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Mathematics Numerical Computation

Trying to reverse engineer an equation

David Faguy

Posted 10 years ago

Hi. I work for a combustion research facility studying various fields from fuel efficiency to alternative fuels to pollution control. We are using software which was written in 1994 (DOS based) to produce a series of 11 points based on a range and a "K-Factor". These points are then used in the calibration of some of the equipment that are in the labs. Due to recent equipment changes, we need to update the software but we do not have access to the original code or the author (he retired a long time ago). As a result, we do not know what algorithms were used to create the data sets. I'm wondering if there is a way to figure out the equation(s) used in the software based on the data sets produced. The only inputs that the software requires are a Range Max. Value (the software always assumes that the minimum value is 0) and a K-Factor. A K-Factor of 1 produces a straight line when plotted while K-Factor other than 1 produces a curve with 0 and the Max Range as fixed points. I used the software to create the following sample data sets using a Max. Range Value of 25: K Factor = 1.00, K Factor = 1.44, K Factor = 0.813 100% 25.0000 25.0000 25.0000 90% 22.5000 22.7252 22.3902 80% 20.0000 20.4404 19.8057 70% 17.5000 18.0362 17.2463 60% 15.0000 15.6191 14.7114 50% 12.5000 13.1517 12.2008 40% 10.0000 10.6322 9.7142 30% 7.5000 8.0591 7.2511 20% 5.0000 5.4305 4.8112 10% 2.5000 2.7448 2.3943 0% 0.0000 0.0000 0.000 I'm hoping that someone out there can help me out as I've hit the end of my admittedly limited math skills. Thanks in advance for any information that you can provide. Dave

POSTED BY: David Faguy

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Kay Herbert

Kay Herbert, Chief scientist, Sloan Valve Co.

Posted 10 years ago

I think if we know more about the physics behind the data it would be easier to find the model

POSTED BY: Kay Herbert

Bill Simpson

Posted 10 years ago

Thanks for the data. It looks like you have one bad data point in the first set. In the "0.4" row and "0.879" column you have 9.345 which appears to be out of line. Perhaps that should have been 5.9345. Looking at the data available, as Vitaliy Kaurov noted, it appears that the largest component is a linear factor. Getting enough information to estimate the equation for that line seems like the first step. Removing that linear factor then seems to show that a quadratic factor remains. Getting enough information to estimate the peak of that parabola seems like the next step. With the three data sets I can try to estimate that peak. Having all six data sets would help determine whether the linear scale factor is proportional to the K factor or whether the relationship is more complicated. Likewise for the peak of the parabola. With that information the max range value then it would be possible to see whether the result is exactly the same as the equation that you have already been given or whether there are differences. If the pattern in the data persists then perhaps the values for x=.5 and x=1. for each of the other combinations of variables may be enough.

POSTED BY: Bill Simpson

David Faguy

Posted 10 years ago

Thanks for the responses. @ Bill Simpson: Unfortunately, the K Factors are hard coded into the software which is the reason we need to figure the equation out. The K Factor for our new equipment does not correspond to any of the hard coded values. The available K Factors are 1.44, 1.23, 1.0, 0.894, 0.879, and 0.813. I've attached a sample spreadsheet with three tables to this post. Also, I ran this problem by some people here with much higher level math Kung-Fu than I have and they came up with the following equation: Y = MP(1-M(F-1)(P-1)) Where: M = Max Range Value, P = Percent of Max Range Value, F = K Factor This equation works well in some cases but is off in others so it needs to be refined if we're going to use it. Attachments: