This work provides an unsupervised learning approach based on a single-valued performance indicator to monitor the global behavior of critical components in a viaduct, such as bearings. We propose an outlier detection method for longitudinal displacements to assess the behavior of a singular asymmetric prestressed concrete structure with a 120 m high central pier acting as a fixed point. We first show that the available long-term horizontal displacement measurements recorded during the undamaged state exhibit strong correlations at the different locations of the bearings. Thus, we combine measurements from four sensors to design a robust performance indicator that is only weakly affected by temperature variations after the application of principal component analysis. We validate the method and show its efficiency against false positives and negatives using several metrics: accuracy, precision, recall, and F1 score. Due to its unsupervised learning scope, the proposed technique is intended to serve as a real-time supervision tool that complements maintenance inspections. It aims to provide support for the prioritization and postponement of maintenance actions in bridge management.