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Could you please help me in this problem?

I have 3 independent variables, (T,H,t) , as inputs and one output P ( I have all data for these inputs and the output, done experimentally measured every hour during one year).

I want to find a formula of this form: P=f(T,H,t) where t is the time in hours and it is always in the x -axis (index), T is temperature, H is humidity, and P is power.

I have all the data, and when I draw them in the same graph during one year, meaning that P , T , and H vs. hours. I found that the behavior of P is oscillating, making a sinusoidal shape over the entire year:

So, if I make a zoom view to this figure, for example from the 2000 th hour of the year to the 3000 th hour, it is clear that it almost has the same shape but it is oscillating.

So, it keeps oscillating and increasing up to the peak point and then it starts decreasing till the end of the year.

So, how can I predict the structure of the formula that relates P with T , H , and t ?

What is the effect of T,H and t on P .

Is there any approach that you advise me to follow?

Sorry for this long question and any help from you is highly appreciated. I read many papers but I could not know how to solve the problem.

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closed as too localized by David Z Apr 23 '12 at 3:32

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sorry need a bit of clarification, do you need the explicit formula for the function in a form like P(T,H,t)=C1*T*sin(t)+C2*H*sin(t)? –  Cem Dec 27 '10 at 19:26
    
It would be very good if you provide 3 plots(P vs T, P vs H , P vs t). –  Pratik Deoghare Dec 27 '10 at 19:27
    
This seems rather similar to physics.stackexchange.com/questions/1971/… –  David Z Dec 27 '10 at 20:01
    
It seems that you're not quite sure what you're looking for in this data. It would be easy enough to fit a sinusoid to the data as a function of time, if you wanted to make an estimate of power usage at any given time of year. On the other hand, if you want to show a correlation between temperature and/or humidity Vs. power use, you could fit this pretty well with a first or second degree polynomial. It all depends what you're looking for, and whether you want your model to reflect a proposed theoretical mechanism, or just estimate the data. For example, why would you assume time dependence? –  Colin K Dec 28 '10 at 2:09
    
If you want to model this data, ask here: stats.stackexchange.com . I would migrate it but there is a lot of answers. –  mbq Jan 27 '11 at 9:22

2 Answers 2

  1. You can train some Neural Networks with your data and then use them for predictions afterwards.
  2. You can use interpolation techniques to arrive at approximate formula from your data.
  3. One cool idea is to try applying models used in Algorithmic Trading for prediction from data.

EDIT: From the graph it looks like

$P \propto T$

$P \propto \frac{1}{H}$

It can also be noted that power is not very sensitive to changes in humidity but is highly correlated with changes in temperature.

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Exactly, this what I mean: P(T,H,t)=C1*T*sin(t)+C2*H*sin(t)+... or any function shape that can find or describe the relation between P and T,H,t. according to the given data. The mathematical model is very essential for my study. Also, ANN cannot give a model, it gives only the results and I will use it later on to verify the model results.It is clear that power is not very sensitive to changes in humidity but is highly correlated with changes in temperature but how can we describe this by a formula? if I provide 3 plots(P vs T, P vs H , P vs t). Should I add these three Power models? thanks –  eng_sub Dec 27 '10 at 20:39
    
As I alluded to above, if this is an essential part of your work, you should really take a step back and think about what you are trying to achieve with a model fit. You can find an equation to fit any data, but that fit will not have any meaning unless the equation represents a good theoretical model. Maybe if you told us more about what you are doing with this data? –  Colin K Dec 28 '10 at 2:15
    
@Colin: I've got a feeling that he really just wants to learn how to fit a plot, and that getting a meaning out of it is beyond his interests. –  Bruce Connor Dec 28 '10 at 5:34
    
@Bruce You're probably right but he should at least know if he wants to fit it as a function of time, or as a function of his other measured variables. There is a huge difference there. –  Colin K Dec 28 '10 at 14:17
    
@colin Certainly. –  Bruce Connor Dec 28 '10 at 14:27

Yes. I think we are missing something here. It might help if we knew what he means by power. If it is power consumption for heating and cooling a city, we can make some gueses as to plausible parameterizations. I'm assuming his hours are hours of the year (8760 hours/year), but then humidity doesn't seem right to me, it should rise at night and be at a minimum during the afternoon (but maybe these are a 24hour averages?). If is is heating and cooling, then t is a proxy for the amount of sunlight available, but it would be much better to have that as an independent variable as it is probably quite important (and quite variable depending upon cloud cover).

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