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Pacejka Model - parameter estimation [help needed]

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#1 lucalic

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Posted 14 April 2016 - 08:47

I am writing a master thesis on the Magic Formula '96 and I find it a bit difficult because I have never come across the parameter estimation and modelling before and I am still  a bit rusty with Matlab (doing MSc in (pure) Maths). I have data for a few tyres and based on this data, I found the starting points and then I estimated the parameters. I have noticed that my results are very dependent on these starting points and I would like to avoid it.
I have read a few research papers and they mention using genetic algorithms and neural networks in order to avoid a use of the initial points but they don't go much into details, they mostly compare these methods to some other. Therefore my questions are the following.
Do you have any suggestion where I should start from, are there any good and reliable materials available on the Internet?
Are there open source codes that deal with the problem I can take a look at?
Any input in highly appreciated!
Thank you in advance!


#2 Dolph

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Posted 14 April 2016 - 17:39

Maybe ask Scawer Roberts from Live For Speed:



#3 Greg Locock

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Posted 15 April 2016 - 00:37

It's a non trivial problem. I've seen times to generate fits drop by a factor of 10 or more in the last 10 years in our proprietary code, that is to say now it is more or less instantaneous. I haven't used any open source fitter, as we need the output in a particular form, and we also write out the surface shape as a table so that we can just do lookup instead of calculating it (hard to believe that's faster but that's what I'm told).


Incidentally we fit Mz separately from Fy. I am often interested in pneumatic trail, (Mz/Fy) and frankly this approach is hopeless. In my opinion you should fit Fy and Mz/Fy. This will give much smoother pneumatic trail plots, and I doubt Mz is much affected.

#4 Greg Locock

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Posted 15 April 2016 - 07:46

Incidentally dolph, people who use pac models are a huge population compared to  people who use real F&M data to generate pac coeffs. i doubt racing game people do much fitting.

#5 Greg Locock

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Posted 15 April 2016 - 22:02

Oh, and I remembered why my super brilliant idea doesn't actually help (it's been a couple of years since i looked at this). At zero toe and camber the tire still generates Fy and Mz. This is called the residual force and the residual aligning torque. Each has two components, the coning part, which pushes the same way regardless of direction of rotation, and the plysteer part, which is rotation dependent. Coning doesn't matter much as the wheels on the same axle cancel, but plysteer is additive. The Fy and RAT can be any sign, or magnitude. It is tunable by the tire manufacturer.


Anyway the result is that the pneumatic trail is a very dodgy calculation near 0, so the traditional approach makes sense.


It might be worth pulling this apart, but it doesn't use anything very fancy



Edited by Greg Locock, 15 April 2016 - 23:05.

#6 Paolo

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Posted 08 May 2018 - 20:40

I might be a couple years late, but my old PhD thesis has a chapter exactly on this topic.

It is easily feasible with evolutive algorithms; I personally prefer to avoid bit strings (traditional genetic algorithm) and use a real coded memetic-evolutive hybrid based on statistic parameters.