Finding parameter to fit known eq. to 3 points?

[JBlackhole]

To all,

I am trying to see if one can find a parameter required to fit a known equation to a set of data points. See attached.

I have an equation Q(w,wn,zeta) and would like to see if it 's possible to find the value of zeta required to fit the Q() for a given data set

Test 1:

For a given range of w values, a value of wm and zeta = 0.04, I calculated the Q value, allocated them to a table to “mimic” a data set (not important but it follows how data is provided. I am trying to work “backward” by trying to find the zeta value required to fits Q at the max value. (Obviously mcad must predict zeta  =0.04 !)

I have set up ‘test 1’ as a root() but nothing is return

Test 2:

  Use a subset of a known data set and see if one can find the zeta value required to fit Q() passing through 3 points of that subset

I know that must people will say that I am tackling the problem the wrong way but I have to start somewhere and that why I am looking for advice

Any pointers by the more mathematically inclined out there would be much appreciated

Thanks

Regards

[AlanStevens]

Do you mean something like in the attached?

Alan

[JBlackhole]

Thanks AlanS. definitely a step forward. I  now understand the mistake I made on my 'test1'

Questions if I may?

1. in the solve block you defined 1 equality.

    Why not 1 equality for each point? See attached for my attempt

2. Why is there no way of plotting the Q() function with the zeta found over the range w? Mind you zeta appears to be too big as it should be <1

[AlanStevens]

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J B wrote:

Thanks AlanS. definitely a step forward. I  now understand the mistake I made on my 'test1'

Questions if I may?

1. in the solve block you defined 1 equality.

    Why not 1 equality for each point? See attached for my attempt

2. Why is there no way of plotting the Q() function with the zeta found over the range w? Mind you zeta appears to be too big as it should be <1

1. It is an equality for each of the three points. They are in a 3x1 vector, and all three are being compared. Although I used different wn for each point, I suspect that a single wn should be used. Given that there are three points of comparison you could use Minerr to find the best combination of wn and zeta.

2.  You should be able to plot Q as a function of w using a value of zeta and a value of  wn.

Alan.

[Werner_E]

I may be missing the overall picture, but as you seem to be disappointed to see three times the same value for zeta, maybe you had something like the following in mind

But then ... are you aware that the way you use your function Q() in that solve block with the first two arguments being the same gives you r=1 in your function Q and Q is not depending on those arguments anymore. So you would not need the solve block, if thats what you want.

[JBlackhole]

Thanks for the input. Just realized that the zeta value must be the same! The function Q() for a given wn & zeta must pass (ideally!) by the 3 points. One cannot have 3 different zeta! I think I had something else in mind and probably confused myself. The zeta factor gives the "narrowness" (and max value) of the peak and wn where the peak occurs.

So AlanStevens 1st suggestion was correct and I think consist of solving

Need to review that in quiet time

[AlanStevens]

I'm not sure that the Q function describes the data well anyway (consider the limit as w tends to zero, for example).  See attached.  (My knowledge of this sort of system is negligible though, so it might not be correct to consider that limit!).

Alan

[JBlackhole]

Thanks for that. Will review attached worksheet a bit later.

Q fn describes data well enough.

Agree. This is part of the testing. Finding out if something meaningful can be done with the approach. I’ll need to go back to see if the set of data selected is “valid” for the approach. I may have picked up a set of data which will never (ever!) work

Current thinking is

1. Select a frequency and get is max value (fnm, Qmax)
2. Find 2 points (f1,Qmax/SQRT(2)) ( f2,Qmax/SQRT(2)) (or nearest as data is discretise)
3. Extract range of data between [f1,f2]. In other words one is working on a sub-set of the data. The Q() fn will never works over a range larger than that
4. Try finding zeta in the Q fn to pass through the 3 selected points

I also attempted (will post something a bit later) your approach with the Minerr() on the data for test 1, and the zeta value returned is not 0.04