Non Deterministic Approaches

The emerging non-probabilistic approaches are redefining the landscape for non-deterministic FE analysis. It is the aim of this paper to give insight into the possible useful applications of these approaches, referring to the generally accepted and widely adopted probabilistic approach.

It is first shown that a clear distinction can be made between different sorts of non-deterministic properties in a numerical model. The existing classification of uncertainties and variabilities is further subdivided in certain variabilities, uncertain variabilities and invariable uncertainties. Based on these different types of non-determinism, the applicability of the different non-deterministic concepts is analysed. Different sources of uncertainty are reviewed, and it is concluded that the probabilistic approach remains the most interesting to tackle problems that are subject to complete and objective probabilistic influences. However, in the presence of uncertain quantities that require subjective information in order to be described numerically, the interval and fuzzy approach become increasingly interesting. Especially for uncertainties, the fuzzy concept is very appropriate because of its implicit subjective nature.

Next, it is shown that in the framework of numerical design analysis, there generally is an evolution of the type of the non-determinism from uncertainty towards variability. Correspondingly, the non-probabilistic approaches tend to be most valuable in early design stages, whereas the probabilistic approach remains indispensable in later stages. This leads to the conclusion that the non-probabilistic approaches should be regarded as complementary rather than competitive to the probabilistic approach. However, not only the class of the non-deterministic properties encountered in the problem definition, but also the intended output determines to what extend the different non-deterministic approaches are appropriate numerical modelling tools for the treated problem. It is discussed how the non-probabilistic approaches can be of value in a typical design process. From the discussion, it has become clear that the value of the non-probabilistic approaches in an absolute reliability analysis is rather limited. It is concluded that non-probabilistic approaches will fail to convince in areas where absolute reliability measures are primordial. However, the application of subjective probability in this context has the same limitations. Absolute reliability analysis should always be performed in a frequentist interpretation, based on objectively available data. A small assumption in the probabilistic description of the input can lead to large misjudgement of the actual reliability of the design. This should always be kept in mind when applying numerical methods for absolute design reliability predictions.