Filter bank approach to create state space models of reduced order frequency dependent vibro-acoustic finite element models

In recent years reduced order modeling techniques for vibro-acoustic systems that are modeled with numerical techniques, such as the finite element method, have been established as a key technology in digital twin design. By reducing the order of the system, the complexity of the model can be alleviated to such a degree that the model can be run in a (near-)real time environment, allowing for integration of the model on an embedded system included with the physical asset, e.g. for state estimation. This paper demonstrates how to create a state space model of a vibro-acoustic finite element model including frequency dependent impedance boundary conditions. These systems are difficult to convert to a state space representation for two reasons: Firstly, the frequency dependency has to be preserved in the reduced order model. Secondly, the state space form only takes the previous time step into account, while the frequency dependent damping behavior would result in a convolution operation. This paper aims to solve both issues by approximating the frequency dependency using a digital filter bank approach, in which the individual filter banks use a frequency independent damping matrix. The filter bank is designed such that a near perfect reconstruction is achieved. Furthermore, it allows for banks with different frequency bandwidths to fine-tune the filter where the impedance changes rapidly as function of frequency. The frequency independent vibro-acoustic models in the filter banks are reduced using a Krylov subspace projection method. The resulting filter bank is converted to a state space form by converting the reduced order model to first order form and rewriting the finite impulse response filters in state space format. A second reduction is performed on these filters, due to the large number of filter coefficients, leading to a small and stable system level state space model.

ISBN:978-83-7880-799-5

Jaar van publicatie:2021

Toegankelijkheid:Open