178 research outputs found
Non-intrusive Balancing Transformation of Highly Stiff Systems with Lightly-damped Impulse Response
Balanced truncation (BT) is a model reduction method that utilizes a
coordinate transformation to retain eigen-directions that are highly observable
and reachable. To address realizability and scalability of BT applied to highly
stiff and lightly-damped systems, a non-intrusive data-driven method is
developed for balancing discrete-time systems via the eigensystem realization
algorithm (ERA). The advantage of ERA for balancing transformation makes
full-state outputs tractable. Further, ERA enables balancing despite stiffness,
by eliminating computation of balancing modes and adjoint simulations. As a
demonstrative example, we create balanced ROMs for a one-dimensional reactive
flow with pressure forcing, where the stiffness introduced by the chemical
source term is extreme (condition number ), preventing analytical
implementation of BT. We investigate the performance of ROMs in prediction of
dynamics with unseen forcing inputs and demonstrate stability and accuracy of
balanced ROMs in truly predictive scenarios whereas without ERA, POD-Galerkin
and Least-squares Petrov-Galerkin projections fail to represent the true
dynamics. We show that after the initial transients under unit impulse forcing,
the system undergoes lightly-damped oscillations, which magnifies the influence
of sampling properties on predictive performance of the balanced ROMs. We
propose an output domain decomposition approach and couple it with tangential
interpolation to resolve sharp gradients at reduced computational costs
A note on the cross Gramian for non-symmetric systems
The cross Gramian matrix is a tool for model reduction and system identification, but it is only applicable to square control systems. For symmetric systems, the cross Gramian possesses a useful relation to the system's associated Hankel singular values. Yet, many real-life models are neither square nor symmetric. In this work, concepts from decentralized control are used to approximate a cross Gramian for non-symmetric and non-square systems. To illustrate this new non-symmetric cross Gramian, it is applied in the context of model order reduction
Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians
In this paper we propose a new Koopman operator approach to the decomposition
of nonlinear dynamical systems using Koopman Gramians. We introduce the notion
of an input-Koopman operator, and show how input-Koopman operators can be used
to cast a nonlinear system into the classical state-space form, and identify
conditions under which input and state observable functions are well separated.
We then extend an existing method of dynamic mode decomposition for learning
Koopman operators from data known as deep dynamic mode decomposition to systems
with controls or disturbances. We illustrate the accuracy of the method in
learning an input-state separable Koopman operator for an example system, even
when the underlying system exhibits mixed state-input terms. We next introduce
a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes
internal subsystem observability and disturbance rejection from unwanted noise
from other subsystems. We derive a relaxation based on Koopman Gramians and
multi-way partitioning for the resulting NP-hard decomposition problem. We
lastly illustrate the proposed algorithm with the swing dynamics for an IEEE
39-bus system.Comment: 8 pages, submitted to IEEE 2018 AC
Model Reduction of Linear PDE Systems: A Continuous Time Eigensystem Realization Algorithm
The Eigensystem Realization Algorithm (ERA) is a well known system identification and model reduction algorithm for discrete time systems. Recently, Ma, Ahuja, and Rowley (Theoret. Comput. Fluid Dyn. 25(1) : 233-247, 2011) showed that ERA is theoretically equivalent to the balanced POD algorithm for model reduction of discrete time systems. We propose an ERA for model reduction of continuous time linear partial differential equation systems. The algorithm differs from other existing approaches as it is based on a direct approximation of the Hankel integral operator of the system. We show that the algorithm produces accurate balanced reduced order models for an example PDE system
Reduced realizations and model reduction for switched linear systems:a time-varying approach
In the last decades, switched systems gained much interest as a modeling framework in many applications. Due to a large number of subsystems and their high-dimensional dynamics, such systems result in high complexity and challenges. This motivates to find suitable reduction methods that produce simplified models which can be used in simulation and optimization instead of the original (large) system. In general, the study aims to find a reduced model for a given switched system with a fixed switching signal and known mode sequence. This thesis concerns first the reduced realization of switched systems with known mode sequence which has the same input-output behavior as original switched systems. It is conjectured that the proposed reduced system has the smallest order for almost all switching time duration. Secondly, a model reduction method is proposed for switched systems with known switching signals which provide a good model with suitable thresholds for the given switched system. The quantitative information for each mode is carried out by defining suitable Gramians and, these Gramians are exploited at the midpoint of the given switching time duration. Finally, balanced truncation leads to a modewise reduction. Later, a model reduction method for switched differential-algebraic equations in continuous time is proposed. Thereto, a switched linear system with jumps and impulses is constructed which has the identical input-output behavior as original systems. Finally, a model reduction approach for singular linear switched systems in discrete time is studied. The choice of initial/final values of the reachability and observability Gramians are also investigated
A simple algorithm for stable order reduction of z-domain Laguerre models
International audienceDiscrete-time Laguerre series are a well known and efficient tool in system identification and modeling. This paper presents a simple solution for stable and accurate order reduction of systems described by a Laguerre model
Digital Filters and Signal Processing
Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide
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