Header

UZH-Logo

Maintenance Infos

High-order statistics in global sensitivity analysis: Decomposition and model reduction


Geraci, Gianluca; Congedo, Pietro Marco; Abgrall, Rémi; Iaccarino, Gianluca (2016). High-order statistics in global sensitivity analysis: Decomposition and model reduction. Computer Methods in Applied Mechanics and Engineering, 301:80-115.

Abstract

Analysis of Variance (ANOVA) is a common technique for computing a ranking of the input parameters in terms of their contribution to the output variance. Nevertheless, the variance is not a universal criterion for ranking variables, since non symmetric outputs could require higher order statistics for their description and analysis. In this work, we illustrate how third and fourth-order moments, i.e. skewness and kurtosis, respectively, can be decomposed mimicking the ANOVA approach. It is also shown how this decomposition is correlated to a Polynomial Chaos (PC) expansion leading to a simple strategy to compute each term. New sensitivity indices, based on the contribution to the skewness and kurtosis, are proposed. The outcome of the proposed analysis is depicted by considering several test functions. Moreover, the ranking of the sensitivity indices is shown to vary according to their statistics order. Furthermore, the problem of formulating a truncated polynomial representation of the original function is treated. Both the reduction of the number of dimensions and the reduction of the order of interaction between parameters are considered. In both cases, the impact on the reduction is assessed in terms of statistics, namely the probability density function. Feasibility of the proposed analysis in a real-case is then demonstrated by presenting the sensitivity analysis of the performances of a turbine cascade in an Organic Rankine Cycles (ORCs), in the presence of complex thermodynamic models and multiple sources of uncertainty.

Abstract

Analysis of Variance (ANOVA) is a common technique for computing a ranking of the input parameters in terms of their contribution to the output variance. Nevertheless, the variance is not a universal criterion for ranking variables, since non symmetric outputs could require higher order statistics for their description and analysis. In this work, we illustrate how third and fourth-order moments, i.e. skewness and kurtosis, respectively, can be decomposed mimicking the ANOVA approach. It is also shown how this decomposition is correlated to a Polynomial Chaos (PC) expansion leading to a simple strategy to compute each term. New sensitivity indices, based on the contribution to the skewness and kurtosis, are proposed. The outcome of the proposed analysis is depicted by considering several test functions. Moreover, the ranking of the sensitivity indices is shown to vary according to their statistics order. Furthermore, the problem of formulating a truncated polynomial representation of the original function is treated. Both the reduction of the number of dimensions and the reduction of the order of interaction between parameters are considered. In both cases, the impact on the reduction is assessed in terms of statistics, namely the probability density function. Feasibility of the proposed analysis in a real-case is then demonstrated by presenting the sensitivity analysis of the performances of a turbine cascade in an Organic Rankine Cycles (ORCs), in the presence of complex thermodynamic models and multiple sources of uncertainty.

Statistics

Citations

2 citations in Web of Science®
1 citation in Scopus®
Google Scholar™

Altmetrics

Downloads

1 download since deposited on 12 Jan 2017
1 download since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2016
Deposited On:12 Jan 2017 11:13
Last Modified:12 Jan 2017 11:13
Publisher:Elsevier
ISSN:0045-7825
Publisher DOI:https://doi.org/10.1016/j.cma.2015.12.022

Download

Preview Icon on Download
Content: Accepted Version
Language: English
Filetype: PDF - Registered users only until 2 April 2018
Size: 1MB
View at publisher
Embargo till: 2018-04-02

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations