Robust design with the aid of cluster algorithms (Fuzzy Cluster Design)
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The problem to be solved is that nonlinear fuzzy structural analysis and fuzzy probabilistic safety assessment do not permit to conclude directly from fuzzy results back to the assigned fuzzy input parameters. There are only few quasi arbitrary distributed crisp points in the space of input parameters. This already known points in the design space can always be separated into permissible and non-permissible ones by the evaluation of the design contrains for respectively assigned result points.
Fig. 1: Problem to be solved: Determination of convex sets of permissible design vectors
Algorithmic procedure
The algorithmic procedure of Fuzzy Cluster Design can be described with the following three steps:
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 Fig. 2: Detected permissible and non-permissible clusters in the design space
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Assessment of alternative design variants
The uncertainty of the alternative design variants is assessed with a robustness measure on basis of an analog to Shannon´s entropy
That means, if the uncertainty design parameters of a design variant takes high in realtion to to uncertainty of the result the assigned structural design is considers as being robust. A second criterion is the comparison of the design constraint dc = perm_zj with the fuzzy results yield from the different design variants. Therefore the fuzzy results have to be transformed into crisp values with the aid of defuzzification methods (e.g. centroid, or methods after Jain and Chen). The design variant that maximizes the equation
References
- Liebscher, M, and Möller, B (2005) Design of structures - solving the inverse problem, In: Compilation of Abstracts of the Third M.I.T. Conference Computational Fluid and Solid Mechanics, edited by K. J. Bathe. M.I.T., Boston, pages 233.
- Möller, B, and Beer, M (2004) Fuzzy Randomness - Uncertainty in Civil Engineering and Computational Mechanics, Springer, Berlin Heidelberg New York.
- Möller, B, Beer, M, and Liebscher, M (2003) Fuzzy Cluster Design: A new way for structural design, In: 9th International Conference on Civil and Structural Engineering Computing, edited by B.H.V. Topping. Civil-Comp Press, Egmond-aan-Zee, pages 285–286.
