Recent advances in sensor technologies and data acquisition systems opened up the era of big data in the field of structural health monitoring (SHM). Data-driven methods based on statistical pattern recognition provide outstanding opportunities to implement a long-term SHM strategy, by exploiting measured vibration data. However, their main limitation, due to big data or high-dimensional features, is linked to the complex and time-consuming procedures for feature extraction and/or statistical decision-making. To cope with this issue, in this article we propose a strategy based on autoregressive moving average (ARMA) modeling for feature extraction, and on an innovative hybrid divergence-based method for feature classification. Data relevant to a cable-stayed bridge are accounted for to assess the effectiveness and efficiency of the proposed method. The results show that the offered hybrid divergence-based method, in conjunction with ARMA modeling, succeeds in detecting damage in cases strongly characterized by big data.