Sensitivity analysis and model order reduction for random linear dynamical systems

Pulch, Roland; Maten, E.J.W. ter; Augustin, F.

doi:10.1016/j.matcom.2015.01.003

Cited by 29 publications

(23 citation statements)

References 37 publications

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“…It follows that the entries ofĤ(s) ∈ C M Nout×Nin include approximations of the PC coefficients for the original transfer function (3), see [16].…”

Section: Stochastic Galerkin Methodsmentioning

confidence: 99%

“…In [16], this reduction has been employed for uniformly distributed parameters. We consider moment matching for a reduction of the system (7), where the Arnoldi algorithm is applied, see [21].…”

Section: Mor For the Sg Systemmentioning

confidence: 99%

“…Moreover, parameterized model order reduction (pMOR) has been developed to preserve deterministic parameters as independent variables in the reduced order models, see [12][13][14][15]. In case of large numbers of random parameters, a reduction of the random space based on a sensitivity analysis is discussed in [16]. Furthermore, reduced basis methods have been investigated for partial differential equations with stochastic influences in [17,18], for example.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Galerkin Methods and Model Order Reduction for Linear Dynamical Systems

Pulch

Maten

2015

Int. J. UncertaintyQuantification

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Linear dynamical systems are considered in the form of ordinary differential equations or differential algebraic equations. We change their physical parameters into random variables to represent uncertainties. A stochastic Galerkin method yields a larger linear dynamical system satisfied by an approximation of the random processes. If the original systems own a high dimensionality, then a model order reduction is required to

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“…It follows that the entries ofĤ(s) ∈ C M Nout×Nin include approximations of the PC coefficients for the original transfer function (3), see [16].…”

Section: Stochastic Galerkin Methodsmentioning

confidence: 99%

Section: Mor For the Sg Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic Galerkin Methods and Model Order Reduction for Linear Dynamical Systems

Pulch

Maten

2015

Int. J. UncertaintyQuantification

Self Cite

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“…Computing S Ti in brute-force approach is often infeasible (requiring computation of up to n − 1 order Sobol indices), but efficient ways exist [10]. Furthermore, surrogate modeling techniques that facilitate the acquisition of S i and S Ti exist such as using Polynomial Chaos Expansions [14,15,16]. We expect that there are shortcuts to economize the computation of I i as well.…”

Section: Comparisonmentioning

confidence: 99%

Variance-based interaction index measuring heteroscedasticity

Ito

Couckuyt

Poles

et al. 2016

Computer Physics Communications

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This work is motivated by the need to deal with models with high-dimensional input spaces of real variables. One way to tackle high-dimensional problems is to identify interaction or non-interaction among input parameters. We propose a new variance-based sensitivity interaction index that can detect and quantify interactions among the input variables of mathematical functions and computer simulations. The computation is very similar to first-order sensitivity indices by Sobol'. The proposed interaction index can quantify the relative importance of input variables in interaction. Furthermore, detection of non-interaction for screening can be done with as low as 4n + 2 function evaluations, where n is the number of input variables. Using the interaction indices based on heteroscedasticity, the original function may be decomposed into a set of lower dimensional functions which may then be analyzed separately.

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“…One of the first publications considering UQ and MOR for microelectronics is [25], where a projection-based MOR method for variational analysis of RLC interconnect circuits was presented. In [26], a projection based reduction of the state space and a reduction of the random space are applied to an electric network with uncertain capacitances, inductances, and conductances. Another example is [27], where a combination of the reduced basis method and stochastic collocation is applied to stochastic versions of the diffusion equation and the incompressible Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification for Maxwell's Equations Using Stochastic Collocation and Model Order Reduction

Benner

Schneider

2015

Int. J. UncertaintyQuantification

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Sensitivity analysis and model order reduction for random linear dynamical systems

Cited by 29 publications

References 37 publications

Stochastic Galerkin Methods and Model Order Reduction for Linear Dynamical Systems

Stochastic Galerkin Methods and Model Order Reduction for Linear Dynamical Systems

Variance-based interaction index measuring heteroscedasticity

Uncertainty Quantification for Maxwell's Equations Using Stochastic Collocation and Model Order Reduction

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