Gaussian process regression for monitoring and fault detection of wastewater treatment processes

Abstract

Monitoring and fault detection methods are increasingly important to achieve a robust and resource efficient operation of wastewater treatment plants (WWTPs). The purpose of this paper was to evaluate a promising machine learning method, Gaussian process regression (GPR), for WWTP monitoring applications. We evaluated GPR at two WWTP monitoring problems: estimate missing data in a flow rate signal (simulated data), and detect a drift in an ammonium sensor (real data). We showed that GPR with the standard estimation method, maximum likelihood estimation (GPR-MLE), suffered from local optima during estimation of kernel parameters, and did not give satisfactory results in a simulated case study. However, GPR with a state-of-the-art estimation method based on sequential Monte Carlo estimation (GPR-SMC) gave good predictions and did not suffer from local optima. Comparisons with simple standard methods revealed that GPR-SMC performed better than linear interpolation in estimating missing data in a noisy flow rate signal. We conclude that GPR-SMC is both a general and powerful method for monitoring full-scale WWTPs. However, this paper also shows that it does not always pay off to use more sophisticated methods. New methods should be critically compared against simpler methods, which might be good enough for some scenarios.

Machine learning techniques for monitoring the sludge profile in a secondary settler tank

“…As discussed for the case of dealing with outliers, a missing data can be reconstructed by using data from the training data set. See Samuelsson et al (2017) where the case of missing data is evaluated for some GPR-based approaches.…”

“…However, if a particular dynamic of the data needs to be captured, a combination of different covariance function should be implemented, such as constant, linear and sinusoidal. See studies by Wilson and Adams (2013), Lloyd et al (2014) and Samuelsson et al (2017) for some examples showing the choice of covariance functions to different data sets. In this case study, the sum of a linear and a squared-exponential function was found feasible, that is, where ( 1 , 2 , 3 , 4 ) are hyperparameters.…”

“…GPR has been used for monitoring and fault detection in different applications (Roberts et al 2012), such as maritime vessel track analysis (Smith et al 2012), change point detection (Garnett et al 2010) and process monitoring (Serradilla et al 2011). GPR has also been used in environmental applications, such as monitoring and fault detection in water monitoring signals (Samuelsson et al 2017), modelling of an anaerobic wastewater treatment system (Ni et al 2012), modelling nitrification process and biomass growth (Ažman and Kocijan 2007) and control of a sequencing batch reactor (Kocijan and Hvala 2013).…”

Short-Term Solar Power Forecasting: A Combined Long Short-Term Memory and Gaussian Process Regression Method

“…(1) Coverage rate (CR) CR [34] is defined as the ratio of the number of observation values within the prediction interval to all the observations, which is given by Equation (22). n c and n are denoted as the number of the former and latter observations, respectively.…”

“…Achieving a reliable fluctuation range of power output is more beneficial to energy dispatching. Based on statistical learning and Bayesian theory, GPR is adapted to solve high-dimensional and nonlinear problems, whose applications can be observed in [21,22]. Thus a highly accurate point prediction and a reliable interval forecasting can be simultaneously obtained by the LSTM-and GPR-based hybrid model (LSTM-GPR).…”