This work proposes a data-driven methodology for identifying critical components in Complex Technical Infrastructures (CTIs), for which the functional logic and/or the system structure functions are not known due the CTI’s complexity and evolving nature. The methodology uses large amounts of CTI monitoring data acquired over long periods of time and under different operating conditions. The critical components are identified as those for which the condition monitoring signals permit the optimal classification of the CTI functioning or failed state. The methodology includes two stages: in the first stage, a feature selection filter method based on the Relief technique is used to rank the monitoring signals according to their importance with respect to the CTI functioning or failed state; the second stage identifies the subset of signals among those highlighted by the Relief technique that are most informative with respect to the CTI state. This identification is performed on the basis of evaluating the performance of a Cost-Sensitive Support Vector Machine (CS-SVM) classifier trained with several subsets of the candidate signals. The capabilities of the methodology proposed are assessed through its application to different benchmarks of highly imbalanced datasets, showing performances that are competitive to those obtained by other methods presented in the literature. The methodology is finally applied to the monitoring signals of the Large Hadron Collider (LHC) of the European Organization for Nuclear Research (CERN), a CTI for experiments of physics; the criticality of the identified components has been confirmed by CERN experts.