An evolutionary approach to dissolved oxygen mathematical modeling: A case study of the Klamath River

Aquaculture has emerged as a crucial sector in many countries. In the Recirculating Aquaculture System (RAS), Dissolved Oxygen (DO) levels are critical to the health of aquatic animals. As DO sensors are costly, a number of studies have proposed a soft sensor technique utilizing machine learning for estimating DO levels in water. However, the existing research work mainly focuses on black-box approaches, which do not provide numerical analysis between the DO levels and the related parameters. To solve this issue, a sequential Genetic Programming (GP) approach with an evolutionary refinement method is proposed to generate a mathematical expression that represents DO levels in water. In particular, a coarse mathematical model is generated using GP and subsequently fine-tuned using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). As a study case, the Klamath River dataset is used to generate the model. The evaluation of our proposed method uses datasets from both the Klamath River and the Fanno Creek. Two models are generated in this paper; one model uses six features, while the other only employs three. The results indicate that the model with six features exhibits relatively higher accuracy. However, it is worth noting that a smaller dataset of features is also capable of achieving generalization of the model.