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Model order reduction
About: Model order reduction is a research topic. Over the lifetime, 3938 publications have been published within this topic receiving 44916 citations.
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TL;DR: QLMOR demonstrates that Volterra-kernel based nonlinear MOR techniques can in fact have far broader applicability than previously suspected, possibly being competitive with trajectory-based methods (e.g., trajectory piece-wise linear reduced order modeling) and nonlinear-projection based methods ( e.g, maniMOR).
Abstract: We present a projection-based nonlinear model order reduction method, named model order reduction via quadratic-linear systems (QLMOR). QLMOR employs two novel ideas: 1) we show that nonlinear ordinary differential equations, and more generally differential-algebraic equations (DAEs) with many commonly encountered nonlinear kernels can be rewritten equivalently in a special representation, quadratic-linear differential algebraic equations (QLDAEs), and 2) we perform a Volterra analysis to derive the Volterra kernels, and we adapt the moment-matching reduction technique of nonlinear model order reduction method (NORM) [1] to reduce these QLDAEs into QLDAEs of much smaller size. Because of the generality of the QLDAE representation, QLMOR has significantly broader applicability than Taylor-expansion-based methods [1]-[3] since there is no approximation involved in the transformation from original DAEs to QLDAEs. Because the reduced model has only quadratic nonlinearities, its computational complexity is less than that of similar prior methods. In addition, QLMOR, unlike NORM, totally avoids explicit moment calculations, hence it has improved numerical stability properties as well. We compare QLMOR against prior methods [1]-[3] on a circuit and a biochemical reaction-like system, and demonstrate that QLMOR-reduced models retain accuracy over a significantly wider range of excitation than Taylor-expansion-based methods [1]-[3]. QLMOR, therefore, demonstrates that Volterra-kernel based nonlinear MOR techniques can in fact have far broader applicability than previously suspected, possibly being competitive with trajectory-based methods (e.g., trajectory piece-wise linear reduced order modeling [4]) and nonlinear-projection based methods (e.g., maniMOR [5]).
173 citations
TL;DR: The aim of these techniques is to circumvent several drawbacks of spectral stochastic approaches and to allow their use for large scale applications, and particularly focus on model reduction techniques based on spectral decomposition techniques and their generalizations.
Abstract: Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the last two decades, a growing interest has been devoted to a new family of methods, called spectral stochastic methods, for the propagation of uncertainties through physical models governed by stochastic partial differential equations. These approaches rely on a fruitful marriage of probability theory and approximation theory in functional analysis. This paper provides a review of some recent developments in computational stochastic methods, with a particular emphasis on spectral stochastic approaches. After a review of different choices for the functional representation of random variables, we provide an overview of various numerical methods for the computation of these functional representations: projection, collocation, Galerkin approaches…. A detailed presentation of Galerkin-type spectral stochastic approaches and related computational issues is provided. Recent developments on model reduction techniques in the context of spectral stochastic methods are also discussed. The aim of these techniques is to circumvent several drawbacks of spectral stochastic approaches (computing time, memory requirements, intrusive character) and to allow their use for large scale applications. We particularly focus on model reduction techniques based on spectral decomposition techniques and their generalizations.
171 citations
TL;DR: In this paper, effective and systematic steps in the mathematical simplification and reduction of physics-based lithium-ion (Li-ion) battery models to improve computational efficiency are presented.
171 citations
TL;DR: In this article, the authors developed a reduced-order small-signal model of a microgrid system capable of operating in both the grid-tied and the islanded conditions.
Abstract: The objective of this study was to develop a reduced-order small-signal model of a microgrid system capable of operating in both the grid-tied and the islanded conditions. The nonlinear equations of the proposed system were derived in the $dq$ reference frame and then linearized around stable operating points to construct a small-signal model. The high-order state matrix was then reduced using the singular perturbation technique. The dynamic equations were divided into two groups based on the small-signal model parameters $\varepsilon$ . The slow states, which dominated the systems dynamics, were preserved, whereas the fast states were eliminated. Step responses of the model were compared to the experimental results from a hardware test to assess their accuracy and similarity to the full-order system. The proposed reduced-order model was applied to a modified IEEE-37 bus grid-tied microgrid system to evaluate systems dynamic response in grid-tied mode, islanded mode, and transition from grid-tied to islanded mode.
166 citations
TL;DR: The problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known ${\cal H}_2$-norm for linear systems is discussed.
Abstract: In this paper, we will discuss the problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known ${\cal H}_2$-norm for linear systems. We...
162 citations