A PhD thesis @ NALAG

TW 2013_01

Maryam Saadvandi
Nonlinear and parametric model order reduction for second order dynamical systems by the dominant pole algorithm
September 13, 2013

Advisor(s): Karl Meerbergen and Wim Desmet

Abstract

Noise and vibration performance is a key parameter for assessing the quality of automotive and aerospace products. In order to gain competitive advantage, manufacturers are continually striving to reduce noise and vibrations levels. The numerical analysis of the acoustic behaviour results in huge mathematical models, in particular,for higher frequency analyses.This leads to high requirements regarding computational and storage resources. Furthermore, the cost increases dramatically when the model has a large number of design variables that have to be taken into account for the development of the optimal design.This motivates the importance of reducing the size of the models in order to reduce the simulation cost.One choice for building such reduced models is algebraicModel Order Reduction (MOR) for linear dynamical systems. The aim of MOR is to reduce the system matrixin such a way that the reduced system has similar input/output behaviour as the original system.The goal of this thesis is to use the Dominant Pole algorithm (DPA) for computing a truncated modal representation of a large scale parametric linear second order dynamical system and also largescale dynamical systems whose matrix has non-linear frequency dependency.First, we adapted the DPA for reducing systems that have an infinite number of poles.Deflation is an important ingredient for this type of methods in order to prevent eigenvalues to be computed more than once.Because of the nonlinearity frequency dependency, classical deflation approaches arenot applicable. Therefore we propose an alternative technique that essentiallyremoves computed poles from the system's input and output vectors. This method appears to be reliablefor computing a large number of dominant poles of the system.Next, we apply the DPA to parametric second orderdynamical system, whose system matrix depends on parameters.We will iteratively compute the parametric dominant poles. We consider twoapproaches. In the first approach, we compute the parameter dependent polesone by one, i.e., all parameters are taken into account together. We will useinterpolation in the parameter space to achieve this. In the second approach,the dominant eigenpairs are computed for a selection of interpolation pointsin the parameter space, independently from each other. As the eigenvectorsare continuous functions of the parameters, we use the already computedeigenvectors from previous parameter values for computing starting values ofthe DPA.