Variance-based sensitivity indices for models with dependent inputs

• Published in: Reliability engineering & system safety Vol. 107; pp. 115 - 121
• Main Authors: Mara, Thierry A., Tarantola, Stefano
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oxford Elsevier Ltd 01.11.2012; Elsevier
• Subjects: ANOVA-HDMR; Applications; Applied sciences; Dependent contributions; Dependent inputs; Exact sciences and technology; Independent contributions; Operational research and scientific management; Operational research. Management science; Risk theory. Actuarial science; Statistics; Variance-based sensitivity indices; ANOVA-HDMR; Dependent contributions; Variance-based sensitivity indices; Independent contributions; Dependent inputs; Input output; Sensitivity analysis; Simplification; Risk analysis; Variance analysis; Modeling; Optimization; Uncertain system; Independent set; independent contributions; dependent inputs; dependent contributions; variance-based sensitivity indices
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2011.08.008

Computational models are intensively used in engineering for risk analysis or prediction of future outcomes. Uncertainty and sensitivity analyses are of great help in these purposes. Although several methods exist to perform variance-based sensitivity analysis of model output with independent inputs only a few are proposed in the literature in the case of dependent inputs. This is explained by the fact that the theoretical framework for the independent case is set and a univocal set of variance-based sensitivity indices is defined. In the present work, we propose a set of variance-based sensitivity indices to perform sensitivity analysis of models with dependent inputs. These measures allow us to distinguish between the mutual dependent contribution and the independent contribution of an input to the model response variance. Their definition relies on a specific orthogonalisation of the inputs and ANOVA-representations of the model output. In the applications, we show the interest of the new sensitivity indices for model simplification setting. ► Uncertainty and sensitivity analyses are of great help in engineering. ► Several methods exist to perform variance-based sensitivity analysis of model output with independent inputs. ► We define a set of variance-based sensitivity indices for models with dependent inputs. ► Inputs mutual contributions are distinguished from their independent contributions. ► Analytical and computational tests are performed and discussed.