(224e) System Visualization Using Real-Time Data-Driven Models Derived from High-Resolution Sensor Profiling

Control systems play a critical role in wastewater/water treatment plants (WWTPs) for guaranteeing effluent quality, energy conservation, and economics [1, 2, 3, 4]. Recently, model predictive control (MPC) has been proposed to maintain the effluent water quality in WWTPs [5, 6, 7]. Development of an effective model that can accurately predict the effluent water state as feedback to a controller is necessary and significant for MPC system design and implementation. The data-driven approach could allow engineers to develop predictive models for use by the control system using data from the actual process under realistic operating conditions. Compared with traditional mechanistic modeling approaches, data-driven models are flexible and labor-saving, and many researchers have made it useful in the processes of WWTP [8, 9, 10, 11, 12]. However, most existing data-driven models have been established upon big data without knowing physical properties of a given system. Since all unit operations in WWTPs are governed by the physical laws, it is pragmatic to establish models revealing the “black box” accounting for some fundamental principles, such as mass conservation. In turn, we achieve highly-predictive, yet extremely simple models which lend themselves for use within MPC.

In this paper, we discuss the development of novel physics-informed data-driven models to simulate dynamic conductivity, pH, and temperature profiles in a continuously-stirred tank. We establish reduced-order multi-compartment models for profiling conductivity and pH in the tank. Specifically, the tank is partitioned into four nominal zones: high, middle, and low zones represent the compartments corresponding with the location of the sensors deployed in the experimental apparatus and a “mixing zone” denotes the bottom region where the stirrer resides. Mixing models are established based on an assumed mass transfer phenomenon between each zone and the conservation of mass. For heat transfer modeling, we invoke the dynamic heat equation with forced convection for homogeneous media.

We conduct a series of experiments to simulate the mass and heat transfer phenomena in the continuous-stirred tank. Specifically, three types of at milli-electrode array (MEA) sensors [13, 14] were deployed lengthwise along the tank's inner surface for profiling conductivity [15], pH [16], and temperature at the high, middle, and low zones. For conductivity and pH experiments, we injected a very small volume of concentrated solution (sodium chloride for conductivity shock and potassium hydroxide for pH shock) and recorded the signals measured by each sensor to profile heterogeneous mixing in the tank. For the temperature profiling experiment, we heated the tank from the bottom and measured the temperature in the three zones.

Deterministic global optimization methods were applied to determine the optimal transport parameter values for model validation. For the conductivity and pH models, we reformulated the dynamic optimization problems into large-scale nonlinear programs using the explicit Euler discretization of the ODEs. We solved these parameter estimation problems to global optimality using the ANTIGONE v1.0 solver [17] in GAMS v24.7.4 [18]. For the heat transfer model, we derived the closed-form analytical solution from the energy conservation equation and solved the global optimization problem using the EAGO v0.2.1 solver (EAGO.jl) [19] in the Julia programming language [20]. We conclude that the physics-informed data-driven modeling methodology developed in this study has great potential to predict physicochemical state and heterogeneity within WWTPs. Such models enable the next-generation WWTPs with energy-optimizing control systems and improved robustness when implemented within MPC .

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