دانلود رایگان مقاله لاتین اتوماتیک سیستم جبری دیفرانسیل از سایت الزویر
عنوان فارسی مقاله:
کاهش مدل اتوماتیک سیستم های جبری دیفرانسیل با تجزیه متعامد
عنوان انگلیسی مقاله:
Automatic model reduction of differential algebraic systems by proper orthogonal decomposition
سال انتشار : 2016
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مقدمه انگلیسی مقاله:
1. Introduction
Many modern mathematical models of real-life processes impose difficulties when it comes to their numerical solution. This holds especially for models represented by nonlinear distributed parameter systems, which are frequent in engineering. Usually, for the numerical solution of distributed parameter systems the original system of infinite order is approximated by one with a finite system order by a semi-discretization, which results in a system of differential algebraic equations. The resulting number of degrees of freedom is usually very high and makes the use of the discretized model inconvenient for model-based process design, process control and optimization (Shi et al., 2006). Thus there is a need for reduced models. Through model reduction, a small system with reduced number of equations is derived. The numerical solution of reduced models should be much easier and faster than the solution of the original problem. On the other hand, the reduced model should be able to reproduce the system behavior with sufficient accuracy in the relevant window of operation conditions and in the relevant range of system parameters. Various methods for nonlinear and linear model reduction have been proposed, particularly in the areas of electrical and mechanical engineering, control design and computational fluid dynamics. Some of them are based on physical simplifications like assumption of perfect mixing, introduction of compartments, equilibrium assumptions, etc. This approach requires physical insight of the modeler and hence is hard to automatize. Another successful approach, which may also be considered as a physical model reduction method, is based on nonlinear wave propagation theory (Marquardt, 1990; Kienle, 2000). It produces reduced model by approximation ofthe spatially distributed solution by profile with a given shape. As in the previous case, this method requires physical process understanding from the user and can be applied only for special systems. The generalized method of moments (Marchisio and Fox, 2005; Lebaz et al., 2016) is a widely used mathematical reduction technique for population balance equations. In this case, the reduced model does not preserve full information on spatial profile. Another mathematical possibility to obtain reduced models is to separate fast and slow subsystems. Slow manifold approximation (Christofides and Daoutidis, 1997) requires complicated symbolic operations, which impose difficulties on the automatization of this method. To sum up, widely used methods for nonlinear model reduction require experienced user; automatic application and integration in a simulation tool is a difficult and challenging task, which has hardly been attempted to our knowledge. On the other hand, there are linear model reduction techniques like balanced truncation (Benner et al., 2000; Heinkenschloss et al., 2011), which are applicable to high order systems and can be automatized quite easily. However, the resulting linear reduced models are onlyvalid locally and not able to capture nonlinear properties of the original system. In this work proper orthogonal decomposition (POD) (Kunisch and Volkwein, 2002; Park and Cho, 1996; Sirovich, 1987; Antoulas, 2005) is used for the development of an automatic procedure for model reduction. This method has been successfully applied for numerous problems in the fields of fluid dynamics, optimal control, and for population balance systems like crystallizers (Krasnyk and Mangold, 2010; Mangold et al., 2015), and granulators (Mangold, 2012). To put it in other words, the model reduction by POD is a proven approach. Nevertheless, applying model reduction by POD manually to complex engineering models is a challenging and tedious task. The idea of this work is to provide a software environment that performs the model reduction by POD automatically with minimal additional input from the user. The work is structured as follows. Section 2 discusses the model reduction method. Technical details of the developed software tool for automatic model reduction are described in Section 3. Section 4 shows the developed software tool in action by applying it to two test models: a nonlinear heat conductor and a continuous fluidized bed crystallizer.
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کلمات کلیدی:
Proper Orthogonal Decomposition for Model ... - ScienceDirect www.sciencedirect.com/science/article/pii/S1474667016443302 by RC Romijn - 2011 - Cited by 3 - Related articles Apr 25, 2016 - This paper presents a generalization of the model reduction method proper orthogonal decomposition to systems of differential-algebraic ... [PDF]Proper Orthogonal Decomposition: Theory and Reduced-Order ... www.math.uni-konstanz.de/numerik/personen/volkwein/teaching/POD-Book.pdf Proper Orthogonal Decomposition: ... POD and Singular Value Decomposition (SVD). 5 ... Reduced-Order Models for Finite-Dimensional Dynamical Systems 49. Proper Orthogonal Decomposition for Model ... - ResearchGate https://www.researchgate.net/.../229016166_Proper_Orthogonal_Decomposition_for_M... This paper presents a generalization of the model reduction method proper orthogonal decomposition to systems of differential-algebraic equations of arbitrary ... Galerkin Proper Orthogonal Decomposition Methods for a General ... https://epubs.siam.org/doi/abs/10.1137/S0036142900382612 by K Kunisch - 2006 - Cited by 492 - Related articles (2017) Automatic model reduction of differential algebraic systems by proper orthogonal decomposition. Computers & Chemical Engineering 97, 104-113. [PDF]Reduced Order Optimal Control of the Convective FitzHugh-Nagumo ... https://arxiv.org/pdf/1703.00008 by B Karasözen - 2017 Feb 28, 2017 - Galerkin method; proper orthogonal decomposition; discrete empirical interpolation ... arXiv:1703.00008v1 [math.NA] 28 Feb 2017 ... the convective FHN equation consists of a semi-linear PDE with monotone cu- bic nonlinear ... A Randomized Proper Orthogonal Decomposition Technique https://arxiv.org › math by D Yu - 2013 - Cited by 9 - Related articles Dec 13, 2013 - Mathematics > Dynamical Systems ... We propose a randomized proper orthogonal decomposition ... Subjects: Dynamical Systems (math.DS). Proper Orthogonal Decomposition Surrogate Models for Nonlinear ... https://www.math.uni-hamburg.de/home/hinze/.../SFB609-Preprint-27-2004_rev.pdf by M Hinze - Cited by 204 - Related articles hinze@math.tu-dresden.de. 2 Institut für ... Proper orthogonal decomposition (POD) provides a method for deriving low order models of ... Error analysis for nonlinear dynamical systems in finite dimensions were car- ried out in [RP02]. [PDF]Proper Orthogonal Decomposition Model Order ... - TU Eindhoven www.win.tue.nl/analysis/reports/rana08-33.pdf by A Verhoeven - Cited by 7 - Related articles differential-algebraic equations of a diode chain by Proper Orthogonal Decompo- ... Here we consider Proper Orthogonal Decomposition (POD) to reduce. [PDF]Automatic model reduction of differential algebraic systems by proper ... iranarze.ir/wp-content/uploads/2016/12/E3042.pdf Proper orthogonal decomposition (POD) is an attractive way to obtain nonlinear ... for the reduction of differential algebraic systems is presented, which is ...
