Log-based predictive maintenance of computing centers is a main concern regarding the worldwide computing grid that supports the CERN (European Organization for Nu-clear Research) physics experiments. A log, as event-oriented ad-hoc information, is quite often given as unstructured big data. Log data processing is a time-consuming computational task. The goal is to grab essential information from a continuously changeable grid environment to construct a classification model. Evolving granular classifiers are suited to learn from time-varying log streams and, therefore, perform online classification of the severity of anomalies. We formulated a 4-class online anomaly classification problem, and employed time windows between landmarks and two granular computing methods, namely, Fuzzy-set-Based evolving Modeling (FBeM) and evolving Granular Neural Network (eGNN), to model and monitor logging activity rate. The results of classification are of utmost importance for predictive maintenance because priority can be given to specific time intervals in which the classifier indicates the existence of high or medium severity anomalies.