Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

Abstract

The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l 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.

New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

“…Sobol's concept is based on the well-known formula of variance decom-position V(Y) = V(E(Y|Xα)) + E(V(Y|Xα)), which separates the output variance into the variance due to the dependence on a parameter group Xα and the residual variance. The difference of variances V(Y) − E(V(Y|Xα)) may be replaced by another sensitivity measure, such as entropy [67] or the difference between superquantile and subquantile [39,40]. The Pearson correlation coefficient corr can be replaced by Spearman's rank correlation or Kendall's τ.…”

“…In the reliability analysis of a structure, the system is characterized by two possible results: unreliability and reliability [35,36]. Although reliability can be assessed without Pf using design quantiles, the SA of design quantiles cannot calculate the interaction effects between load and resistance [37][38][39][40]. The correlation methods [41,42], Sobol SA [14,15]; density-based SA [43,44]; entropy-based SA [45,46]; quantile-based SA [47,48] and [37][38][39][40]; SA in Multiple Criteria Decision Making (MCDM) [49,50]; and other SA types [51,52] are effective in their applications, but may not work properly in reliability tasks.…”

Symmetric and Asymmetric Data in Solution Models

“…The application fields of the proposed solution models rather often involved different engineering problems. Much attention was given to civil engineering in terms of construction project management [56,58] and the analysis of building structures [59,61]. Three papers analysed the optimisation of supply chains [62,64,66].…”

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

“…Other types of SA include quantile-oriented methods [28][29][30][31][32][33], probability of failure [34][35][36][37][38][39][40][41], or decision-making approaches [42][43][44][45]. The subject of interest of these types of SA is the reliability of the system, which cannot be examined using SA distribution types.…”