Non Deterministic Approaches

It is clear from the experience in design and testing of engineering structures that nominal designs do not fully capture the behavior of real components. The models used by engineers can be very good approximations of reality and can be efficiently used to obtain useful results. However, since they are models, there is always a certain degree of abstraction from reality that cannot be taken into account.

Moreover, real systems are not "deterministic" in the pure sense. There is always a certain degree of uncertainty or variability in the properties that describe them and their performance (static, dynamic, fetigue life etc.) is never perfectly reproducible. This makes the task of modeling them even thougher.

It is clear that realistic modeling and simulation of complex systems must take into account the non deterministic nature of the system and the environment. The term "non deterministic" means that the response of a system is not perfectly predictable because of the existence of uncertainty in the system, the environment or human interaction with the system.

In this handbook, as in all the other parts of this website, a clear dinstinction is made on the source of non determinism, depending if this source is reducible or irredubile. In particular, using the definitions proposed by Oberkampf, it is possible to identify two types of uncertainty:

1. Aleatory Uncertainty: also referred in literature as irreducible uncertainty, inherent uncertaint, variability and stochastic uncertaint. The mathematical representation essentially always used for aleatory uncertainty is a probability or e frequency distribution.
2. Epistemic Uncertainty: as a source of non deterministic behaviour derives from lack of knowledge of the system or the environment. In literature, it is also referred to as reducible uncertainty, subjective uncertainty and cognitive uncertainty.

In this handbook some of the techniques used to deal include variablity and/or uncertainty modeling in the engineering design process will be explained and the mathematical basis for them will be given. The application of these techniques can be found in the articles, application and special cases sections of this website.