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 as you can see from the following ($P$ and time only):
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.
But this is only for only one independent variable which is time in hours.
Now, how if we include the effect of temperature and humidity and draw these vectors along with the power vs. time, to see how power is changing with respect to $T$, $H$, and $t$ rather than $t$ only:
So, how can I predict the structure of the formula that relates $P$ with $T$, $H$, and $t$?
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.