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Burgers' equation is a nonlinear scalar partial differential equation, commonly used as a testbed for model order reduction techniques and error estimates. Model order reduction of the parameterized Burgers' equation is commonly done by using the reduced basis method. In this method, an error estimate plays a crucial rule in both accelerating the offline phase and quantifying the error induced after reduction in the online phase. In this study, we introduce two new estimates for this reduction error. The first error estimate is based on a Lur'e-type model formulation of the system obtained after the full-discretization of Burgers' equation. The second error estimate is built upon snapshots generated in the offline phase of the reduced basis method. The second error estimate is applicable to a wider range of systems compared to the first error estimate. Results reveal that when conditions for the error estimates are satisfied, the error estimates are accurate and work efficiently in terms of computational effort.

Burgers' equation is a nonlinear scalar partial differential equation, commonly used as a testbed for model order reduction techniques and error estimates. Model order reduction of the parameterized Burgers' equation is commonly done by using the reduced basis method. In this method, an error estimate plays a crucial rule in both accelerating the offline phase and quantifying the error induced after reduction in the online phase. In this study, we introduce two new estimates for this reduction error. The first error estimate is based on a Lur'e-type model formulation of the system obtained after the full-discretization of Burgers' equation. The second error estimate is built upon snapshots generated in the offline phase of the reduced basis method. The second error estimate is applicable to a wider range of systems compared to the first error estimate. Results reveal that when conditions for the error estimates are satisfied, the error estimates are accurate and work efficiently in terms of computational effort.

Automated Managed Pressure Drilling (MPD) is a method for fast and accurate pressure control in drilling operations. The achievable performance of automated MPD is limited, firstly, by the control system and, secondly, by the hydraulics model based on which this control system is designed. Hence, an accurate hydraulics model is needed that, at the same time, is simple enough to allow for the use of high performance controller design methods. This paper presents an approach for nonlinear Model Order Reduction (MOR) for MPD systems. For a single-phase flow MPD system, a nonlinear model is derived that can be decomposed into a feedback interconnection of a high-order linear subsystem and low-order nonlinear subsystem. This structure, under certain conditions, allows for a nonlinear MOR procedure that preserves key system properties such as stability and provides a computable error bound. The effectiveness of this MOR method for MPD systems is illustrated through simulations., Team DeSchutter

Automated Managed Pressure Drilling (MPD) is a method for fast and accurate pressure control in drilling operations. The achievable performance of automated MPD is limited, firstly, by the control system and, secondly, by the hydraulics model based on which this control system is designed. Hence, an accurate hydraulics model is needed that, at the same time, is simple enough to allow for the use of high performance controller design methods. This paper presents an approach for nonlinear Model Order Reduction (MOR) for MPD systems. For a single-phase flow MPD system, a nonlinear model is derived that can be decomposed into a feedback interconnection of a high-order linear subsystem and low-order nonlinear subsystem. This structure, under certain conditions, allows for a nonlinear MOR procedure that preserves key system properties such as stability and provides a computable error bound. The effectiveness of this MOR method for MPD systems is illustrated through simulations., Team Bart De Schutter

Purpose - Model order reduction (MOR) has been widely used in the electric networks but little has been done to reduce higher index differential algebraic equations (DAEs). The paper aims to discuss these issues. Design/methodology/approach - Most methods first do an index reduction before reducing a higher DAE but this can lead to a loss of physical properties of the system. Findings - The paper presents a MOR method for DAEs called the index-aware MOR (IMOR) which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks. Originality/value - MOR has been widely used to reduce large systems from electric networks but little has been done to reduce higher index DAEs. Most methods first do an index reduction before reducing a large system of DAEs but this can lead to a loss of physical properties of the system. The paper presents a MOR method for DAEs called the IMOR which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

We introduce a model order reduction (MOR) procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. The decoupling procedure in differential and algebraic part is based on the projector and matrix chain which leads to the definition of tractability index. The differential part can be reduced by using any MOR method, we use Krylov-based projection methods to illustrate our approach. The reduction on the differential part induces a reduction on the algebraic part. In this paper, we present the method for index-1 differential-algebraic equations. We implement numerically this procedure and show numerical evidence of its validity.

Purpose - Model order reduction (MOR) has been widely used in the electric networks but little has been done to reduce higher index differential algebraic equations (DAEs). The paper aims to discuss these issues. Design/methodology/approach - Most methods first do an index reduction before reducing a higher DAE but this can lead to a loss of physical properties of the system. Findings - The paper presents a MOR method for DAEs called the index-aware MOR (IMOR) which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks. Originality/value - MOR has been widely used to reduce large systems from electric networks but little has been done to reduce higher index DAEs. Most methods first do an index reduction before reducing a large system of DAEs but this can lead to a loss of physical properties of the system. The paper presents a MOR method for DAEs called the IMOR which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

We introduce a model order reduction (MOR) procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. The decoupling procedure in differential and algebraic part is based on the projector and matrix chain which leads to the definition of tractability index. The differential part can be reduced by using any MOR method, we use Krylov-based projection methods to illustrate our approach. The reduction on the differential part induces a reduction on the algebraic part. In this paper, we present the method for index-1 differential-algebraic equations. We implement numerically this procedure and show numerical evidence of its validity.

In this paper, popular model reduction techniques from the fields of structural dynamics, numerical mathematics and systems and control are reviewed and compared. The motivation for such a comparison stems from the fact that the model reduction techniques in these fields have been developed fairly independently. In addition, the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique, on the basis of the desired objectives and properties of the model reduction problem. In particular, a detailed review is given on mode displacement techniques, moment matching methods and balanced truncation, whereas important extensions are outlined briefly. In addition, a qualitative comparison of these methods is presented, hereby focusing both on theoretical and computational aspects. Finally, the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example., QC 20130815

Contains fulltext : 75447.pdf (publisher's version ) (Open Access)

Contains fulltext : 75447.pdf (publisher's version ) (Open Access)