# n-dimensional data clouds

#### joewill

##### New Member
Hi there!

I have to deal with measured data from engine oil pumps. The table containing the data from a test run contains eg these variables (=columns):

pump rpm
oil pressure
oil temperature
oil flow amount

Now I need to know eg the flow at given values of the other three variables. In most cases, the exact "point" in this 4-dimensional space is not available. So I have to set tolerances for the three constraining variables and average the points which are within the tolerance. This works OK in densely populated areas, but not in sparsely populated areas, because I would have to make the tolerances so big that the results are not usable (too many "wrong" points get hit). Inter-/extrapolating from the nearest points would be much better, but programming that seems a little hard to me.

Any hints?

Thank you very much in advance,

Joe

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##### MrExcel MVP
HI - welcome to the board!

I assume that flow rate is related to pump rpm / temp / pressure by a formula of some kind? If so, you might be able to use Solver to help...see

http://216.92.17.166/board/viewtopic.php?topic=23107&forum=2

This message was edited by PaddyD on 2002-10-15 20:46

#### Joe Was

##### MrExcel MVP
Your problem can be solved using "The Ratio of Inequality."

If Pump RPM/Oil Temprature=Oil Pressure/Oil Flow Amoumnt

Set Flow Amount = to "X" then solve for "X"

Then Flow Amount ==> (Oil Temprature x Oil Pressure) / Pump RPM

Change the variable names to their Row-Column positions add the resulting formula to a cell and you should have your answer for all data conditions. JSW

#### joewill

##### New Member
Hi there,

thank you very much for your suggestions. I'm not quite sure though how could use the solver to figure out a formula from a 4-dimensional array... Right now it seems to me that the solver can only deal with one target cell and one excplicitly given target value. Can it help me to find out the coefficients A,B,C for a formula like

flow=A*pressure + B*rpms + C*temperature

which is valid for a range of target cells?

Maybe I don't see the wood for the trees...

Yours,

Joe

#### joewill

##### New Member
Sorry for SPAMing, I just got an idea how to get the coefficients using the solver's help... I'll try that now.

#### joewill

##### New Member
OK, I'm a step further...
Now I'm able to use the solver to provide me coefficients for Nth grade polynoms which approximate my data, but it works only for a 1-dimensional data curve (eg flow=f(pressure) ).
When I try to get a formula for flow=f(pressure,rpms) solver fails telling me the problem was too big...

The formula I tried was

flow = (A*rpms)/(B*pressure+C*pressure^2+D)

A 2nd grade polynom is sufficient for describing the flow/pressure relationship at a given rpm.

What are the limits for excel's solver?

Another issue is that often the solver needs more than one try to come to a good solution, though values for precision are reasonable large. Is there a guide on how to use solver for polynomic approximation of data?

Sincerely yours,

Joe

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