Application of dynamic condensation for model order reduction in real-time hybrid simulations

Abstract

This paper presents an algorithm for model order reduction in real-time hybrid simulations. The bottleneck of hybrid simulations are usually the finite element computations that must be performed in real time. The common approach to deal with this inconvenience is to involve powerful computing hardware. In the following paper opposite approach is presented—a new algorithm is proposed for reducing the model order. This allows to perform hybrid simulations more efficiently while maintaining high accuracy. The algorithm is based on dynamic condensation where the degrees of freedom are divided into masters and slaves, and system matrices are transformed in a way that only masters are kept. The transformation process is complex however, it is performed offline, therefore a relatively high computational effort is made a priori to make real-time calculations more efficient. The dynamic condensation algorithm was adapted to the requirements of hybrid simulations. The proper selection of masters is crucial for accuracy therefore, a novel approach based on evolutionary optimization is implemented. Numerical and experimental examples are provided. The examples prove that by implementing the proposed algorithms the following effects are achieved: (a) the time step of hybrid simulation can be significantly decreased when using implicit integration (increasing the accuracy of the measured dynamic behavior), (b) explicit integration can be sometimes implemented where it was previously not possible in real time, (c) smaller hardware resources can be involved (all computations in real-time hybrid simulations during the experiments were performed on a small microcontroller).