FUZZY CLUSTER MODELING OF BIOGAS ENERGY OUTPUT

Abstract

This study presents a fuzzy clustering-based approach to modeling and predicting the energy output of biogas plants depending on the composition of organic feedstock. The main objective of the research was to apply the Fuzzy C-means (FCM) clustering algorithm to categorize various feedstock combinations and use these cluster affiliations to forecast biogas yield. The dataset used in the study includes normalized values for several types of biomass—namely, corn silage, sugar beet residue, grain, manure, and animal slurry—measured in kilograms, with the corresponding output energy expressed in kWh. The input data underwent min-max normalization, ensuring that all feature values were scaled into the [0, 1] interval. Missing or infinite values were replaced by feature-wise mean values. After preprocessing, the FCM algorithm was applied in the MATLAB environment, and the dataset was clustered into three groups based on the feedstock composition. The centroids of the clusters corresponded to normalized average energy outputs of 0.5459, 0.4204, and 0.5224 respectively. The fuzzy membership values allowed each sample to partially belong to multiple clusters, capturing the intrinsic vagueness of the feedstock properties. Using these memberships, a fuzzy phase-based model was developed to estimate the biogas output for any given input combination by computing a weighted average of the cluster outputs. The predictive performance of the model, evaluated using root mean square error and mean absolute error, achieved values of 0.35 and 0.23 respectively in normalized units, indicating satisfactory accuracy in modeling the relationship between feedstock composition and biogas energy yield. Moreover, the fuzzy approach enables adaptability and robustness in cases where the feedstock composition deviates from previously observed combinations, allowing real-time evaluation even in the absence of identical historical samples. The research also emphasizes the potential of fuzzy clustering to detect suboptimal or anomalous operating conditions through shifts in cluster memberships over time. This opens up opportunities for integrating the model into real-time control and monitoring systems of biogas facilities. Despite its advantages, the method remains sensitive to the initial number of clusters and requires complete input matrices, which should be addressed in future studies through hybrid fuzzy-neural or deep learning enhancements.