Clouds for modelling uncertainties in robust space system design
The ACT is assessing a promising new approach for an autonomous and robust design, based on the concept of clouds combining the concept of a fuzzy set and that of a probability distribution.
Traditional modelling of uncertainties faces several problems. In current methods considering worst case analysis the ignorance of distributions of uncertain variables or the ignorance of correlations between uncertain data, respectively, sometimes leads to drastic underestimations of error probabilities (cf. ). Moreover, even provided the knowledge of the multivariate probability distributions, in higher dimensions the numerical computation of the error probabilities is very expensive, if not impossible.
Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution (cf. , ). They capture useful properties of the probabilistic and fuzzy uncertainties, enabling the user to utilize the collected empirical information (even if very limited in amount) in a reliable, validated way. Being a hybrid between probabilistic and deterministic models, clouds can provide a risk analysis using tools from global optimization and constraint satisfaction techniques. The numerical techniques for solving such problems have become much more reliable and powerful in the recent past and allow to compute bounds for the expected values of any multivariate functions of design processes, and also for probabilities of qualitative statements involving design variables.
For given confidence levels the clouds provide regions of relevant scenarios affecting the worst case. In robust design, a design is considered unsafe if one of the relevant scenarios does not satisfy the safety-requirements. Currently the concept is applied to the problem of optimization of robust spacecraft system design. The goal is to find the optimal spacecraft design with regard to the constraint that the design should not be unsafe and to the uncertainty information provided by expert spacecraft designers.
Links & references
- A. Neumaier. Clouds, fuzzy sets and probability intervals. Reliable Computing 10, pages 249-272, 2004. [pdf]
- A. Neumaier. Uncertainty modeling for robust verifiable design. Slides. [pdf]
- D. Dubois and H. Prade. Interval-valued fuzzy sets, possibility theory and imprecise probability. In Proceedings of International Conference in Fuzzy Logic and Technology, 2005.
- S. Ferson, L. Ginzburg, and R. Akcakaya. Whereof one cannot speak: When input distributions are unknown. Risk Analysis, in press, 1996. [pdf]
- A. Neumaier, M. Fuchs, E. Dolejsi, T. Csendes, J. Dombi, B. Banhelyi, and Z. Gera. Application of clouds for modeling uncertainties in robust space system design. ACT Ariadna Research ACT-RPT-05-5201, European Space Agency, 2007. Available on-line here .