Quantifying "Cliffs" in Design Space

TL;DR

This paper investigates the narrow, sensitive regions in design parameter space called 'cliffs' where small changes or uncertainties can cause significant variations in system performance, especially in indeterminate systems.

Contribution

It introduces the concept of 'cliffs' in design space and analyzes their impact on system performance and predictability in engineering.

Findings

Identification of 'cliffs' as critical regions in design space

Performance sensitivity is heightened near 'cliffs'

Uncertainty effects are amplified in 'cliffs' regions

Abstract

This paper studies the regions of parameter space of engineering design in which performance is sensitive to design parameters. Some of these parameters (for example, the dimensions and compositions of components) constitute the design, but others are intrinsic properties of materials or Nature. The paper is concerned with narrow regions of parameter space, "cliffs", in which performance (some measure of the final state of a system, such as ignition or non-ignition of a flammable gas, or failure or non-failure of a ductile material subject to tension) is a sensitive function of the parameters. In these regions performance is also sensitive to uncertainties in the parameters. This is particularly important for intrinsically indeterminate systems, those whose performance is not predictable from measured initial conditions and is not reproducible.