# Structured vector fitting framework for mechanical systems

@article{Werner2021StructuredVF, title={Structured vector fitting framework for mechanical systems}, author={Steffen W. R. Werner and Ion Victor Gosea and Serkan Gugercin}, journal={ArXiv}, year={2021}, volume={abs/2110.09220} }

In this paper, we develop a structure-preserving formulation of the data-driven vector fitting algorithm for the case of modally damped mechanical systems. Using the structured pole-residue form of the transfer function of modally damped second-order systems, we propose two possible structured extensions of the barycentric formula of system transfer functions. Integrating these new forms within the classical vector fitting algorithm leads to the formulation of two new algorithms that allow the…

## References

SHOWING 1-10 OF 22 REFERENCES

Structure-preserving model reduction for mechanical systems

- Mathematics
- 2003

This paper focuses on methods of constructing of reduced-order models of mechanical systems which preserve the Lagrangian structure of the original system. These methods may be used in combination…

Data-driven Structured Realization

- Mathematics, Computer ScienceArXiv
- 2016

This approach extends the Loewner realization framework to a more general system structure that includes second-order (and higher) systems as well as systems with internal delays.

Data-Driven Identification of Rayleigh-Damped Second-Order Systems

- Computer Science, MathematicsArXiv
- 2019

This paper proposes an identification of the corresponding second-order system, extending the Loewner framework for this class of systems, having internal Rayleigh damping, by means of a data-driven approach.

Vector Fitting for Matrix-valued Rational Approximation

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2015

This work extends the previous framework of VF for scalar-valued rational functions to include the construction of effective rational approximations to matrix-valued functions, a problem which presents significant challenges that do not appear in the scalar case.

Quadrature-Based Vector Fitting for Discretized H2 Approximation

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2015

This work shows that one can improve the performance of VF significantly, by using a particular choice of frequency sampling points and properly weighting their contribution based on quadrature rules that connect the least squares objective with an $\Hardy_2$ error measure.

Rational approximation of frequency domain responses by vector fitting

- Mathematics
- 1999

The paper describes a general methodology for the fitting of measured or calculated frequency domain responses with rational function approximations. This is achieved by replacing a set of starting…

A comparison of second-order model order reduction methods for an artificial fishtail

- Computer ScienceAutom.
- 2019

This paper considers an artificial fishtail as an example for a complex mechanical system with a second-order large-scalemodel, which is derived by using the finite element method.

A framework for the solution of the generalized realization problem

- Mathematics
- 2007

In this paper we present a novel way of constructing generalized state space representations [E, A, B, C, D] of interpolants matching tangential interpolation data. The Loewner and shifted Loewner…

On the scalar rational interpolation problem

- Mathematics, Computer ScienceMath. Control. Signals Syst.
- 1996

This work uses Gröbner bases of submodules of the free module of rank 2 over the polynomial ring in one variable and extends previous work on the key equation of error control coding theory.

Transfer function synthesis as a ratio of two complex polynomials

- Mathematics
- 1963

Experimental frequency response data obtained from a linear dynamic system is processed to obtain the transfer function as a ratio of two frequency-dependent polynomials. The difference between the…