Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles
The article introduces quantile deviation <i>l</i> as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of <i>l</i> are presented. The proposed sensitivity indices are compared with quan...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/2/263 |
| _version_ | 1797415180807700480 |
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| author | Zdeněk Kala |
| author_facet | Zdeněk Kala |
| author_sort | Zdeněk Kala |
| collection | DOAJ |
| description | The article introduces quantile deviation <i>l</i> as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of <i>l</i> are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance. |
| first_indexed | 2024-03-09T05:44:09Z |
| format | Article |
| id | doaj.art-6c7b71797cdf4c4497409b5896a51daa |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:44:09Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6c7b71797cdf4c4497409b5896a51daa2023-12-03T12:22:29ZengMDPI AGSymmetry2073-89942021-02-0113226310.3390/sym13020263Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and SubquantilesZdeněk Kala0Department of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech RepublicThe article introduces quantile deviation <i>l</i> as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of <i>l</i> are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance.https://www.mdpi.com/2073-8994/13/2/263sensitivity analysisbucklingreliabilitysafetyquantilesuperquantile |
| spellingShingle | Zdeněk Kala Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles Symmetry sensitivity analysis buckling reliability safety quantile superquantile |
| title | Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles |
| title_full | Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles |
| title_fullStr | Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles |
| title_full_unstemmed | Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles |
| title_short | Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles |
| title_sort | global sensitivity analysis of quantiles new importance measure based on superquantiles and subquantiles |
| topic | sensitivity analysis buckling reliability safety quantile superquantile |
| url | https://www.mdpi.com/2073-8994/13/2/263 |
| work_keys_str_mv | AT zdenekkala globalsensitivityanalysisofquantilesnewimportancemeasurebasedonsuperquantilesandsubquantiles |