The complexity of systems like bridges increases the risk of undetected damage, potentially causing catastrophic failures. Structural Health Monitoring (SHM) is essential for timely maintenance, reducing repair costs, and saving lives, but it faces measurement uncertainties due to aging or sensor failures. This paper presents a novel SHM framework to identify sensor malfunctions in the presence of structural damage, exclude faulty sensors, and maintain high confidence in a low level of epistemic uncertainty for measured and derived data. The framework evaluates consistency among data sources and considers combinatorics within the sensor network to collect evidence for levels of uncertainty. Sensor errors are mapped to α-levels, forming probability distributions to assess expected level of epistemic uncertainty and exclude compromised sensors based their contribution in reducing or increasing uncertainty. A realistic case study on a 9-meter steel lattice mast with synthetic data from a validated Finite Element model demonstrates the methodology.