No abstract

No abstract

In this article, an algorithm guaranteeing asymptotic stability for parametric model order reduction by matrix interpolation is proposed for the general class of high-dimensional linear time-invariant systems. In the first step, the system matrices of the high-dimensional parameter-dependent system are computed for a set of parameter vectors. The local highorder systems are reduced by a projection-based reduction method and stabilized, if necessary. Secondly, the low-order systems are transformed into a consistent set of generalized coordinates. Thirdly, a new procedure using semidefinite programming is applied to the low-order systems, converting them into strictly dissipative form. Finally, an asymptotically stable reduced order model can be calculated for any new parameter vector of interest by interpolating the system matrices of the local loworder models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications. The method is illustrated by two numerical examples. ARTICLE HISTORY

A method to preserve stability in parametric model order reduction by matrix interpolation for the whole parameter range is proposed for high-order linear timeinvariant systems. In the first step, system matrices of the highdimensional parameter-dependent system are computed for a discrete set of parameter vectors. The local high-order systems are reduced by a projection-based reduction method. Secondly, the reduced models are made contractive by solving lowdimensional Lyapunov equations. Thirdly, they are transformed into a consistent set of generalized coordinates for accurate interpolation results. These three steps are done offline and the matrices of the local systems are stored. Finally, a stable reduced order model for a new parameter vector can be calculated online by interpolating the precomputed matrices of the local low-dimensional models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications.

No abstract

Dynamic systems with time-varying parameters arise in numerous industrial applications, e.g. in structural dynamics or systems with moving loads. A spatial discretization of such systems often leads to high-dimensional linear parameter-varying models, which need to be reduced in order to enable a fast simulation. In the following we present time-varying parametric model order reduction (p(t)MOR) based on matrix interpolation and apply this novel framework to a system with moving load. Model Reduction:• p(t)MOR by Matrix Interpolation applied• Order of locally reduced systems:Further study:• Interpretation of the new matrix Projective pMOR: Choose appropriate projection matrices to approximate the state-vector by . Application for Systems with Moving Loads Projective p(t)MOR:Analogously, we aim to approximate the state-vector by Systems with Moving Loads:• position of the acting load varies with time

This thesis deals with model order reduction of parameter-dependent systems based on interpolation of locally reduced system matrices. A Black-Box method is proposed that automatically determines the optimal design parameters and delivers a reduced system with desired accuracy. In addition, the method is extended to stability preservation and interpolation for high-dimensional parameter spaces.

A black-box method for parametric model order reduction is presented that includes method selection, model refinement and error prediction using a cross-validation-based error indicator. The method is demonstrated for the interpolation of reduced system matrices.