Finding cyclic function from points with more than 2 indep. variales

I am doing my master thesis in Electrical engineering about the impact of the humidity and

temperature on power consumption

I have a problem that is related to statistics, numerical methods and mathematics topics

I have real data for one year (year 2000)

Every day has 24 hours records for temperature, humidity, power consumption

So, the total points for one parameter, for example, temperature is 24*366 = 8784 points

I classified the pattern of the power to three patterns:

Daily, seasonally and to cover the whole year

The aim is to find a mathematical model of the following form:

P = f ( T , H , t , date )

Where,

P = power consumption, T = temperature, t = time in hours from 1 to 24, date = the date number in the year from 1 to 366 ( or date number in a month from 1 to 31)

I started drawing in Matlab program a sample day, 1st August showing the effect of time,

humidity and temperature on power consumption::

http://www7.0zz0.com/2010/12/11/23/264638558.jpg

Then, I make the analysis wider to see what changes happened when drawing this day with the next day:

http://www7.0zz0.com/2010/12/11/23/549837601.jpg

After that I make it wider and include the 1st week of august:

http://www7.0zz0.com/2010/12/11/23/447153078.jpg

Then, the whole month, august:

http://www7.0zz0.com/2010/12/12/00/120820248.jpg

Then, starting from January, I plot power and temperature for 1st six months without

humidity (only for scaling):

http://www7.0zz0.com/2010/12/12/00/908911392.jpg

with humidity :

http://www7.0zz0.com/2010/12/12/00/102651717.jpg

Then, the whole year plot without humidity: ( P,T,H have constant values but I separate H only for scaling since H values are too much higher than P and H and that cause shrinking of the plot making small plots for P and T)

http://www7.0zz0.com/2010/12/11/23/290259320.jpg

and finally with humidity:

http://www7.0zz0.com/2010/12/11/23/842530863.jpg

The reason I have plotted these figures is to follow the behaviors of all parameters. How P is changing with respect to Temperature, Humidity, and time in hours and time in day number.

It is clear that these figures represent cyclic behavior but this behavior is not

constant. It is starting to increase and then decrease during the whole year.

For example the behavior of 1st Janu开发者_如何学Pythonary is almost the same as any other day in the year

but the difference is in shifting up or down, left or right.

Also, Temperature and Humidity are almost sinusoidal. However, Power consumption behavior is not purely sinusoidal as seen in the following figure:

http://www7.0zz0.com/2010/12/12/00/153503144.jpg

I am not expert in statistics and numerical methods, and this matter now does not have relation with electrical engineering concept.

The results I am aiming to get are:

Specify the day number in the year from 1 to 366, then specify the hour in that day, temperature and humidity also will be specified. All of these parameters are to be specified by the user

The result:

The mathematical model should be capable to find the power consumption in that specific hour of that day.

Then, the Power found from the model will be compared to the measured real power from the

data and if the values are very close to each other, then the model will be accurate and

accepted.

I am sorry for this long question. I actually read many papers, many helps but I could not

reach to the correct approach of how to find one unified model by following the curves

behavior from starting till the end of the year and also having more than one independent

variable has disturbed me a lot.

I hope this problem is not difficult for statistics and mathematics experts.

Any help will be highly appreciated,

Thanks in advance

Regards

---

About this:

"Also, Temperature and Humidity are almost sinusoidal. However, Power consumption behavior is not purely sinusoidal"

Seems in local scale (several days/weeks order) temperature and humidity can be expressed as periodic train of Gaussians:

After such assumption we can model power consumption as superposition of temperature and humidity trains of Gaussians. Consider this opencalc spreadsheet chart:

in which f1 and f2 are train of gaussians (here only 4 peaks, but you may calculate as many as you need for data fitting) and f3 is superposition of these two trains,- just

(f12 + f22)1/2

However i don't know to what degree power consumption follows the addition of train of gaussians. You may invest time to explore this possibility.

Good luck!