Please help me for modeling with Least square,is my modeling good?

Hi every one. My plant is a Hot furnace with 6 zone and each zone has total measure gas and total measure air, in result inputs is 12 and 1 output, i tried model it with least square, the picture shows clearly compare between my model output and real output,the red grapgh is output model and blue graph is real output, please help me about my approach and correction of result. Thanks alot.

[dpb]

Not a lot to go on including such things as how did you write the model, is the plot representative of a time series (in which case OLS is probably not the analysis tool to use), etc., etc, etc, ...

[mostafa]

Hi dpb, thanks alot for your comment, my model produce from a black box system, i have just the air and gas consumption and thier pressure, and the plot is acoording to the time series, i write the code of Least square by general method and i didnt use any toolbox. Please help me for improve my result. Best regards.

[dpb]

This is really not a Matlab question, per se. Multivariate time series modeling is a tremendously large area of application and research. There's no way I can sit here and tell you specifically what to do to improve your model (especially w/o any real knowledge of the system and no data) and to do so other than in more than just a broadbrush indication really turns into consulting in a hurry.

I don't know your situation; if you're in a university setting I suggest consulting via your advisor with someone w/ some modelling experience to provide some guidance. If this is a business application then you need to find that same type of person in-house or seriously consider some outside expert help I think.

Particularly, probably what is lacking in your modeling is any consideration of the serial correlation in variables.

[mostafa]

Sir, it is really a matlab question, becuase i wrote it by matlab code, i thing my code is true and if it is require for helping my code i will write it here or send it to you, my clearly question is that is my approach true? is it require any technic and many other formula for improve it? this university project, unfortunately my advisor is n't in my access for a time, and i decided ask it from tis site for improve my technic and my programing skill in matlab, i am new in modeling and matlab programming. Can you tell me espetialy what is serial correlation? Thanks alot.

[dpb]

That there is code written in Matlab doesn't change the fact that the question you're asking is "what modelling techniques should I be implementing for this specific problem?" not a problem in Matlab itself. It appears you likely have implemented an OLS solution correctly for what you've done--the problem is that more than likely that isn't the right solution for the problem. But, that's outside the scope of Answers forum and is potentially a seriously complicated question. It's simply impossible to get sufficient background data on the process and all to be able to responsibly make any definitive recommendation.

The basic assumption of both simple and multiple regression analysis is that the error terms are independent from each other ("uncorrelated"). In a case like yours where data are taken over time for a physical process, it's highly likely that the results for any output parameter are strongly influenced by the value of the same parameter one or more timesteps prior to the current one. If this is so, error estimates from the resulting model are underestimated and can be drastically so.

Also, as you observe in your fitted response (which, btw, as an indication of just how little we know about the problem, you've not even told us what parameter you're trying to estimate), when your model gets off, it stays off for a while. That's a real indication that you need some terms besides those at the present time.

There's no indication again in what you've presented of what sort of time interval is between measurements, what the residence time of the air/fuel mixture in the furnace might be, etc., etc., etc., all of which and much more than you can expect a volunteer to know are likely key inputs to the resolution of the problem. And, of course, in the end you may find that it's not feasible to model the system much more accurately from such a set of data alone.

I commend to your attention two texts --

Box and Jenkins, Time Series Analysis , the seminal work on ARIMA models specifically designed for such types of problems and

Box, Hunter, and Hunter, Statistics for Experimenters, a guidebook for what you need to know to not get into too much trouble. I would especially commend to your attention in the latter the section in Chapter 14 entitled "Hazards of Fitting Regression Equations to Happenstance Data".

I'm guessing the data were simply taken over a period of observation of the operation of the furnace whereas I would suggest that for modeling besides the aforementioned issues regarding the time-nature of these data that you should really be looking at setting up design conditions and observing the steady-state behavior on those conditions where you control the various inputs at known levels.

You're in a very complex area of investigation here, unfortunately, and there's no easy answer to the questions you pose (which are, incidentally, good questions to raise it's just more than can possibly deal with here realistically).

[dpb]

A survey paper that looks like a good introductory starting point, maybe...

http://sites.poli.usp.br/d/pmr5406/Download/papers/1742.pdf

[mostafa]

Thanks alot for your attention, i have so many problem and question about systems identification, how can i ask you? here or in another location?

[dpb]

As noted, the TMW Answers forum is really not intended to be a technical consulting venue so it really isn't appropriate to really try to do a tutorial on non-Matlab subjects (even tho there is a Toolbox on the subject I think?) herein.

And, unfortunately, I'm not in a position to be able to spend much time at the moment on such a task...I don't have a better answer than that which I gave initially of trying to find some local help, sorry.