Adaptive sampling of nonlinear system trajectory for Model Order Reduction

Trajectory based methods approximate nonlinear dynamical systems by a weighted superposition of dimensionally reduced linear systems. The linear systems are obtained by multiple linearisations at points spread across a training trajectory. The points have to be judiciously selected, as the quality of approximation and complexity of the reduced order model is dependant on them. In this work, limitations of the previous schemes used for linearisation point selection are pointed out and areas of improvement are identified. A new strategy, based on the insights gained from a study of the previous ones is suggested. The new method is an innovative way to identify parts of the nonlinear system trajectory where more linearisation points are needed or redundant ones have been formed. It is based on a new error measure, indicative of how well a linear system represents the nonlinear system evolution in its neighbourhood. Additionally, it requires no new information about the nonlinear system and gives considerably improved results without increasing the computational burden.