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From: MOOON MOOON on 2 Jun 2010 11:15


dear all,

Hello,

I need your help in this matter,

I am doing my thesis in master program
in electrical engineering,

the discription of the subject is:

we have two input vectors ( included in one vector):

T ( temperature ) and H ( humidity ), there is a corresponding one input

P ( power demand ), and all these data are normalized

I have thousands of data for these values done for many years

for sample example: ( lassume that we have the data for 5 hours )

T_H=[0.3333 0.3333 0.3542 0.3750 0.3750; 0.6970 0.8384 0.6869 0.7980 0.7677]

and the corresponding P is:

P=[0.6561 0.6618 0.6568 0.6694 0.6622]

I need to draw a curves relating all data,

and THE MOST IMPORTANT THING WHICH IS THE AIM OF THE THESIS IS :

finding ( inventing ) a formula depending on the curves drawn that relates
the power as an output with the temperature & humidity as inputs,

meaning:

P = f (T,H)

for example: the formula model will be:

P = a0 + a1 * T + a2*H*sin(T) + a3*T^3*H + a4*T*H

then finding a0,a1,a2 and a3 and this is easy and I
know how to find them.

BUT, my problem is how can I find this above example model function P ?
is it by dividing the curve to parts and then finding a function
for each part ? but how is this done by MATLAB ?
Any idea ?


Can anybody help me? I am appreciating any help.
and remember, any service will be valuable for me
and gives me a great advance toward my thesis.
this is real, since I have searched in the internet
and many books but I didn't get the answer.

Best regards
From: dpb on 2 Jun 2010 11:47
MOOON MOOON wrote:
....
> I am doing my thesis in master program in electrical engineering,
> the discription of the subject is:
>
> we have two input vectors ...
> T ( temperature ) and H ( humidity ), [and] a corresponding ...
> P ( power demand ), ...
>
> I have thousands of data for these values done for many years
....
> ...THE AIM OF THE THESIS IS ...
> finding ( inventing ) a formula depending on the curves drawn that relates
> the power as an output with the temperature & humidity as inputs,
>
> meaning:
>
> P = f (T,H)
....
> BUT, my problem is how can I find this above example model function P ?
> is it by dividing the curve to parts and then finding a function
> for each part ? but how is this done by MATLAB ?
> Any idea ?
>
>
> Can anybody help me? I am appreciating any help.
> and remember, any service will be valuable for me
> and gives me a great advance toward my thesis.
> this is real, since I have searched in the internet
> and many books but I didn't get the answer.
....

Well, if you could look it up in a book there wouldn't be much point in
doing it as a thesis, would there? :)

I'd suggest you start by considering the underlying process of the
system from whence the data came and see if you can derive a basis for a
physical model relating the observed response to the input which can
then be used to fit the necessary coefficients.

Obviously, looking at the data visually would seem to be a useful thing
to do. I'd guess that unfortunately w/o a fair amount of other
ancillary data relating to ambient conditions (unless they were actually
controlled or the device is in a limited operating environment) you may
be in the quandary of trying to fit what Box, et al. call "happenstance
data". I commend to you specifically Section 14.7 from
_Statistics_For_Experimenters_, Box, Hunter and Hunter,
Wiley-Interscience for a discussion of the pitfalls of such efforts and
the entire reference as a general guiding light.

--
From: MOOON MOOON on 2 Jun 2010 12:17


Thanks for your response,

In a book point, I mean that the method and the approach

of finding the formula from a curve, not the exact answer

and also I have thousands of data which is difficult - as I think -
to fit a formula..


best regards
From: Walter Roberson on 2 Jun 2010 12:24
MOOON MOOON wrote:

> we have two input vectors ( included in one vector):
>
> T ( temperature ) and H ( humidity ), there is a corresponding one input
>
> P ( power demand ), and all these data are normalized
>
> I have thousands of data for these values done for many years
>
> for sample example: ( lassume that we have the data for 5 hours )
>
> T_H=[0.3333 0.3333 0.3542 0.3750 0.3750; 0.6970 0.8384 0.6869 0.7980
> 0.7677]
>
> and the corresponding P is:
>
> P=[0.6561 0.6618 0.6568 0.6694 0.6622]
>
> I need to draw a curves relating all data,
>
> and THE MOST IMPORTANT THING WHICH IS THE AIM OF THE THESIS IS :
>
> finding ( inventing ) a formula depending on the curves drawn that relates
> the power as an output with the temperature & humidity as inputs,
>
> meaning:
>
> P = f (T,H)
>
> for example: the formula model will be:
>
> P = a0 + a1 * T + a2*H*sin(T) + a3*T^3*H + a4*T*H
> then finding a0,a1,a2 and a3 and this is easy and I
> know how to find them.
>
> BUT, my problem is how can I find this above example model function P ?

There are literally an infinite number (aleph one) of curves that will
fit any finite set of data, and so there is no mechanical method to come
up with "the right" curve. You will need to consider a number of
physical interactions in order to decide what kind of curves might be
physically reasonable.

When you are doing your analysis, please keep in mind the limited
accuracy of your measurements. If you find functions f and g that both
fit the data, with g calculated as having a "better" fit than f, then
that does not necessarily mean that g is a better explanation than f is:
it could be purely due to floating point limitations when applied to the
data. For thesis-level work, you should work through the calculations
using interval arithmetic with the intervals being proportional to the
precision of the normalized readings. For example, in the values you
show, the second pair of T and H values is a relative outlier, but it
would be less of an outlier if it were the case that the temperature
sensor reacted more slowly to temperature changes than the humidity
sensor reacted to humidity changes.
From: dpb on 2 Jun 2010 12:26
MOOON MOOON wrote:
>
>
> Thanks for your response,
>
> In a book point, I mean that the method and the approach
> of finding the formula from a curve, not the exact answer
>
> and also I have thousands of data which is difficult - as I think -
> to fit a formula..

Fitting isn't a problem irregardless of the number of points; that's
just computer work.

Determining a model that has some reason to be used as the function is,
as you note, the trick.

Since you say you have years of data and again unless the environment
was controlled or you have ancillary data that monitored those
conditions, one interesting thing might be to plot the data based on day
of year to see how consistent it is over those years. That's just one
of the most obvious exploratory ideas...

I repeat my admonition about happenstance data...

--
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