Topological analysis to enhance the understanding of transdisciplinary engineering

In engineering, the design of a product relies heavily on a design specification; a co-creation of customer and engineer which captures the requirements. Subjectivity is intrinsic to this process. Whilst engineers typically have a high appreciation of the technical aspects of design, the detailed knowledge of environmental and socioeconomic (ESE) implications are often held elsewhere. As such, efficient and effective design is critically dependent on the processes underpinning knowledge transfer. However, the information interfaces between engineering and the requirements of our swiftly changing civilisation remain indirect and suboptimal, and the unintended consequences of design choices are becoming increasingly serious.

Transdisciplinary engineering bridges knowledge boundaries interfacing with engineering (e.g. social science). This paper explores whether topology (a branch of pure mathematics) presents an opportunity to analyse the complex interdependency of transdisciplinary engineering information. Topology and geometry describe the structure of objects such as connectedness or the number of holes and have recently provided a suite of powerful and robust tools for analysing high-dimensional data sets. However, the real-world implementation of the term topology is still evolving. Interviews with engineering organisations, revealed that topology is almost exclusively interpreted as ‘Topology Optimisation’ in the context of advanced design and manufacturing. To date, mathematical processes for critically and systematically examining the topology of systems have not been transferred through to the engineering industry. This paper compares how topology is interpreted by the engineering industry, compared to academic literature, and reflects on the opportunities of applying the mathematical theory of topological analysis to transdisciplinary engineering data.