G. Fuchs, A. Steindl, S. Jakubek:
"Local Jacobian based Galerkin Order Reduction for the Approximation of Large-Scale Nonlinear Dynamical Systems";
International Journal of Mathematical Models and Methods in Applied Sciences (eingeladen),
In automotive applications large-scale nonlinear dynamical
models are utilized for hardware-in-the-loop simulations and
model-based controller design. A projection-based order reduction
of these models, on the one hand, yields substantial advantages in
computational speed and on the other hand, simplifies the controller
design procedure. In this work a mathematical-empirical approach is
chosen for the order reduction of a real-time diesel engine model. It
is based on recorded time-snapshots for typical system excitations.
Flat and nonlinear Galerkin approximations are obtained by projection
onto a lower-dimensional sub-space. In the nonlinear Galerkin
approach a novel scheme for the reconstruction of the omitted states
is introduced. It makes use of the local model parameters in the
local Jacobian matrix, obtained from a linearization of the complete
nonlinear model for various points of a local model network. The
results from the application of the reduction methods to the engine
model are presented and discussed for different reduced model orders
and the benefits of the iteration scheme are demonstrated.
Diesel engine modeling, Model order reduction, Singular value decomposition, Snapshot method, Galerkin methods, Local model network
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