Search arXivSearch

arXiv · 2401.12822

Deep Learning Based Simulators for the Phosphorus Removal Process Control in Wastewater Treatment via Deep Reinforcement Learning Algorithms

Abstract

Phosphorus removal is vital in wastewater treatment to reduce reliance on limited resources. Deep reinforcement learning (DRL) is a machine learning technique that can optimize complex and nonlinear systems, including the processes in wastewater treatment plants, by learning control policies through trial and error. However, applying DRL to chemical and biological processes is challenging due to the need for accurate simulators. This study trained six models to identify the phosphorus removal process and used them to create a simulator for the DRL environment. Although the models achieved high accuracy (>97%), uncertainty and incorrect prediction behavior limited their performance as simulators over longer horizons. Compounding errors in the models' predictions were identified as one of the causes of this problem. This approach for improving process control involves creating simulation environments for DRL algorithms, using data from supervisory control and data acquisition (SCADA) systems with a sufficient historical horizon without complex system modeling or parameter estimation.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Esmaeel Mohammadi, Mikkel Stokholm-Bjerregaard, Aviaja Anna Hansen, Per Halkjær Nielsen, Daniel Ortiz-Arroyo, Petar Durdevic. 2024-01-23. Deep Learning Based Simulators for the Phosphorus Removal Process Control in Wastewater Treatment via Deep Reinforcement Learning Algorithms. https://doi.org/10.1016/j.engappai.2024.107992

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

This paper presents a two-stage framework for constrained feedback control of input-affine nonlinear systems. Offline, an approximate value function for the unconstrained problem is computed, for example using Hamilton--Jacobi--Bellman (HJB)-based policy iteration. Online, the proposed quadratic program (QP) minimizes the pre-Hamiltonian evaluated using the approximate value-function gradient subject to safety constraints enforced by control barrier functions (CBFs). This architecture decouples performance optimization from constraint enforcement, allowing constraints to be modified without recomputing the value function. As in CBF-QP architectures based on control Lyapunov functions (CLFs), safety is enforced as a hard constraint; however, the performance objective targets approximate optimality rather than a prescribed Lyapunov decay. Numerical results on a linear 2-state hovercraft and a nonlinear 9-state spacecraft attitude-control problem show agreement with the constrained open-loop optimal control problem (OCP) benchmark in the linear case, and performance close to the OCP benchmark, improving on CLF-based controllers, in the nonlinear case.

eess.SY

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY