This paper proposes a novel anomaly detection methodology for industrial systems based on Digital Twin (DT) ecosystems. In addition to DTs, conceived as a digital representation of a physical entity, this paper proposes a new concept of DT focused on modeling connections between physical behaviors. This new DT concept is called Snitch Digital Twin (SDT). The scope of the SDT is the study of variations between behaviors and support the detection of anomalies between them. The behavior of each physical entity is characterized by three spatiotemporal features computed from each collected measurement. Behavioral anomalies are identified and quantified through modular patterns based on quantile regression and behavioral indexes. Finally, the robustness of the proposed methodology is assessed by comparing it with the other two commonly used algorithms based on Kernel Principal Component Analysis (KPCA) and One-Class Support Vector Machines (OCSVM) in a case study application. The case study is based on the diagnosis of the cooling system of a powergenerator diesel engine. The results obtained prove the advantages and goodness of this novel methodology compared to the two traditional algorithms.