Black-, gray-, and white-box modeling of biogas production rate from a real-scale anaerobic sludge digestion system in a biological and advanced biological treatment plant

Abstract

Artificial intelligence-based methodology [artificial neural network (ANN) and fuzzy logic] and a multiple regression-based analysis were conducted for modeling of the biogas production rate from a real full-scale sludge digestion process. In the computational analysis, five process-related parameters such as influent sludge flow rate, total solids content, total volatile solids content, alkalinity, and volatile fatty acids concentration were considered as the input variables for the proposed models. In the ANN-based modeling, a benchmark comparison of 11 backpropagation (BP) algorithms was employed in the first step, and the scaled conjugate gradient algorithm was chosen as the best BP algorithm in terms of their respective mean squared errors. According to the selected BP algorithm (scaled conjugate gradient BP), the number of neurons at the hidden layer was optimized as 14, and the coefficient of determination (R-2) was obtained as 0.65 for the optimal three-layer ANN structure (5:14:1). In the second part of the study, a MISO (multiple-input single-output)-type fuzzy-logic model was developed, and five input variables were fuzzified in a knowledge-based manner. For the fuzzy subsets, trapezoidal membership functions were implemented with 10 and 20 levels, and a Mamdani-type fuzzy inference system (FIS) was used to employ 394 rules in the if-then form. The product, summation, and centroid methods were employed, respectively, for implication, aggregation, and defuzzification processes conducted in the FIS. Fuzzy logic-produced forecasts were compared with the estimations obtained from both ANN-based model and a polynomial multiple regression-based model (employed as the third part of this study) derived in this study. Findings of this study clearly indicated that compared to ANN model and conventional multiple regression approach, the proposed MISO fuzzy logic-based model produced smaller deviations and exhibited a superior predictive performance on forecasting biogas production rate from a full-scale treatment plant with a satisfactory R-2 value of 0.88.