I am looking for a good method to combine a set of curves into a single curve.

Those curves have been produced by performing a measurement/testing n-number of times under similar conditions. What I am trying to achieve is to get a single curve which represents statistically the most likely distribution of points if I perform the same test/measurement next time.

Would some type of regression achieve this goal?

Below you will find some example data for Q (flow) and H (head) for a pump rotating at 1245 rpm. So each measurement at constant rpm gives a curve for Q and H.

Q: 12,1557261    H: 8,1434835
Q: 24,3704478    H: 6,93492
Q: 40,9583469    H: 5,3908751
Q: 55,8666517    H: 3,4994621
Q: 63,8760173    H: 2,4220055
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    $\begingroup$ Would you please post a link to example data from several of these measurement runs? $\endgroup$ – James Phillips Dec 11 '18 at 20:07
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    $\begingroup$ Most likely yes, regression is fine. One consideration: are these periodic data like a heartbeat where the period has to be estimated statistically? $\endgroup$ – AdamO Dec 11 '18 at 20:15
  • $\begingroup$ @JamesPhillips Sorry for the late reply. I posted some example data above. $\endgroup$ – Midas Dec 14 '18 at 10:59
  • $\begingroup$ @AdamO : Sorry for the late reply. The answer is no. It is the flow and head of a pump rotating a constant speed. Regression seems to be doing a nice job, I just don't know if I do this the right way. First I do a multivariate regression where my input is speed in rpm and the output is the flow. Then I do the same thing for speed and head. Then I join those output together to get a curve. The single curve I produced was very very accurate when compared to real life data. Still, I don't know if I was lucky or if I did the right thing. $\endgroup$ – Midas Dec 14 '18 at 11:03

I found that the Bleasdale yield density equation, "1.0 / pow((a + b*x), (-1.0/c))", gave an OK fit to your example data with parameters a = 2.6123446529575759E+01, b = -3.5195352662517970E-01 and c = 1.4724868235916486E+00 and if you would like to try some other data sets I used my zunzun.com online curve fitter for this specific equation at http://zunzun.com/Equation/2/YieldDensity/Bleasdale/ to perform the fit. I personally think a surface fit of the type "Q = f(H, RPM) might have more utility as a general purpose equation, as a 3D surface equation would allow selection of optimum RPM - this is why I had asked for several data runs, so that I could search for a simple 3D surface equation. Here is a graph of my fit for the Bleasdale yield density equation. bleasdale

  • $\begingroup$ Thank you! I will give this approach a try and compare to what I achieved using multivariate regression. I'll get back with feedback . $\endgroup$ – Midas Dec 15 '18 at 14:41

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