An Application of Bond Graph Modeling in Developing Mathematical Relationships for Qualitative Information

Introducing smart systems in impoverished communities can facilitate social progress. This is realized through improvements in the fulfillment of needs, well-being, and quality of life. Thus, developing solutions that support and sustain a community is crucial. For example, microgrids can provide access to electricity. These systems are effective in powering devices that support health, agriculture, and other aspects of living. However, challenges with microgrid power management can inhibit social development if the energy supply is insufficient. Renewable energy sources are common in microgrid systems. The intermittent nature of these sources can lead to fluctuations in the available energy. The energy supply can also become insufficient as the demand increases over time. As such, understanding the interactions between the social and technical systems is necessary in sustaining development. Additionally, other resources may be needed in fulfilling needs and contributing to the quality of life. The availability of these resources may also impact the technical system and the community. For example, a water pumping or irrigation system may rely on both electricity and water. Thus, understanding the relationships between these systems is needed in developing solutions that continue to support the community as it progresses. 

Developing sustainable solutions requires an understanding of the interactions between systems; social, technical, environmental, and economic. These interactions have both quantitative and qualitative components. While both the quantitative and qualitative information provide insight for decision making in design, the qualitative information can be challenging to incorporate. The dynamic nature and subjectivity of the qualitative information furthers the complexity of representing and modeling the system relationships. Qualitative components have been modeled using System Dynamics, Agent-Based Modeling, and other Mixed Methods. Yet, there is still a need to develop mathematic equations for the interactions between components. Mathematically representing the qualitative connections between social, technical, and environmental systems can support modeling. Moreover, a better understanding of the qualitative interactions between systems provides insight for decision-makers.

We present an application of Bond Graph modeling for the development of mathematical representations for qualitative information. We examine the relationships between access to electricity, access to water, and quality of life in a community. The relationships between access to electricity and water are selected for a simplified demonstration of the proposed method. However, it is recognized other factors contribute to quality of life. The approach presented is part of a larger framework for integrating qualitative information in quantitative analysis. The framework is anchored in decision making for sustainable development.