Abstract
In recent years, a great effort has been taken focused on the development of reduced order modeling techniques of dynamical systems. This necessity is pushed by the requirement for efficient numerical techniques for simulations of dynamical systems arising from structural dynamics, controller design, circuit simulation, fluid dynamics and micro electromechanical systems.We introduce a method to calculate the minimum upper $\mathcal{L}_2$ error bound of a linear time invaritant reduced order model considering any possible unitary initial conditions (IC). As a consequence, the proposed method calculates the unitary IC vector which leads to the maximum $\mathcal{L}_2$ norm of the error. Based on this error bound, it is discussed the capacity of a reduced order system to approximate the free transient response in the worst case scenario.
Highlights
Even with the advances in computer technology, which considerably increased computational processing capacity and storage in the last decades, the demand for increasing the complexity of dynamical systems is still a major concern
A great effort is being taken towards the development of methods to calculate reduced order models (ROM) that reproduce the main dynamic characteristics of a high order model (HOM) with a reduced demand on computational processing capacity, memory and computing time [1, 2, 3, 6, 7, 11, 21]
The a priori knowledge of error bounds allows the comparison of different Model Order Reduction (MOR) methods and for consequence the selection of the most suitable method to each application based on a prescribed threshold for the ROM error
Summary
Even with the advances in computer technology, which considerably increased computational processing capacity and storage in the last decades, the demand for increasing the complexity of dynamical systems is still a major concern To handle this problem, a great effort is being taken towards the development of methods to calculate reduced order models (ROM) that reproduce the main dynamic characteristics of a high order model (HOM) with a reduced demand on computational processing capacity, memory and computing time [1, 2, 3, 6, 7, 11, 21]. The determination of error bounds associated with reduced models plays an important role in the development of such Model Order Reduction (MOR) methods. It allows to predict the maximum (or minimum) error associated to the lower order approximation without the need of performing excessively time-demanding simulations. In the literature one can find proposals of different H∞-norm error bounds for different modal MOR methods [6, 25, 14]
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