Moment independent sensitivity analysis utilizing polynomial chaos expansion

Moment independent sensitivity analysis utilizing polynomial chaos expansion

Stať ve sborníku mimo WoS a Scopus

An important part of uncertainty quantification is a sensitivity analysis (SA). There are several types of SA methods in scientific papers nowadays. However, it is often computationally demanding or even not feasible to obtain sensitivity indicators in practical applications, especially in a case of mathematical models of physical problems solved by the finite element method. Therefore, it is often necessary to create a surrogate model in an explicit form as an approximation of the original mathematical model. It is shown, that it is beneficial to utilize Polynomial Chaos Expansion (PCE) as a surrogate model due to its possibility of a powerful postprocessing (statistical analysis and analysis of variance). The basic theory of PCE and global sensitivity analysis is briefly overviewed with a special attention to a moment-independent sensitivity analysis (taking whole distribution of random variables into account). The paper is mainly focused on a moment-independent sensitivity analysis based on PCE and Cramér-von Mises distance and a novel methodology for its derivation directly from PCE without time-consuming double-loop Monte Carlo simulation is presented. The proposed method is validated on simple analytical examples and obtained results are discussed.

An important part of uncertainty quantification is a sensitivity analysis (SA). There are several types of SA methods in scientific papers nowadays. However, it is often computationally demanding or even not feasible to obtain sensitivity indicators in practical applications, especially in a case of mathematical models of physical problems solved by the finite element method. Therefore, it is often necessary to create a surrogate model in an explicit form as an approximation of the original mathematical model. It is shown, that it is beneficial to utilize Polynomial Chaos Expansion (PCE) as a surrogate model due to its possibility of a powerful postprocessing (statistical analysis and analysis of variance). The basic theory of PCE and global sensitivity analysis is briefly overviewed with a special attention to a moment-independent sensitivity analysis (taking whole distribution of random variables into account). The paper is mainly focused on a moment-independent sensitivity analysis based on PCE and Cramér-von Mises distance and a novel methodology for its derivation directly from PCE without time-consuming double-loop Monte Carlo simulation is presented. The proposed method is validated on simple analytical examples and obtained results are discussed.

Sensitivity anaylysis, Polynomial Chaos Expansion, Cramer von Mises distance

Sensitivity anaylysis, Polynomial Chaos Expansion, Cramer von Mises distance

NOVÁK, L.; NOVÁK, D.

2020

11.09.2019

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