The dissolved oxygen ramp is immoral: facing global water challenges with mathematical analysis

The water sector is increasingly relying on data-driven approaches to create proxy measurements. These approaches are often trained with data covering only few situations, resulting in a lack of robustness and increasing the risk of false predictions. Therefore, robust approaches are needed for data-driven proxy measurements (i.e. soft sensors), especially for water recovery and reuse. In climate science and robotics, Dynamical Systems Analysis) is used to explore a wide range of system behaviour and uncover conditions of high uncertainty, and potential tipping points. DSA allows the systematic analysis of model dynamics, and the measurable features caused by these dynamics. We created a novel DSA workflow for soft-sensor development to measure water quality. Herein, we demonstrate that the integration of DSA into soft-sensor development adds robustness by revealing all mathematically possible combinations of state variables that lead to a feature. It can thus detect possible interferences and help design the soft sensor to avoid these. We used DSA for the falsification of a ramp-feature-based soft sensor and found that, despite a published, successful laboratory and real-world application, the ramp feature is immoral. Such an immorality implies that false predictions could occur. However, the DSA analysis uncovered under which operational conditions the ramp becomes a robust soft sensor feature. Targeted experiments will be necessary to confirm the boundary of the robust conditions in the real world.