Possibility theory based safety assessment

An assessment of the safety of structures may be carried out on the basis of different known safety concepts (global safety factor, semiprobabilistic approach using partial safety factors, probabilistic approximation solution using first- and second-order reliability theory, probabilistic `exact' solution). The application of these concepts presupposes special knowledge concerning input values, e.g., permissible or prescribed values, quantile values, distribution function. This especially applies to probabilistic methods. Inaccuracies and statistically nondescribable uncertainties in the input data are either ignored in these methods or only accounted for approximately using crisp bounds. Fuzzy set theory enables such uncertainties to be described mathematically and processed in the analysis of structures. The uncertain results of fuzzy structural analysis may be evaluated by various methods. In this article a safety assessment method is described based on possibility theory. In contrast to the above-mentioned concepts, the safety assessment of structures described here takes into account nonstochastic uncertainties and subjective estimates of objective values by experts based on possibility theory. It is possible by this means to obtain sufficiently reliable descriptions of the input data for further processing. The uncertainties introduced into the analysis are later reflected in the results. A realistic description of system behavior is obtained by applying high-quality algorithms in the structural analysis. The uncertain results serve as a starting point for the safety assessment. The method described here forms a supplement to safety concepts already in use.