Connecting Qualitative and Quantitative Analysis Through Bond Graph Modeling and System Dynamics

Access to resources can contribute to social progress in extremely impoverished communities. The introduction of cyber-physical systems for electricity, water, and irrigation facilitates greater fulfillment of needs. Yet, the availability of resources may be inconsistent or lacking. The social dynamics of the community can provide insight into how the available resources support well-being. Thus, the cyber-physical system requires the addition of a social consideration to become cyber-physical-social systems. However, the social considerations typically include qualitative parameters. This prompts the need for integrating qualitative and quantitative information. In this paper, we present a method for mathematically representing qualitative and quantitative relationships. This is achieved by connecting Bond Graph Modeling and System Dynamics. The Bond Graph model is used to mathematically represent relationships between qualitative and quantitative elements. These relationships are used in the System Dynamics analysis. The method is anchored in expanding cyber-physical to cyber-physical-social systems through incorporating both qualitative and quantitative information in the systems analysis. The mathematical connectivity of qualitative and quantitative information is a key feature of this approach. A test problem in resource allocation is used to demonstrate the function and flexibility of the method. This is anchored in connecting qualitative and quantitative information in the analysis.