CP diagram extended model fit

[Henrik Johansson]

I am currently using the "extended" model in the CP diagrams.

Why is the model going through all the X-marks exept the 1s one?

[Mark Liversedge]

The extended model fit using an envelope (or hull) fit.

Basically, each of the parameters are given sensible (but wrong) starting values.

Then the following is done until all the parameters (CP, W' etc) converge (stop changing).

• Look for highest value for CP - looking at datapoints in the flatter area of the PD curve (Aerobic interval) to see which one yields the highest value using the other current estimated parameter values
  
• Look for highest value for W' - looking at datapoints in the first part of the PD curve (Anaerobic interval) to see which one yields the highest value using the other current estimated parameter values
• Look for highest value for Pmax - looking at datapoints in the first few seconds (Short Anaerobic interval) of the PD curve to see which one yields the highest value using the other current estimated parameter values
• Look for highest value for CP  decay - looking at datapoints in the low tail (Long Aerobic) of the PD curve to see which one yields the highest value using the other current estimated parameter value

The points that yield the highest values are marked on the plot with a blue cross -- these are the limits of the hull.

So in summary, the envelope fit searches for a maximal fit using parts of the curve that influence the parameters most greatly - short durations for Pmax and W' and longer durations for CP and CP decay. You can configure the interval sections in the CP plot setttings, but would recommend using the defaults.

It is important to understand that the fit is applied to a large number of points, that the final fit is a hull and that it meets the MMP curve at the maxima. We do this because;

a) MMP will always contain a large number of sub-maximal points

b) We want to encourage modelling with data from short periods (<4-6weeks) so need to tolerate lumpy MMP curves

c) We can easily constrain parameters and use a large number of observations in an computationally efficient way (which ensures a maximal fit that is physiologically plausible).

With v3.5-DEV we have also added Least Squares fits along with marking and using Performance Test (as intervals in a ride file). I am currently working on adding a jackknife method to help quantify any bias and errors.

I'll probably end up posting a long note here (like this one!?) since I've also started a series of tutorials on the CP model and goldencheetah in collaboration with Dr Len Parker Simpson and some support from other well known academics with expertise in modelling with CP.

You can watch the CP explainer here: https://vimeo.com/283303558 (see if you can spot the two painfully embarrassing mistakes I make). I'm working on another for working with the models in GC, should be publishing this weekend.

Cheers,

Mark

[Henrik Johansson]

The "marked on the plot with a blue cross" are what I refer to as "X-marks".
These appear to be properly identified, but then the Pmax one (the one at 1s) is ignored and the model plot is ~150W below it. Is this on purpose or is something wrong?

[Mark Liversedge]

The key here is the parameters are constrained to be physiologically plausible.

I'd try LM with CP2/CP3 models. Are there tests / maximal efforts in the 3-20 min range ?

I know its boring and I say the same thing all the time, but tests are best when fitting models.

Mark

[Ale Martinez]

it looks like the fit is using 90" and 120" points, probably you can find a better fit playing with the Short Anaerobic and Anaerobic search intervals to force more separation between them.

[Henrik Johansson]

Found this old plot:

http://markliversedge.blogspot.com/2013/12/goldencheetah-extended-cp-model.html

There the red dashed line is dead on Pmax just as I think it should be.

Appears that there is something wrong/limiting with the scaling/size of the cyan dashed "fast" "alactic" component - at least for my data.

 

Have changed the parameters but there is only marginal changes.

There are identified maximal efforts (yellow dots) from 5s to 41minutes.

Is this just happening for me or is this common behavior?

Is the extended model a Morton model ? (his modifications of the Margaria one)

[Mark Liversedge]

What tests have you performed?