Accurate differentiation between damage-related anomalies and data errors is a critical challenge in bridge monitoring. This paper presents a data-driven framework for anomaly detection and classification, addressing the question: How can anomalies be classified in multi-sensor bridge monitoring to distinguish structural changes from noise? The framework combines an adapted anomaly taxonomy with a deep neural network trained on synthetic data. It is validated using long-term monitoring data from a railway bridge, incorporating strain gauges, accelerometers, and an inclinometer. In offline training, the model achieves high precision, recall, and F1-scores, effectively detecting anomaly classes across sensor types. For online prediction, it provides anomaly type percentages and visualizations over daily, weekly, and annual timeframes, distinguishing frequent noiserelated anomalies from rare anomalies signaling structural changes. Requiring one month of training data, the framework delivers a scalable solution for bridge monitoring and lays the groundwork for future self-learning anomaly detection in infrastructure management.