Towards a unified framework for interval based qualitative computational matrix structural analysis

Qualitative reasoning about physical system behavior is one of the things engineers do to assess the "reasonableness" of the outputs from their numerical simulations, but such reasoning is typically assumed to be an exclusively human activity under the rubric of "engineering judgement". It is the authors' contention that such reasoning can be rendered in a computational manner and that Interval Analysis (IA) provides the mathematical foundations to do so. Using Interval Analysis, the notion of operations with numbers is replaced with operations on sets of numbers. Representation of structural parameters with sets of known values permits a simultaneous parametric study. Using concepts from Qualitative and Order of Magnitude Reasoning, interval methods are augmented to perform levels of both qualitative and quantitative mechanical reasoning. Whereby interval techniques employ tight numerical intervals, it is possible to use large or even infinite intervals in order to apply qualitative computational techniques. A logic based implementation facilitated prototyping as well as approaching the unification of the various forms of analysis. Examples discussed in this paper will demonstrate that such a link between qualitative and quantitative techniques exists within a framework of interval analysis.