I found the process of detection of model structure in reduced models very trial and error based. I think we always prefer to have linear models like ARX(Autoregressive Exogenous) model instead of nonlinear models like NARX( Nonlinear Autoregressive Exogenous) model whether our main model is no-linear.
I need some help and guidance in the procedure of detection of the model structure. Is there any MATLAB toolbox or software for this purpose?
Dear Mehrdad,
There is no systematic rule for choosing this or that model, it depends on the system as well as on what you want to do with this model.
For more information about this subject, i suggest you to see links and attached files on topic.
https://www.tandfonline.com/doi/abs/10.1080/00207170310001635419?
scroll=top&needAccess=true&journalCode=tcon20
https://core.ac.uk/download/pdf/144449522.pdf
https://www.mathworks.com/help/deeplearning/ug/design-time-series-narx-feedback-neural-networks.html
Article Neural network based predictive control of personalized heat...
Article Using ARX and NARX approaches for modeling and prediction of...
Best regards
That would depend on the linearity of the system. For highly nonlinear systems, linear models (ARX, ARMAX, etc.) do not work well.
There is no reliable non-linearity test on collected data before performing the modeling. You either know that for a fact from the domain knowledge or reach to that conclusion after linear models fail to provide good performance in model validation against validation data.
Dear Mehrdad Vojdani
It would certainly depend upon the model you actually want achieve. You can definitely go for an ARX model if you want the model to be a linear one even if the system is nonlinear. Additionally, looking for various models to fit the data is also a part of system identification. Therefore, there is nothing wrong to go for trial and error thing.
Dear Mehrdad Vojdani,
I agree with Sanjeev Kumar: based on the parsimony principle, just go for linear models. Do a good job in validating them. If you are convinced that no linear model can correctly represent what you need to have in a model, in what concerns the system being described, then you move on to nonlinear models. Notice that NARX only says that autoregressive and exogenous regressors are combined in a nonlinear way, but you still have to choose the model class i.e. polynomial, rational, neural etc. When it comes to this each representation will have its own set of tools...
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