finding function or equation

[6543210000]

Hello

This is my question :

1)We have 1000 inputs. For Example :
input{x_1, x_2, x_3, x_4}

2)And also we have 1000 outputs for our inputs.
For Example :
output{y_1} for input{x_1, x_2, x_3, x_4}
output{y_2} for input{x_5, x_6, x_7, x_8}

3)We have a function or an equation which returns
an output for our inputs.
function : y_1 = f(x_1, x_2, x_3, x_4)

Now :
I need MATLAB to find that function or equation from my
outputs and inputs. I mean :

My inputs are : x_1, x_2, x_3, x_4
My output is : y_1
And desired equation is something like below :
y_1 = f(x_1, x_2, x_3, x_4) =
(x_1^2 + x_2*1/2) - (x_3^3 + x_4)

Thank you so much
Mahdi Heidari

 

[MikeyP]

This is not a Matlab probelm. This is a regression analysis or system identification problem.

Where does your input and output data come from? What is the context?

M

--
Dr Michael F Platten

 

[6543210000]

At first thank you for your reply.

My Inputs are parameters of a building
which is in fire. Those parameters are :
1) Capacity
2) Fieryness
3) Time of burning
4) area of building

and output is Energy of building which is in fire. I need
a function or an equation to tell me :
A building with above parameter has how much energy ?
For example :
f(Capacity,Fieryness,TimeOfBurning,AreaOFBuilding)=Energy

I have 1000 numbers for any inputs and outputs but I need
a equation for those.

Again thank you.

 

[VisiGoth]

MikeyP is correct. This is a sys ID problem. What are the models in your domain? That is the first step. If your industry has no idea, then there is a lot of work to do. This is not a MATLAB issue. MATLAB can be used to help and even has specialized toolboxes. There used to be a toolbox on frequency domain ID following the LeJung (spelling? My memory is poor) book. Do searches on Akeike information. Determine if your domain is best modeled in the time domain directly or if a transformend doamin like frequency is better. Is a polynomial or Volterra beter or coupled low order differential equations.

If you know you model is simply a low order polyniomial with integre coefficients, then just do a least squares fit. If you have known functions, build your matrices of those functions and do pinv or equivalent.