From Probabilistic to Quantile-Oriented Sensitivity Analysis: New Indices of Design Quantiles

• Main Author: Zdeněk Kala
• Format: Article
• Language: English
• Published: MDPI AG 2020-10-01
• Series: Symmetry
• Subjects: sensitivity analysis; reliability; failure probability; quantile; civil engineering; limit states
• Online Access: https://www.mdpi.com/2073-8994/12/10/1720

In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability <i>P</i>_f of a structure. Although the reliability is usually expressed via <i>P</i>_f, Eurocode building design standards assess the reliability using design quantiles of resistance and load. The presented case study showed that quantile-oriented SA can provide the same sensitivity ranking as <i>P</i>_f-oriented SA or local SA based on <i>P</i>_f derivatives. The first two SAs are global, so the input variables are ranked based on total sensitivity indices subordinated to contrasts. The presented studies were performed for <i>P</i>_f ranging from 9.35 × 10⁻⁸ to 1–1.51 × 10⁻⁸. The use of quantile-oriented global SA can be significant in engineering tasks, especially for very small <i>P</i>_f. The proposed concept provided an opportunity to go much further. Left-right symmetry of contrast functions and sensitivity indices were observed. The article presents a new view of contrasts associated with quantiles as the distance between the average value of the population before and after the quantile. This distance has symmetric hyperbola asymptotes for small and large quantiles of any probability distribution. Following this idea, new quantile-oriented sensitivity indices based on measuring the distance between a quantile and the average value of the model output are formulated in this article.