Magdeburg Lectures on Optimization and Control: Damping optimization in mechanical systems using sampling-free model reduction
MALOC Event Series
- Date: Sep 25, 2020
- Time: 03:00 PM - 04:00 PM (Local Time Germany)
- Speaker: Zoran Tomljanović
- Location: Virtual
- Host: Jointly organized by: Faculty of Electrical Engineering and Information Technology, Faculty of Mathematics, Max Planck Institute Magdeburg and Center for Dynamic Systems: Biosystems Engineering
We consider vibration analysis and vibration reduction for mechanical
systems. Vibration reduction is very important in the study of
mechanical systems and it is usually achieved by damping optimization.
In damping optimization, the principal goal is to determine an optimal
external damping matrix which will ensure optimal evanescence of
system's solution (i.e. evanescence of deviation from its
equilibrium). One can consider different optimality measures for that
purpose, which depend on particular applications. Thus, in the first
part of the talk we present problem formulation and give an overview of a
different optimality measures. In the second part of the talk we are
focused on sampling-free model reduction of systems, which can be
applied for efficient damping optimization. Furthermore, t
his can be also applied for model reduction of linear dynamical systems
having an affine parameter dependence that allow low-rank variation in
the state matrix. We propose an approach that requires neither parameter
sampling nor parameter space exploration. Instead, we represent the
system response function as a composition of four subsystem response
functions that are nonparametric with a purely parameter-dependent
function. The parametric structure of our reduced system representation
lends itself very well to the development of optimization strategies
making use of efficient cost function surrogates. We discuss this in
detail for damping optimization of vibrating structures. We illustrate
our approach on a class of numerical examples.