Modeling Performance of Butterfly Valves Using Machine Learning Methods

Control of airflow of activated sludge systems has significant challenges due to the non-linearity of the control element (butterfly valve). To overcome this challenge, some valve manufacturers developed valves with linear characteristics. However, these valves are 10–100 times more expensive than butterfly valves. By developing models for butterfly valves installed characteristics and utilizing these models for real-time airflow control, the authors of this paper aimed to achieve the same accuracy of control using butterfly valves as achieved using valves with linear characteristics. Several approaches were tested to model the installed valve’s characteristics, such as a formal mathematical model utilizing Simscape/Matlab software, a semi-empirical model, and several machine learning methods (MLM), including regression, support vector machine, Gaussian process, decision tree, and deep learning. Several versions of the airflow-valve position models were developed using each machine learning method listed above. The one with the smallest forecast error was selected for field testing at the 55.5 × 10 3 m 3 / day 12 MGD City of Chico activated sludge system. Field testing of the formal mathematical model, semi-empirical model, and the regularized gradient boosting machine model (the best among MLMs) showed that the regularized gradient boosting machine model (RGBMM) provided the best accuracy. The use of the RGBMMs in airflow control loops since 2019 at the City of Chico wastewater treatment plant showed that these models are robust and accurate (2.9% median error).