Model Order Reduction of Parameterized Nonlinear Systems by Interpolating Input-Output Behavior (original) (raw)
Related papers
Model Order Reduction of Nonlinear Systems in Circuit Simulation: Status and Applications
Lecture Notes in Electrical Engineering, 2011
In this document we review the status of existing techniques for nonlinear model order reduction by investigating how well these techniques perform for typical industrial needs. In particular the TPWL-method (Trajectory Piecewise Linear-method) and the POD-approach (Proper Orthogonal Decomposion) is taken under consideration. We address several questions that are (closely) related to both the theory and application of nonlinear model order reduction techniques. The goal of this document is to provide an overview of available methods together with a classification of nonlinear problems that in principle could be handled by these methods.
Model order reduction of parameterized circuit equations based on interpolation
Advances in Computational Mathematics, 2015
In this paper, the state-of-the-art interpolation-based model order reduction methods are applied to parameterized circuit equations. We analyze these methods in great details, through which the advantages and disadvantages of each method are illuminated. The presented model reduction methods are then tested on some circuit models.
Advances in Intelligent Systems and Computing, 2014
New technologies and multi-physical description of subsystems have forced designers to consider nonlinear effects for more accurate modelling leading to increased complexity of mathematical models . Such complex models are non-trival to analyse and to develop control algorithms. Consequently, increasing complexity of circuit designs causes the need for model order reduction (MOR) techniques that are capable of reducing nonlinear models and decreasing computational cost of simulating nonlinear systems. MOR techniques for linear time invariant (LTI) systems are well established [2]. On the other hand MOR for nonlinear systems is an open problem [1]. There are several ways of obtaining reduced order model (ROM) for nonlinear systems via model-based approach such as linear approximation(LA) [3], bilinearisation, proper orthogonal decomposition (POD), quadratic approximation (QA) and trajectory piecewise linear (TPWL) approximation, etc.
Truly Nonlinear Model-Order Reduction Techniques
7th. Int. Conf. on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems
Model-order reduction (MOR) aims at automatic creation of compact and sufficiently accurate approximations of large-scale simulation models for efficient system design and optimization. While MOR is reaching the maturity in the area of linear system, nonlinear MOR applications are still quite sparse. Most of the existing nonlinear MOR approaches employ polynomial approximation of the nonlinear model operator that limits the applicability of the resulting reduced models. The objective of this paper is to introduce a class of truly nonlinear MOR techniques that do not alter the original nonlinear model formulation in the process of MOR subspace projection. The existing and new techniques for the accurate subspace creation and efficient nonlinear projection are discussed separately.
Model order reduction for multi-terminals systems : with applications to circuit simulation
2011
Ever since its beginnings in the 1950’s, the integrated circuit (IC) has profoundly changed our lives. The way we work, travel, communicate, or address medical problems today has been facilitated by advances in microelectronics, which permit more functionality to be built on the same silicon area, at decreasing cost. As the feature size of devices on a chip shrink and circuits operate at increasing frequencies, the electromagnetic coupling effects between different IC components can no longer be ignored. To understand their impact on chip performance, these so called parasitic effects must be simulated. Parasitic networks are often so large, that state of the art simulation tools are insufficient to handle them: the simulations are either too lengthy, or cannot be carried out at all. The mathematical reason behind this is that the underlying systems are too large to be solved with the numerical algorithms implemented in simulation software. Model order reduction (MOR) provides one a...
Parameterized model order reduction of nonlinear dynamical systems
2005
In this paper we present a parameterized reduction technique for non-linear systems. Our approach combines an existing non-parameterized trajectory piecewise linear method for non-linear systems, with an existing moment matching parameterized technique for linear systems. Results and comparisons are presented for two examples: an analog non-linear circuit, and a MEM switch.
Model Order Reduction for Nonlinear Differential Algebraic Equations in Circuit Simulation
Progress in Industrial Mathematics at ECMI 2006, 2008
DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Model Order Reduction for Nonlinear IC Models
IFIP Advances in Information and Communication Technology, 2009
In this paper we demonstrate model order reduction for a nonlinear academic model of a diode chain. Two reduction methods, which are suitable for nonlinear differential algebraic equation systems are used, the Trajectory PieceWise Linear approach and the Proper Orthogonal Decomposition with Missing Point Estimation.