101 research outputs found
Dominant Subspaces of High-Fidelity Nonlinear Structured Parametric Dynamical Systems and Model Reduction
In this work, we investigate a model order reduction scheme for high-fidelity
nonlinear structured parametric dynamical systems. More specifically, we
consider a class of nonlinear dynamical systems whose nonlinear terms are
polynomial functions, and the linear part corresponds to a linear structured
model, such as second-order, time-delay, or fractional-order systems. Our
approach relies on the Volterra series representation of these dynamical
systems. Using this representation, we identify the kernels and, thus, the
generalized multivariate transfer functions associated with these systems.
Consequently, we present results allowing the construction of reduced-order
models whose generalized transfer functions interpolate these of the original
system at pre-defined frequency points. For efficient calculations, we also
need the concept of a symmetric Kronecker product representation of a tensor
and derive particular properties of them. Moreover, we propose an algorithm
that extracts dominant subspaces from the prescribed interpolation conditions.
This allows the construction of reduced-order models that preserve the
structure. We also extend these results to parametric systems and a special
case (delay in input/output). We demonstrate the efficiency of the proposed
method by means of various numerical benchmarks
1 Model order reduction: basic concepts and notation
This is the first chapter of a three-volume series dedicated to the theory and ap
plication of Model Order Reduction (MOR) .We motivate and introduce the basic con-
cepts and notation, with reference to the two main cultural approaches to MOR: the
system-theoretic approach employing state-space models and transfer functionc con-
cepts (Volume1), and the numerical analysis approach as applied to partial differen-
tial operators (Volume2) ,for which project ion and approximation in suitable function
spaces provide a rich set of tools for MOR.The set two approaches are complementary
but share.Despite the sometimes different opted language and notation,they also
share the main ideas andkey concepts, which are briefly summarized in this chapter.
The material is presented so that all chapters in this three-volume series are put into
context, by high lighting the specific problems that they address. An overview of all MOR applications in volume 3 is also provided
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