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

Zdeněk Kala

doi:10.3390/sym13020263

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.

Highlights

Traditional sensitivity analysis (SA) methods are focused on model output [1]
Low and high quantiles represent a significant part of the analysis of reliability, in the design of building structures
The quantile deviation l was defined as the difference between superquantile and subquantile

Summary

Introduction

Traditional sensitivity analysis (SA) methods are focused on model output [1]. SA is a computational procedure that divides and quantifies the uncertainty of input variables according to their influence on the uncertainty of the output of the mathematical model.Variance-based SA (generally called Sobol SA) introduces uncertainty as variance and decomposes the variance of the output of the model or system into portions that can be attributed to inputs or sets of inputs [2,3]. Traditional sensitivity analysis (SA) methods are focused on model output [1]. SA is a computational procedure that divides and quantifies the uncertainty of input variables according to their influence on the uncertainty of the output of the mathematical model. Variance-based SA (generally called Sobol SA) introduces uncertainty as variance and decomposes the variance of the output of the model or system into portions that can be attributed to inputs or sets of inputs [2,3]. In a more general form, SA can be defined as the study of how the output of a system is related to, and is influenced by, its inputs. Research does not usually end with obtaining the output as a random variable or histogram, but other specific point estimates, such as quantiles, are needed. What influences the variance may or may not have the same influence on the quantile

Results

Discussion

Conclusion