System identification in simulation
 

I am working with a simulation in 2d of a jet (input) coming from the end of a wall. The environment is at a certain temperature, and the the jet is inputting air at a lower temperature. There are measurements of the temperature along this wall. There are vortices, etc. I am given the input/output data and have to construct a model (even though the system is not linear, it's based on DNS eqns, so a first order linear model will be obtained). What I really need is to make this input jet a sinusoid at a certain frequency and record the output. Repeat with the jet at a different frequency, record output, etc. Something like 128 different frequencies. The simulation takes a long time to run though, so I would like to know if there are any techniques for system identification within simulations. The software is already running and I can choose any kind of input. The real problem is how to reduce the time needed to generate data for these 128 different simulations. Thanks

Re: System identification in simulation
 

Hello! 1.Not all 128 freq. will lead towards instability, it should be calculated. So, only for those, that Real(Freq)>0 ,must be considered. BTW, 2D will differ from 3D instability, so pay attention. 2.If you are planning to change initial conditions withing the process of simulation, that might lead towards wrong results, so i guess you must consider all data, satisfying (1.) as initial conditions.

Regards! Nick.

Re: System identification in simulation
 

Thanks for your help. To build a proper model though, I will need to find the frequency response to various frequencies, not only the ones that lead to instability. I have tried with the input signal being a composite of sinusoids at the frequencies I'm interested in. However, the results are not satisfactory. Part of it is due to the smearing of the peaks in the frequency spectrum when using the FFT when you have a signal with various frequencies, and ranging from low to high frequencies. The standard system identification involves sweeping at different frequencies the input signal and noting the output. With a simulation though, this takes a very long time. Are there any common solutions to this problem? Or is it just a matter of obtaining faster hardware and just accept that it will take days to see any results from these computations? Thanks

Luis.

Re: System identification in simulation
 

Try giving an input which will excite multiplie frequencies..white noise input perhaps. In theory a step function would be good too but this problematic in a CFD code since the derivatives need to be evaluated.

Re: System identification in simulation
 

can you suggest some good refrence for the system identification

Re: System identification in simulation
 

I think it's kind of hard to find just one reference, since the literature I've seen is sometimes very dense and didn't give me too much insight into it. Senior or 1st year graduate Control textbooks usually have a chapter on frequency response (Feedback Control of Dynamic Systems by franklin, powell,emami-naeimi has a chapter on the response of a sinusoid input, chapter 8 or 9 if I remember). This is one way to do sysid, basically excite the system with a sinusoid at one frequency, and record the output. Repeat with different frequencies and you construct a model. Also power spectral density may be used to construct these models. http://turbulence.ucsd.edu/ has a good paper highlighting the major techniques related to CFD models. Check out especially: "The emerging roles of model-based control theory in fluid mechanics" (5th paper from bottom) I think you can get documentation at the mathworks website about the system identification toolbox in matlab. It does a good job at explaining the basics. Hope it helps

Luis

Re: System identification in simulation
 

Thank you very much!