Probabilistically modelled geometrical imperfections for reliability analysis of vertically loaded steel frames

Jindra, Daniel; Kala, Zdeněk; Kala, Jiří

doi:10.1016/j.jcsr.2024.108627

Journal of Constructional Steel Research

2024

DOI: 10.1016/j.jcsr.2024.108627

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Probabilistically modelled geometrical imperfections for reliability analysis of vertically loaded steel frames

Daniel Jindra,

Zdeněk Kala,

Jiří Kala

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Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

Kala

2024

Mathematics

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This paper introduces innovative sensitivity indices based on Cliff’s Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol’ method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff’s Delta, originally used for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff’s Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff’s Delta δC2, exhibit properties analogous to those in the Sobol’ sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a framework for evaluating the contributions of input variables on structural reliability. The results demonstrate that the Cliff’s Delta method provides a more accurate estimate of Pf. In one case study, the Cliff’s Delta approach reduces the standard deviation of Pf estimates across various Monte Carlo run counts. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff’s Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff’s Delta is a disadvantage. Future research should optimize computational demands, especially for small values of Pf.

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Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

Kala

2024

Mathematics

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Probabilistically modelled geometrical imperfections for reliability analysis of vertically loaded steel frames

Cited by 1 publication

References 45 publications

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

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