Fault Detection in Wastewater Treatment Systems Using Multiparametric Programming

Abstract

In this work, a methodology for fault detection in wastewater treatment systems, based on parameter estimation, using multiparametric programming is presented. The main idea is to detect faults by estimating model parameters, and monitoring the changes in residuals of model parameters. In the proposed methodology, a nonlinear dynamic model of wastewater treatment was discretized to algebraic equations using Euler’s method. A parameter estimation problem was then formulated and transformed into a square system of parametric nonlinear algebraic equations by writing the optimality conditions. The parametric nonlinear algebraic equations were then solved symbolically to obtain the concentration of substrate in the inflow, , inhibition coefficient, , and specific growth rate, , as an explicit function of state variables (concentration of biomass, ; concentration of organic matter, ; concentration of dissolved oxygen, ; and volume, ). The estimated model parameter values were compared with values from the normal operation. If the residual of model parameters exceeds a certain threshold value, a fault is detected. The application demonstrates the viability of the approach, and highlights its ability to detect faults in wastewater treatment systems by providing quick and accurate parameter estimates using the evaluation of explicit parametric functions.

Enhanced data-driven monitoring of wastewater treatment plants using the Kolmogorov–Smirnov test

“…The study in ref. 10 presents a methodology for fault detection in WWTPs based on parameter estimation and multiparametric programming. This method involves the estimation of model parameters and the continuous monitoring of changes in residuals associated with these parameters.…”

A Combined H 2 / H ∞ Approach for Robust Joint Actuator and Sensor Fault Estimation: Application to a DC Servo-Motor System

“…Finally, it should be noted that the proposed approach is devoted to linear systems. There are, of course, approaches that can be used to tackle fault diagnosis of nonlinear systems using a nonlinear model description directly [34,35,36]. However, the approach proposed in this paper can be extended to nonlinear systems by modeling them as linear parameter-varying (LPV) or Takagi–Sugeno ones.…”