I have a state space model - linear or non-linear. I know that there is (are) wrong parameter(s) in the model (the model structure is correct though). Is there a method to isolate the wrong parameter(s)?
Please, specify your model, or give example. Otherway your question is not understandable.
Eugene F Kislyalov: Let us say there is a spring mass damper system, in which the parameters are the mass, damping coefficient and spring constant. And one (or many) of these parameters is wrong (due to improper identification, or drift over time). How to identify these parameters?
I must add that it has to be done on-line. Stopping the process and identifying the model all over again is trivial. Any data based technique will be helpful.
In your case damping coefficient is quality factor Q and spring constant devided by mass is squared frequency, i.e. measurable quantities. You can control them on-line and compare with your parameters.
Regards,
Eugene.
You could attempt to compute derivative of some kind of fittness performance index with respect to parameters (you can do it for example by solving variational equation). The largest (absolute) value of derivative should at least suggest the faulty parameter.
For linear systems, and certain classes of non-linear systems, you can, in theory, uniquely learn the parameters of a model from the output, if your input is persistently exciting. For linear systems, this means that your input has a sufficient number of frequency components. If you don't know anything about the parameters of your model, white noise is usually the best practical option. I would recommend this paper as a starting point: http://www.sciencedirect.com/science/article/pii/0167691187900272
http://www.sciencedirect.com/science/article/pii/0167691187900272
This is a constrained system identification problem. First you identify a discrete or continuous black box state space model. If you identified a discrete model, then convert to continuous time. Then apply a similarity transformation T to bring the system to physical coordinates. This leads to a system of equations such as A T = T A*, B = T B*, and C T = C*, where [A, B, C] are the identified system matrices and [A*, B*, C*] are the physical matrices involving [M, D, K], the mass, damping, and stiffness matrices (need to be symmetric), you need to formulate a constrained optimization problem to find the physical parameters M, D, and K, subject to symmetry. Now, your physical model is as good as your as your discrete or continuous black box model. Normally this procedure works well in practice. See the enclosed paper.
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