Numerical non-determinism in a design process

The general objective of the application of numerical tools in a design process is to increase the design quality of an initial prototype by simulation of its realistic physical behaviour. While numerical analyses have proven to be very valuable in increasing design quality, an exact quantification of the design quality reached through the analysis is not always straightforward. This is mainly due to the fact that in any step of the design, there remains non-determinism in the numerical analysis. There generally is an evolution of the type of non-determinism encountered during a typical design process. Or as formulated by Ross [43]: As more information about a problem becomes available, the mathematical description of non-determinism can transform from one theory to the next in the characterization of the uncertainty as the uncertainty diminishes or, alternatively, as the information granularity increases and becomes specific.

Section "Discussion of introduction of non-determinism in the engineering process" has shown that more information on a product becomes available as design decisions are taken. The evolution of non-determinism in a typical design process as described above is illustrated in figure 5. The numerical prediction of the actual design quality improves over the design process. In the early stages, the non-determinism in the numerically predicted design quality is mainly driven by model uncertainties, whereas in later stages, variability becomes more important. This figure also indicates the evolution of the numerical concepts that are most appropriate for the dominant class of the occurring non-determinism.

Typical occurrence of non-determinism in the product quality predictions during a design process

Figure 5: Typical occurrence of non-determinism in the product quality predictions during a design process

Individual model properties are modelled with fuzzy numbers in the initial design stages. After some design decisions are taken, the property is described by an interval with fixed bounds. As soon as production has started, actual values of that property exhibit a distribution.