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Structural Health Monitoring (SHM) of critical infrastructure comprises a major pillar of maintenance management, shielding public safety and economic sustainability. Although SHM is usually associated with data-driven metrics and thresholds, expert judgement is essential, especially in cases where erroneous predictions can bear casualties or substantial economic loss. Considering that visual inspections are time consuming and potentially subjective, artificial-intelligence tools may be leveraged in order to minimize the inspection effort and provide objective outcomes. In this context, timely detection of sensor malfunctioning is crucial in preventing inaccurate assessment and false alarms. The present work introduces a sensor-fault detection and interpretation framework, based on the well-established support-vector machine scheme for anomaly detection, combined with a coalitional game-theory approach. The proposed framework is implemented in two datasets, provided along the 1st International Project Competition for Structural Health Monitoring (IPC-SHM 2020), comprising acceleration and cable-load measurements from two real cable-stayed bridges. The results demonstrate good predictive performance and highlight the potential for seamless adaption of the algorithm to intrinsically different data domains. For the first time, the term "decision trajectories", originating from the field of cognitive sciences, is introduced and applied in the context of SHM. This provides an intuitive and comprehensive illustration of the impact of individual features, along with an elaboration on feature dependencies that drive individual model predictions. Overall, the proposed framework provides an easyto-train, application-agnostic and interpretable anomaly detector, which can be integrated into the preprocessing part of various SHM and condition-monitoring applications, offering a first screening of the sensor health prior to further analysis.