Truncated balanced realization of a stable non-minimal state-space system

Model order reduction of a dynamical linear time-invariant system appears in many applications from science and engineering. Numerically reliable SVD-based methods for this task require in general O(n 3 ) floating-point arithmetic operations, with n being in the range 10 3 − 10 5 for many practical applications. In this paper we investigate the use of graphics processors (GPUs) to accelerate model reduction of large-scale linear systems by off-loading the computationally intensive tasks to this device. Experiments on a hybrid platform consisting of state-of-the-art general-purpose multi-core processors and a GPU illustrate the potential of this approach.

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“…BT model reduction [13,14,15,16] belongs to the family of absolute error methods, which aim at minimizing…”

Section: Svd-based Methods For Model Reductionmentioning

confidence: 99%

Accelerating Model Reduction of Large Linear Systems with Graphics Processors

Benner

Ezzatti

Kreßner

et al. 2012

Applied Parallel and Scientific Computing

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“…For the brevity of this paper, we do not review the balanced truncation method here, but refer the reader who is not familiar with this method to [2,29]. Based on the derived results, we develop a so-called parametric balanced truncation method as follows.…”

Section: Energy Norm Based Error Estimatesmentioning

confidence: 99%

Solving Parameter-Dependent Lyapunov Equations Using the Reduced Basis Method with Application to Parametric Model Order Reduction

Sơn¹,

Stykel²

2017

SIAM J. Matrix Anal. & Appl.

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Abstract. Our aim is to numerically solve parameter-dependent Lyapunov equations using reduced basis method. Such equations arise in parametric model order reduction. We restrict ourselves to systems that affinely depend on the parameter as our main ingredient is the min-Θ approach. In those cases, we derive various a posteriori error estimates. Based on these estimates, Greedy algorithms for constructing reduced basis are formulated. Thanks to the derived results, a novel so-called parametric balanced truncation model reduction method is developed. Numerical examples are presented.

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“…As A is assumed to be stable and thus P and Q are positive semi-definite, there exist Cholesky factorizations P = S T S and Q = R T R. In the so-called squareroot balanced truncation (SRBT) algorithms [24,25] these are used to define the truncation matrices…”

Section: Large Scale Sparse Standard State Space Systemsmentioning

confidence: 99%

Efficient balancing-based MOR for large-scale second-order systems

Benner

Saak

2011

Mathematical and Computer Modelling of Dynamical Systems

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Large-scale structure dynamics models arise in all areas where vibrational analysis is performed, ranging from control of machine tools to microsystems simulation. These models result from a finite element analysis being applied to their mechanical structure. Therefore they are in general sparse, but very large, since many details have to be resolved. This accounts for unacceptable computational and resource demands in simulation and especially control of these models. To reduce these demands and to be able to compute solutions and controls in acceptable, i.e. applicable, time frames model order reduction is applied. Classically modal truncation is used for this task. The reduced order models (ROMs) generated are normally relatively large and often need manual modification by addition of certain technically motivated modes. That means they are at least partially heuristic and cannot be generated fully automatic. Engineers are therefore searching for alternate reduction methods.Here we will concentrate on the application of balancing based model order reduction techniques. A central topic is to provide a reduced order model for the construction and parameterization of a practicable controller for the application. Our main focus will be on presenting a way to efficiently compute the ROM exploiting the sparsity and second order structure of the FEM semi-discretization, rather than presenting a new reduction technique.

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Truncated balanced realization of a stable non-minimal state-space system

Cited by 188 publications

References 9 publications

Accelerating Model Reduction of Large Linear Systems with Graphics Processors

Accelerating Model Reduction of Large Linear Systems with Graphics Processors

Solving Parameter-Dependent Lyapunov Equations Using the Reduced Basis Method with Application to Parametric Model Order Reduction

Efficient balancing-based MOR for large-scale second-order systems

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