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Model Reduction (model + reduction)
Terms modified by Model Reduction Selected AbstractsFASTER, EASIER FINITE ELEMENT MODEL REDUCTIONEXPERIMENTAL TECHNIQUES, Issue 5 2000T.A. Deiters First page of article [source] Model Reduction in Emulsion Polymerization Using Hybrid First Principles/Artificial Neural Networks Models, 2,MACROMOLECULAR THEORY AND SIMULATIONS, Issue 2 2005Gurutze Arzamendi Abstract Summary: A "series" hybrid model based on material balances and artificial neural networks to predict the evolution of weight average molecular weight, , in semicontinuous emulsion polymerization with long chain branching kinetics is presented. The core of the model is composed by two artificial neural networks (ANNs) that calculate polymerization rate, Rp, and instantaneous weight-average molecular weight, from reactor process variables. The subsequent integration of the material balances allowed to obtain the time evolution of conversion and , along the polymerization process. The accuracy of the proposed model under a wide range of conditions was assessed. The low computer-time load makes the hybrid model suitable for optimization strategies. Effect of the monomer feed rate on . [source] Computationally Efficient Algorithm For Frequency-Weighted Optimal H, Model ReductionASIAN JOURNAL OF CONTROL, Issue 3 2003Fen Wu ABSTRACT In this paper, a frequency-weighted optimal H, model reduction problem for linear time-invariant (LTI) systems is considered. The objective of this class of model reduction problems is to minimize H, norm of the frequency-weighted truncation error between a given LTI system and its lower order approximation. A necessary and sufficient solvability condition is derived in terms of LMIs with one extra coupling rank constraint, which generally leads to a non-convex feasibility problem. Moreover, it has been shown that the reduced-order model is stable when both stable input and output weights are included, and its state-space data are given explicitly by the solution of the feasibility problem. An efficient model reduction scheme based on cone complementarity algorithm (CCA) is proposed to solve the non-convex conditions involving rank constraint. [source] Stochastic Model Reduction by Maximizing IndependenceASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3-4 2005Hui Zhang By analysing information descriptions in state space models of linear stochastic systems, this paper proposes two model reduction methods via principles of maximizing independence and conditional independence among the reduced state vector, respectively. These methods are based on state aggregation. The independence and conditional independence are measured by the Kullback-Leibler information distance. It is demonstrated that the maximum conditional independence method is not only applicable to stable systems, but also applicable to unstable systems. Simulation results illustrate the efficiency of the present methods. [source] Reduction and identification methods for Markovian control systems, with application to thin film depositionINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2004Martha A. Gallivan Abstract Dynamic models of nanometer-scale phenomena often require an explicit consideration of interactions among a large number of atoms or molecules. The corresponding mathematical representation may thus be high dimensional, nonlinear, and stochastic, incompatible with tools in nonlinear control theory that are designed for low-dimensional deterministic equations. We consider here a general class of probabilistic systems that are linear in the state, but whose input enters as a function multiplying the state vector. Model reduction is accomplished by grouping probabilities that evolve together, and truncating states that are unlikely to be accessed. An error bound for this reduction is also derived. A system identification approach that exploits the inherent linearity is then developed, which generates all coefficients in either a full or reduced model. These concepts are then extended to extremely high-dimensional systems, in which kinetic Monte Carlo (KMC) simulations provide the input,output data. This work was motivated by our interest in thin film deposition. We demonstrate the approaches developed in the paper on a KMC simulation of surface evolution during film growth, and use the reduced model to compute optimal temperature profiles that minimize surface roughness. Copyright © 2004 John Wiley & Sons, Ltd. [source] Model reduction of interconnected linear systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2009H. Sandberg Abstract The problem of model reduction of linear systems with certain interconnection structure is considered in this paper. To preserve the interconnection structure between subsystems in the reduction, special care needs to be taken. This problem is important and timely because of the recent focus on complex networked systems in control engineering. Two different model reduction methods are introduced and compared in this paper. Both methods are extensions to the well-known balanced truncation method. Compared with earlier work in the area these methods use a more general linear fractional transformation framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that reduce to classical bounds in special cases are derived. The so-called structured Hankel singular values are used in the methods, and indicate how important states in the subsystems are with respect to a chosen input,output map for the entire interconnected system. It is shown how these structured Hankel singular values can be used to select an approximation order. Finally, the two methods are applied to a model of a mechanical device. Copyright © 2008 John Wiley & Sons, Ltd. [source] A remark on ,Model reduction for singular systems via covariance approximation'OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2006Dabo Xu Abstract This note comments on the results of the paper, ,Model reduction for singular systems via covariance approximation', (Optim. Contr. Appl. Meth. 2004; 25:263,278), which studied model reduction for singular system via covariance approximation. Although the proposed new error criterion reflects the capacity of the impulsive behaviour for singular systems, there exists shortcomings due to the fixed matrix Br in the process of optimization, which remarkably matters. In order to avoid this drawback, the model reduction problem is reformulated and a genetic algorithm is used to deal with the optimization problem. A numerical example is provided to show the effectiveness and improvement of the proposed algorithm. Copyright © 2006 John Wiley & Sons, Ltd. [source] MATLAB based GUIs for linear controller design via convex optimizationCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2003Wathanyoo Khaisongkram Abstract Owing to the current evolution of computational tools, a complicated parameter optimization problem could be effectively solved by a computer. In this paper, a CAD tool for multi-objective controller design based on MATLAB program is developed. In addition, we construct simple GUIs (using GUIDE tools within MATLAB) to provide a visual approach in specifying the constraints. The linear controller design problem can be cast as the convex optimization subjected to time domain and frequency domain constraints. This optimization problem is efficiently solved within a finite dimensional subspace by a practical ellipsoid algorithm. In the design process, we include a model reduction of the resulting controller to speed up the computational efficiency. Finally, a numerical example shows the capability of the program to design multi-objective controller for a one-link flexible robot arm. © 2003 Wiley Periodicals, Inc. Comput Appl Eng Educ 11: 13,24, 2003; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.10035 [source] Solving inverse electromagnetic problems using FDTD and gradient-based minimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2006Erik Abenius Abstract We address time-domain inverse electromagnetic scattering for determining unknown characteristics of an object from observations of the scattered field. Applications include non-destructive characterization of media and optimization of material properties, for example, the design of radar absorbing materials. Another application is model reduction where a detailed model of a complex geometry is reduced to a simplified model. The inverse problem is formulated as an optimal control problem where the cost function to be minimized is the difference between the estimated and observed fields, and the control parameters are the unknown object characteristics. The problem is solved in a deterministic gradient-based optimization algorithm using a parallel 2D FDTD scheme. Highly accurate analytical gradients are computed from the adjoint formulation. The inverse method is applied to the characterization of layered dispersive media and the determination of parameters in subcell models for thin sheets and narrow slots. Copyright © 2006 John Wiley & Sons, Ltd. [source] A subspace approach to balanced truncation for model reduction of nonlinear control systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2002Sanjay Lall Abstract In this paper, we introduce a new method of model reduction for nonlinear control systems. Our approach is to construct an approximately balanced realization. The method requires only standard matrix computations, and we show that when it is applied to linear systems it results in the usual balanced truncation. For nonlinear systems, the method makes use of data from either simulation or experiment to identify the dynamics relevant to the input,output map of the system. An important feature of this approach is that the resulting reduced-order model is nonlinear, and has inputs and outputs suitable for control. We perform an example reduction for a nonlinear mechanical system. Copyright © 2002 John Wiley & Sons, Ltd. [source] Feedback control of dissipative PDE systems using adaptive model reductionAICHE JOURNAL, Issue 4 2009Amit Varshney Abstract The problem of feedback control of spatially distributed processes described by highly dissipative partial differential equations (PDEs) is considered. Typically, this problem is addressed through model reduction, where finite dimensional approximations to the original infinite dimensional PDE system are derived and used for controller design. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain finite dimensional ordinary differential equation (ODE) models using the method of weighted residuals. A common approach to this task is the Karhunen-Loève expansion combined with the method of snapshots. To circumvent the issue of a priori availability of a sufficiently large ensemble of PDE solution data, the focus is on the recursive computation of eigenfunctions as additional data from the process becomes available. Initially, an ensemble of eigenfunctions is constructed based on a relatively small number of snapshots, and the covariance matrix is computed. The dominant eigenspace of this matrix is then utilized to compute the empirical eigenfunctions required for model reduction. This dominant eigenspace is recomputed with the addition of each snapshot with possible increase or decrease in its dimensionality; due to its small dimensionality the computational burden is relatively small. The proposed approach is applied to representative examples of dissipative PDEs, with both linear and nonlinear spatial differential operators, to demonstrate its effectiveness of the proposed methodology. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Model reduction of interconnected linear systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2009H. Sandberg Abstract The problem of model reduction of linear systems with certain interconnection structure is considered in this paper. To preserve the interconnection structure between subsystems in the reduction, special care needs to be taken. This problem is important and timely because of the recent focus on complex networked systems in control engineering. Two different model reduction methods are introduced and compared in this paper. Both methods are extensions to the well-known balanced truncation method. Compared with earlier work in the area these methods use a more general linear fractional transformation framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that reduce to classical bounds in special cases are derived. The so-called structured Hankel singular values are used in the methods, and indicate how important states in the subsystems are with respect to a chosen input,output map for the entire interconnected system. It is shown how these structured Hankel singular values can be used to select an approximation order. Finally, the two methods are applied to a model of a mechanical device. Copyright © 2008 John Wiley & Sons, Ltd. [source] A remark on ,Model reduction for singular systems via covariance approximation'OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2006Dabo Xu Abstract This note comments on the results of the paper, ,Model reduction for singular systems via covariance approximation', (Optim. Contr. Appl. Meth. 2004; 25:263,278), which studied model reduction for singular system via covariance approximation. Although the proposed new error criterion reflects the capacity of the impulsive behaviour for singular systems, there exists shortcomings due to the fixed matrix Br in the process of optimization, which remarkably matters. In order to avoid this drawback, the model reduction problem is reformulated and a genetic algorithm is used to deal with the optimization problem. A numerical example is provided to show the effectiveness and improvement of the proposed algorithm. Copyright © 2006 John Wiley & Sons, Ltd. [source] ,, model reduction for uncertain two-dimensional discrete systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2005Huijun Gao Abstract This paper investigates the problem of ,, model reduction for two-dimensional (2-D) discrete systems with parameter uncertainties residing in a polytope. For a given robustly stable system, our attention is focused on the construction of a reduced-order model, which also resides in a polytope and approximates the original system well in an ,, norm sense. Both Fornasini,Marchesini local state-space (FMLSS) and Roesser models are considered through parameter-dependent approaches, with sufficient conditions obtained for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved using standard numerical software. In addition, the development of zeroth order models is also presented. Two numerical examples are provided to show the effectiveness of the proposed theories. Copyright © 2005 John Wiley & Sons, Ltd. [source] Analysis of critical motions of floating structuresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Marc-André Pick Validation of numerical methods for describing the motion of a ship in sea conditions by adequate experiments is a major research field in ocean engineering. For the development of a method for the systematic determination of critical and safe operational conditions and for the classification of capsize scenarios bifurcation analyses are performed. The computational effort for these analyses is enormous using a full model describing the nonlinear dynamics of a floating body. Therefore, a method for model reduction is currently being developed at the Institute of Mechanics and Ocean Engineering at TUHH. Bases for the validation of this new method are experiments conducted in the institute's wave tank. The determination of position and attitude of the body is performed with an integrated measurement system: An inertial measurement unit and a video system are combined using an extended Kalman Filter. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On ,, model reduction for discrete-time linear time-invariant systems using linear matrix inequalities,ASIAN JOURNAL OF CONTROL, Issue 3 2008Yoshio Ebihara Abstract In this paper, we address the ,, model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the ,, optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting. [source] | |||||||||||||