A bilinear identification‐modeling framework from time domain data

Karachalios, Dimitrios S.; Gosea, Ion Victor; Antoulas, Athanasios C.

doi:10.1002/pamm.201900246

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…The parameters can be recovered from LF by considering the 2nd kernel as a univariate rational function, but the pole residue form needs a special treatment and is usually quite challenging. Similar studies have been proposed in [12,17] for inferring bilinear or quadratic systems respectively, where an improvement towards bilinear identification was shown in [16] and in the current study.…”

Section: Polynomial Liftingsupporting

confidence: 89%

A framework for fitting quadratic-bilinear systems with applications to models of electrical circuits

Karachalios¹,

Gosea²,

Antoulas³

2021

Preprint

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In this contribution, we propose a data-driven procedure to fit quadratic-bilinear surrogate models from data. Although the dynamics characterizing the original model are strongly nonlinear, we rely on lifting techniques to embed the original model into a quadratic-bilinear format. Here, data represent generalized transfer function values. This method is an extension of methods that do bilinear, or quadratic inference, separately. It is based on first fitting a linear model with the classical Loewner framework, and then on inferring the best supplementing nonlinear operators, in a least-squares sense. The application scope of this method is given by electrical circuits with nonlinear components (such as diodes). We propose various test cases to illustrate the performance of the method.

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Section: Polynomial Liftingsupporting

confidence: 89%

A framework for fitting quadratic-bilinear systems with applications to models of electrical circuits

Karachalios¹,

Gosea²,

Antoulas³

2021

Preprint

Self Cite

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“…In that case, its impulse response can be approximated by a Volterra series which is precisely the response of affine models. Here again for stability issues, instead of solving (27), one may similarly consider solving the problem (28), putting the nonlinearity on the output equation only, i.e. setting N = 0 r×r and Â = A r , min…”

Section: Structured Nonlinear Model Inferencementioning

confidence: 99%

“…The result of this model inference is reported in Figures 6 and 7, illustrating the responses with respect to the raw data, the (maximal/mean) errors and eigenvalues dispersion. Note that to preserve stability one solves the structured problems ( 25) and (28) instead of ( 24) and (27).…”

Section: Rough Grid: Process Illustrationmentioning

confidence: 99%

“…On the other side, non-intrusive methods refer to approaches where only input to state or input to output data are available. Within this category, one can mention input-output frequencydomain data-driven model approximation in the Loewner framework (LF), proposed in its linear version in [34,6] and extended to bilinear in [2,20] and very recently to time-domain bilinear in [27]. The LF, as the IRKA (or transfer function IRKA), is an interpolatory method dedicated to data-driven cases where frequency response is accessible, instead of models.…”

Section: Introduction 1intrusive and Non-intrusive Reduced Order Mode...mentioning

confidence: 99%

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Mixed interpolatory and inference non-intrusive reduced order modeling with application to pollutants dispersion

Poussot-Vassal¹,

Sabatier²,

Sarrat³

et al. 2020

Preprint

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On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the underlying phenomena. The approach is essentially based on linear dynamical systems and approximation theory. More specifically, it sequentially involves the interpolatory Pencil and Loewner framework, known to be both very versatile and scalable to large-scale data sets, and a linear least square problem involving the raw data and reduced internal variables. With respect to intrusive methods, no prior knowledge on the operator is needed. In addition, compared to the traditional non-intrusive operator inference ones, the proposed approach alleviates the need of measuring the original full-order model internal variables. It is thus applicable to a wider application range than standard intrusive and non-intrusive methods. The rationale is successfully applied on a large eddy simulation of a pollutants dispersion case over an airport area involving multi-scale and multi-physics dynamical phenomena. Despite the simplicity of the resulting low complexity model, the proposed approach shows satisfactory results to predict the pollutants plume pattern while being significantly faster to simulate.

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