# How to compare dynamic systems of different degree of abstraction?

I'm modelling a vehicle as a multibody system in Matlab/Simulink. My goals are:

1. Have a realistic simulation model so I don't have to do prototype measurements all the time.

2. Solve specific parameter estimation tasks and apply driver assistance control mechanisms.

Now for the first task I created a detailed multibody model that imitates the real vehicle's suspension kinematics, has a tire model and so forth.

For the second task, this model would of course be taking too much computational effort for a real-time application on a vehicle's ECU. That is why I created additional models with reduced complexity for different purposes (e.g. a single-track model).

Now I would like to know not only how "well" the complex model matches the real vehicle, but also to what degree the "interesting" dynamics of the complex model correspond to the simplified ones.

What I would like to avoid is just using test signals and looking at graphs to see if they are "kind of similar". A more in-depth approach that gives me mathematically more or less sound results would be nice. Numerical solutions are perfectly fine though, I don't expect to find nice analytical approaches for complex nonlinear systems.

I am looking for literature or some guidance on this kind of problem. I am sure sensitivity analysis is an important part of the solution and I already found some resources on that. But it doesn't help too much when I want to compare 2 models (or model and reality).

I am thankful for every hint!

• You should add your equations of motion. It is difficult to give advice without seeing the system ode. – MrYouMath May 9 '17 at 20:25
• The complex system has about 50 state variables, so the ode (I couldn't even simply write it down because I used Simscape) wouldn't be too helpful I'm afraid. Even the simpler models still have quite complex ode's. So my question is basically how can I determine which states/dynamics are important and how can I compare two dynamic systems? – Marius Oei May 10 '17 at 14:35
• I know this is a broad topic, that's why I'm looking for literature. I couldn't really find anything helpful so far. But I feel like there has to be research on validation of dynamic models and on the evaluation of reduced-order models. – Marius Oei May 10 '17 at 14:40
• Is you ODE linear time invariant? – fibonatic Dec 3 '17 at 17:44
• The most general way to approach this is through comparison in the frequency domain. If a single metric is required then you want the Vinnicombe gap (or Nu-gap) distance. – welf Jul 22 '18 at 12:23