Bin Point Selection
Last updated 2007-09-18 11:11 PDT

Bin Point Selection

When choosing RPM or load bins on a VE table (or any other table or curve, for that matter), you must use care. The phenomenon being represented by the table almost always has non-linear behavior, yet the table is usually used by a linear interpolation algorithm, to fit straight lines between the values at a finite number of bin points.

Using the same curve, I've chosen two different sets of bin points along the X- (bottom) axis. In the case called "fixed spacing," I've merely used every other division of the graph to make my choice. This turns out to produce pretty good correlation with the curve, except for one region, marked "A."

On the second curve, I've chosen my points in an attempt to reduce the size of the error in the first graph's region "A," but now I have more significant errors along the remainder of the curve.

Automating bin selection for a 2-D curve such as shown here is pretty simple, perform a spline (or similar) fit on the known curve points and then do an optimization to minimize the area of the error regions, using the non-endpoint X values as the variables. (Generalizing this to 3D surfaces would simply minimize the volume of the error regions.) But...

First we must ask, which bin choice is better? It all depends on the application. Assume that the X axis is RPM and Y is VE. If this curve represents an an engine used for street use, then I put forth that the first set ("fixed") is much better. Most of the running time will be spent down in the lower RPM range, right where the "smooth" spacing curve has it's biggest errors (see region marked "B"). It is not likely to spend much time up in the top RPM range, where the "A" region is causing problems.

On the other hand, if this this is a racing engine, then we'll probably be operating up in the top RPM regions, in which case neither set of bin values is appropriate, we should slide them up to the right and get less error up top.

So, in order to automate bin selection more appropriately, you must weight the region of the curve that is most important for the engine's intended purpose.

 
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