All three airmass numbers are describing the same entity, thus they supposed to be identical.  Assuming that the engine is a closed system, we should be able to assume that the airmass in the intake should result in the same airmass approximated by the wideband sensor on the exhaust side.  This is a perfect setup for performing calibrations.  We can either calibrate the MAF by juxtapositioning the MAF-resulting CAM against the CAM from the exhaust.  The same idea can be done in parallel for the SD model, placing SD calculations' based CAM against the CAM from the exhaust side.

IFR*IPW*AFRwb=15*MAF/RPM

 

IFR*IPW*AFRwb=GMVE*MAP/TEMP


Once you perform all these calculations for your log, you end up with three new columns, and they all estimate cylinder airmass.  In the perfect world, they would be identical.  In this world, they won't.  It would be pertinent however to take a look at how do the resulting values differ from each other when you look at them not one value at the time, but as a whole dataset.

The silly side effect of doing calibrations this way is that if you plot the various CAM pairings against each other, they should form a straight line, after all y=x, so all points in the set should be of the (x,x) form, for example (0.1,0.1), (0.3,0.3), (0.55,0.55) etc...  This makes it very appealing to look at this problem graphically, as most data should be right along the y=x line, while the more troublesome data points will be easily spotted simply by visual inspection of the graph.  We'll see more of this later, but for now just try to expand your thinking from single-point calculations to calculations for a whole set, and their graphical representation.



So this picture has the CAM from fuel on the horizontal axis, and it has the two airmass predictors (MAF, SD) on the vertical axis, grouped by color.  The numbers on the axis are the values for the airmass.  As you can see, there's some obvious outliers, and no clue to their source.  So how would one go about getting to the bottom of the source of the outliers?

Excel isn't particularly useful for exploratory data analysis.  Matlab has some new 'data brushing' functionality in it, but it's still a bit clunky.  A while back I found a program that is quite perfectly suited for such a task:  Tableau.  Officially it's a program for 'business intelligence,' whatever that means.  I use it because it's lighting quick to adapt to changes, which allows me to rip through hundreds of different scenarios and ways of looking at the same data.  Not only it does the regular charting, but you can group, filter, color, summarize, subtotal, etc on just about any number of parameters.  I've been using it for few years now, but I haven't had a really good clear case where I could show off why it's cool.  Searching for the source of outliers in a large dataset is a good showcase of what it can do for us.

First, I did a graph of SD-sourced CAM against the fuel consumption-sourced CAM.  That we've seen already.  So the new thing here, is I colored the data samples according to their corresponding MAP value.  On the right side you get a little color scale of which color gets used for what MAP value.  The scaling of the colors is adjustable, and I adjusted the center (gray values) to be at 35kPa which is a common value for MAP at idle.  This way all samples with MAP smaller than 35kPa are red, and everything above 35kPa is green.  I did this to isolate at what conditions do the outliers occur.  We clearly see that all outliers are very red (below <35kPa).  So it is not likely that knock retard could be a cause of these skewed readings, as knock usually occurs under high pressure, which is not the case here.  So what else could it be?  How about temperatures?



IAT also does not seem to be the cause, as the outliers seem to have the same values as many other samples that fall directly in line.  What about ECT?  All I had to do is change the source of color from IAT to ECT, and we get a new graph.



ECT also has a variety of values for the outliers, but again, no clear pattern emerges in which the outliers would react to different ECT than the 'proper' values.  What else could it be?  How about different throttle inputs?


In this graph I scaled the coloring in such a way that the off-throttle/very light throttle would show up as gray.  There's a definite uniformity in that the outliers all occured at off-throttle/very light throttle.  So let's summarize what we know so far:  outliers occur are independent of temperatures, and they occur only at very light throttle and very low MAP values.  Could it be deceleration?  If it is, DFCO could be activating, wreaking havoc on fueling.  So how else would the DFCO show up in our data?  If it lives up to it's name, it cuts fuel delivery, causing abnormally high lean condition.  Let's color up our graph based on the AFR from the wideband sensor:


AFR is definitely significantly lean in all the outliers.  So I think it is quite safe to say, that the DFCO caused lean condition is the cause behind some of the CAM estimations being severely off, creating these visually sticking out outliers.

Another not only cool, but also very useful part of Tableau is the ability to select groups of points, for either inclusion or exclusion.  I selected all the outliers, and I excluded them from the graph, creating this:


Isn't is a much cleaner graph?  Look at the values on the axis--no more samples with 1.6g/cyl, which is achievable only on a FI car with a generous amount of boost.  There are still some values that stick out, that are not exactly on the trend line, but they are the inherent noise in the system.

Now that we know how to get rid of outliers, let's compare MAF and SD directly against each other:

 

MAF is on the bottom, SD is up top.  They both have noise, but they both also do a very good job of sticking to the trend line.  The MAF seems to be a little noisier, especially on the low end of airmass values, where SD seems to excel.  This is exactly why the GM uses the hybrid MAF/SD model:  they leverage the stability of SD for lower airmass situation, and MAF for the higher airmass.  It it quite literally the best of both worlds.

 

Since everything we've done so far been graphical, let's take a look at some numbers, to see if they back up what we could see by observing patterns.  

 

There's a bunch of statistics tricks that are used to describe how closely two functions are to each other.  I'm not going to explain all of them here, but here's the rundown for these who know what they mean:

Trend Lines Model  

 

MAF:

SSE (sum squared error):  2.19023 

MSE (mean squared error):  0.0002055 

R-Squared:  0.998423 

Standard error:  0.0143366 

p (significance):  < 0.0001 

 

SD:

SSE (sum squared error):  1.07925 

MSE (mean squared error):  0.0001014 

R-Squared:  0.999398 

Standard error:  0.01007 

p (significance):  < 0.0001 

 

SD wins overall.  Better R^2, lower SSE and MSE, smaller standard deviation of errors.  

 

That was for the cases where we cleaned up the data.  Out of curiosity, let's see how they fair when we look at the data before the cleanup.

 


 

 

MAF:

SSE (sum squared error):  22.7658 

MSE (mean squared error):  0.0020751 

R-Squared:  0.983645 

Standard error:  0.0455531 

p (significance):  < 0.0001 

 

SD:

SSE (sum squared error):  29.177 

MSE (mean squared error):  0.0026694 

R-Squared:  0.983759 

Standard error:  0.0516667 

p (significance):  < 0.0001 

 

 

 

In this case, MAF does a little better than SD.

 

So to wrap up:  

  • Exploratory data analysis doesn't necessarily have to be painful and laborious.  
  • Outlier explanation can be meaningful and insightful.  
  • GM had good reasons to go with the hybrid MAF/SD model.

 

Hopefully this cleared some things up, as I've been getting a lot of questions lately about my methods of calibration.