16 research outputs found
On Reduced Input-Output Dynamic Mode Decomposition
The identification of reduced-order models from high-dimensional data is a
challenging task, and even more so if the identified system should not only be
suitable for a certain data set, but generally approximate the input-output
behavior of the data source. In this work, we consider the input-output dynamic
mode decomposition method for system identification. We compare excitation
approaches for the data-driven identification process and describe an
optimization-based stabilization strategy for the identified systems
Optimization of damping positions in a mechanical system
This paper deals with damping optimization of the mechanical system based on the minimization of the so-called "average displacement amplitude". Further, we propose three different approaches to solving this minimization problems, and present their performance on two examples
Using second-order information in gradient sampling methods for nonsmooth optimization
In this article, we show how second-order derivative information can be
incorporated into gradient sampling methods for nonsmooth optimization. The
second-order information we consider is essentially the set of coefficients of
all second-order Taylor expansions of the objective in a closed ball around a
given point. Based on this concept, we define a model of the objective as the
maximum of these Taylor expansions. Iteratively minimizing this model
(constrained to the closed ball) results in a simple descent method, for which
we prove convergence to minimal points in case the objective is convex. To
obtain an implementable method, we construct an approximation scheme for the
second-order information based on sampling objective values, gradients and
Hessian matrices at finitely many points. Using a set of test problems, we
compare the resulting method to five other available solvers. Considering the
number of function evaluations, the results suggest that the method we propose
is superior to the standard gradient sampling method, and competitive compared
to other methods
Structure Preserving Model Order Reduction by Parameter Optimization
Model order reduction (MOR) methods that are designed to preserve structural
features of a given full order model (FOM) often suffer from a lower accuracy
when compared to their non structure preserving counterparts. In this paper, we
present a framework for MOR based on direct parameter optimization. This means
that the elements of the system matrices are iteratively varied to minimize an
objective functional that measures the difference between the FOM and the
reduced order model (ROM). Structural constraints are encoded in the
parametrization of the ROM. The method only depends on frequency response data
and can thus be applied to a wide range of dynamical systems. We illustrate the
effectiveness of our method on a port-Hamiltonian and on a symmetric second
order system in a comparison with other structure preserving MOR algorithms.Comment: 26 pages, 7 figure