(340q) Subspace-Based Model Identification for Wastewater Treatment

Rising concerns about environmental protection are placing increasingly stringent requirements on wastewater treatment plants (WWTPs), thus highlighting the need for more reliable and efficient modeling, monitoring and control methods. Treatment plants can benefit from making better use of the available resources through improved automation and using process system engineering techniques. A good quantitative understanding of the process is often the core around which control and optimization formulations are designed to enable plants to meet certain specs and manage resources. In practice, there are two main modeling techniques: first-principles (mechanistic) models and data-driven models. First-principles (mechanistic) models are built using explicit knowledge of the process and invoke fundamental physical and chemical laws that describe the system. Detailed first-principles models exist in the general area of wastewater treatment and are valuable in capturing the general trend of the process variables but are typically not able to predict variable information precisely. The task of building and maintaining first-principles models and calibrating it to specific wastewater treatment units continues to be a challenge. The inability of these models to predict the behaviour of WWTPs quickly and correctly implies that these models cannot be used to tightly control wastewater treatment plants, in turn limiting the plant’s ability to meet the tight specifications imposed on WWTPs.

This work leverages some of the recent results in the area of data-driven modeling for batch processes [1,2] to obtain a model which relates a set of typical measured outputs from a WWTP to a set of typical manipulated inputs, such that the model is useful for predicting the behaviour of the outputs. A data-driven model is trained and subsequently validated on simulated output data generated for a simplified WWTP layout in GPS-X, a wastewater treatment simulator developed by Hydromantis. Subspace identification algorithms are utilized to obtain a discrete LTI model. The model is then validated on a unique dataset different from that used during model identification to evaluate how accurately the estimated model is able to reproduce the dynamic system behaviour. Following an initial state estimation period employing a Luenberger observer, the subspace model is allowed to predict the behaviour of the outputs using future values of the inputs and the predictions are compared to the observed process outputs. The efficacy of subspace identification in obtaining an appropriate model that is able to accurately describes the dynamics of the simplified wastewater treatment process and is valuable for prediction purposes is demonstrated in this work.

[1] Data-driven modeling and quality control of variable duration batch processes with discrete inputs, B. Corbett, P. Mhaskar, Industrial & Engineering Chemistry Research 56 (24), 6962-6980, 12, 2017

[2] Subspace identification for data‐driven modeling and quality control of batch processes, B. Corbett, P. Mhaskar, AIChE Journal 62 (5), 1581-1601, 58, 2016.