## Invariant Excitations

One focus of our method development for system simulation is the invariant system excitation.

# Invariant Excitations

The computer-aided simulation of dynamic systems requires a mathematical model of the real system and an excitation model (incl. corresponding excitation signal) to adequately describe the interface of the dynamic system to the external environment.

In the context of vehicle simulation, the tire model together with a digital road profile is the typical excitation model used. Another approach would be to excite the vehicle directly using the measured wheel hub forces and moments, in other words, doing without the road profile and tire model.

#### Tire model and road profile

However, between these two approaches there is a major difference: Together, the tire model and the road profile define a so called invariant excitation model, i.e., the excitation does not depend on the simulated system - the vehicle model - but rather can be used to simulate different vehicle options (with the same tires). However, measured wheel hub forces and moments very much depend on the measured vehicle having a suitable vehicle type; they are not invariant, but are rather system dependent and can only be used to excite a model of the measured vehicle.

Invariant excitation models are very desirable in terms of cost and effort, measured drives with many vehicle variants are expensive and time consuming. On the other hand, the appropriate invariant models are often not available.

#### I6D Method

In response, ITWM has recently developed the so called I6D method and registered a patent for it. On the basis of the relatively easy to measure wheel forces and moments as well as the structural movements on one (!) reference vehicle, a 6D road profile is identified by the introduction of a 6D tire replacement model. It uses a special sub-system approach that leads to a mathematical optimal control problem, which can be efficiently solved with the appropriate algorithms with no iterations. The introduced tire replacement model and the identified road profile form a pair that is used as the excitement model. This pair has certain invariant properties and can be used to simulate other variants, i.e., different from the measured vehicle.

Although the I6D method is primarily developed to calculate invariant excitation models for vehicle simulation, it can also be applied to analogous problems for the calculation of invariant excitation models of other dynamic systems.