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A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables

Article dans une revue avec comité de lecture
Auteur
VUILLOD, Bruno
1002421 Institut de Mécanique et d'Ingénierie [I2M]
ccMONTEMURRO, Marco
1002421 Institut de Mécanique et d'Ingénierie [I2M]
ccPANETTIERI, Enrico
1002421 Institut de Mécanique et d'Ingénierie [I2M]
HALLO, Ludovic

URI
http://hdl.handle.net/10985/24587
DOI
10.1016/j.ress.2023.109177
Date
2023-06
Journal
Reliability Engineering & System Safety

Résumé

The model-based system engineering approach consists of assembling subsystems together to model a complete system. In this context, some functional blocks can have a considerable influence on the overall behaviour of the system. A preliminary identification of the influence of the subsystems on the output responses can help reducing the complexity of the overall system, with a negligible impact on the overall accuracy. Therefore, pertinent indicators must be introduced to achieve this goal. To this purpose, in this work, some well-established methods and algorithms for global sensitivity analysis (GSA) of linear and non-linear systems with independent input variables, i.e., approaches based on Sobol’s indices (different algorithms are considered), and Shapley’s effect, are compared on both benchmark functions and real-world engineering problems. Specifically, in this paper, real-world engineering problems dealing with linear and non-linear systems are modelled through commercial finite element software and/or dedicated programming languages for solving complex non-linear dynamics models, like Modelica. Regarding Modelica models, an efficient strategy based on functional mock-up units is presented to speed up the simulation of highly non-linear dynamic systems. All numerical models are interfaced with the algorithms used for GSA through ad-hoc routines coded in Python environment. For each problem, a systematic comparison between the results provided by the different algorithms making use of Sobol’s indices and Shapley’s indices is performed, in terms of reliability, accuracy and computational costs.

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Fin d'embargo:
2024-01-15
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  • Institut de Mécanique et d’Ingénierie de Bordeaux (I2M)

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