Abstract
In applications, the analysis of the effect of uncertain parameters on the stability of linear(ized) delay differential equations is a crucial question. Such uncertainties are often modelled as random quantities in a suitable probabilistic framework and, as a result, the spectral abscissa, which determines the stability of the deterministic delay differential equations and depends on the parameters, is a random variable. Within this context, Polynomial Chaos Expansions reveal to be a powerful tool to represent random quantities and to perform uncertain quantification and sensitivity analysis. Here we present a numerical method, called the Stochastic Infinitesimal Generator approach, to efficiently compute the expansion coefficients of the numerical spectral abscissa, showing its application to variance-based global sensitivity analysis through the computation of the Sobol’ indices. The technique implements the non intrusive spectral projection methods and makes use also of the so-called Padua points to reduce the computation cost. Some numerical examples are given.
The work of R.V. was partially supported by INdAM GNCS 2017 project “Analisi e sviluppo di metodologie numeriche per certi tipi non classici di sistemi dinamici” and is part of the project SiDiA, “Sistemi Dinamici e Applicazioni,” PRID 2017. R.V. is member of the INdAM Research group GNCS.
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Vermiglio, R., Zamolo, A. (2022). Sensitivity Analysis for Stability of Uncertain Delay Differential Equations Using Polynomial Chaos Expansions. In: Valmorbida, G., Michiels, W., Pepe, P. (eds) Accounting for Constraints in Delay Systems. Advances in Delays and Dynamics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-89014-8_8
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