Keywords: structural robustness, design under uncertainty, robust design, inverse problem, cluster analysis, fuzzy analysis.

Structural robustness is of increasing interest in civil engineering to cope with hazards, risks, and uncertainty. We have to ensure a proper behavior of the structure despite uncertainty of structural and environmental parameters. Changes of design parameters should not have dramatic effects. To achieve these goals, structural robustness needs to be incorporated as an objective in the design process. The new numerical approach can be applied in combination with a nonlinear structural analysis and any initial uncertainty analysis, such as Monte Carlo simulation, interval analysis or fuzzy analysis.

A measure for structural robustness is developed based on the understanding of robustness introduced by Taguchi [1] in consumer goods industry. A structure is considered as robust if it can withstand the entire spectrum of occasional or frequent fluctuations in environmental conditions without noticeable effects on its serviceability. This concerns the system performance under normally fluctuating conditions, in contrast to the occasional understanding of robustness as appropriate performance of a system under exceptional conditions. Moreover, the robustness measure is defined in conjunction with a non-stochastic uncertainty model according to fuzzy set theory. This enables the consideration of merely vaguely predictable fluctuations of structural parameters, which are particularly suitable in early design stages when clear probabilistic specifications are problematic.

Design parameters are specified as uncertain over a reasonable value range. Further uncertain parameters are quantified according to the available information. All uncertainty is processed through a structural analysis by simulation, for example, Monte Carlo simulation. This initial analysis provides a set of points in the space of the design parameters and associated structural response. By means of design constraints permissible design parameter combinations are identified and lumped together via cluster analysis. From each cluster, an associated design variant is constructed in the form of suitable ranges for design parameters. For each design variant, the robustness is computed as the ratio between the uncertainty of the input quantities and the uncertainty of the associated structural responses, in terms of an entropy measure.

The optimum design variant is determined by solving a three-criteria optimization problem. Criterion one is the traditional optimization criterion, such as a minimum mass or minimum cost. Criterion two is the maximum robustness of the structure. This aims at a structural behavior that is only marginally affected by uncertainty and by changes in the design parameters during the production process and service life of the structure. Criterion three concerns a maximum size of the suitable range of design parameters. This provides the engineer with comfortable decision margins during construction and production. The proposed design method has been tested on academic, as well as on industrial examples.

1

G. Taguchi, S. Chowdhury, Y. Wu, "Taguchi's Quality Engineering Handbook", Wiley, Hoboken, NJ, 2005.

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