Optimal flow sensor placement on wastewater treatment plants

Experimental design for evaluating WWTP data by linear mass balances

“…eliminating unmeasured variables and linear dependencies from the set of mass balances. Graph-based methods (Kretsovalis and Mah, 1988), as applied by Villez et al (2016) to determine the optimal layout of flow sensors, constitute an alternative way to analyse redundancy. Graph-based method is intuitive (directly related to topology) and may avoid numerical problems in matrix inversion (particularly when dealing with larger and sparse matrices).…”

“…Even though data reconciliation has been widely applied in (bio)chemical engineering for decades (Madron et al, 1977;Madron and Veverka, 1992;van der Heijden et al, 1994b), this concept so far has received relatively little attention in wastewater treatment process engineering. Some studies applied the concept of redundancy analysis and variable classification, which are closely related to the principles and objectives of data reconciliation, for sensor fault detection (Villez et al, 2016(Villez et al, , 2015(Villez et al, , 2013b or for describing redundancy in the data set (Spindler, 2014). In other studies, data reconciliation was directly applied for the validation of a WWTP process data set for modelling, process optimization or plant performance evaluation (Behnami et al, 2016;Meijer et al, 2015Meijer et al, , 2002Puig et al, 2008).…”

“…every solution, the corresponding cost of additional measurements is calculated as the sum of the individual costs of additional measurements , similar to the approach ofVillez et al (2016): weighing vector, in which each element is .The average variance of new estimates of key process variables (inversely related to accuracy), is calculated relative to the variance for the so-called reference solution, according to Eq. 2, and is termed # .…”

A general-purpose method for Pareto optimal placement of flow rate and concentration sensors in networked systems - With application to wastewater treatment plants

“…Le (2019) evaluates his own symbolic implementation of the method for identication of redundant relationships described in Spindler (2014) to be very time-consuming. Villez et al (2016) is a rare study where cost, information richness, and redundancy are considered as independent objectives for optimization. To this end, the objective for information-richness quanties the number of variables that are structurally observable (denition below).…”

“…Among each of these sets of optimization problems, the rst problem consists of placement of ow rate sensors only (problem 1 and 5). This problem is selected to compare the performance of the methods proposed in this work with the methods used inVillez et al (2016) and is therefore solved with the original toolbox (SOAR v1.2) and the newest version (SOAR v2.0). Optimization problem 2, 3, and 4 concern placement of sensors for ow rates and one component in WWTP1.…”