Robustness investigations
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In order to discriminate between robustness and sensitivity of a
structural design a clear definitions of each other is required.
Robustness
A structural design is considered as being robust, if deviations from the desired values of structural parameters yields to reasonable low deviations of structural responses. As robustness can not be measured in absolute terms only relative measure can be fomulated.
Sensitivity
The sensitivity describes the amount of influence of a structural design parameter regarding structural results. As robustness, the sensitivity of a stuctural design can only be measured relativly.
In
most applications there is no knowlegde about the exact value of the
deviations of the structural parameters. Thus they are interpreted as
uncertain and can be described with different uncertainty models.
If the uncertainty model fuzziness is applied, the fuzzy design parameters are mapped to fuzzy structural results with the aid of the fuzzy structural analysis. The uncertainty of fuzzy set can be assessed with an analog to Shannon´s entropy and is defined by
The
Shannon´s entropy represents the "steepness" of the membership function.
When assessing a crisp set the measure value H(Ãi) = 0 is obtained. The
most uncertain set where all elements of this set have a membership
value of μ(Ãi) = 0.5 (exept the mean value) the value of H(Ãi) yields its
maximum.
A relative Robustness measure is defined by the
ratio of the Shannons entropy of the fuzzy design parameters to the
Shannons entropy of the fuzzy results
High values of Br indicate a robust structural design. This relative robustness measure Br can be used in conjunction with the Fuzzy Cluster Design or any other analysis methods using the uncertainty model fuzziness where decisions between structural design variants have to be made.
References
- Möller, B, and Beer, M (2004) Fuzzy Randomness - Uncertainty in Civil Engineering and Computational Mechanics, Springer, Berlin Heidelberg New York.
- Beer, M, Liebscher, M, and Möller, B (2004) Structural Design under Fuzzy Randomness, In: Proceedings of the NSF workshop on Reliable Engineering Computing, edited by Rafi L. Muhanna and Robert L. Mullen. NSF, pages 215–234 (hardcover), 1–21 (CD-ROM).
- Beer, M, Möller, B, and Liebscher, M (2003) Processing uncertainty in structural analysis, design and safety assessment, In: Fourth International Symposium on Uncertainty Modeling and Analysis (ISUMA), edited by B.M. Ayyub and N.O. Attoh-Okine. ISUMA, College Park MD 34-39, pages 1–6.
- 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.
- Rommelfanger, H (1988) Fuzzy Decision Support-Systeme, Springer, Berlin Heidelberg.
