Digital Twin technology has been widely applied in various industry domains. Modern industrial systems are highly complex consisting of multiple interrelated systems, subsystems and components. During the lifecycle of an industrial system, multiple digital twin models might be created related to different domains and lifecycle phases. The integration of these relevant models is crucial for creating higher-level intelligent systems. The Cognitive Digital Twin (CDT) concept has been proposed to address this challenge by empowering digital twins with augmented semantic capabilities. It aims at identifying the dynamics and interrelationships of virtual models, thus to enhance complexity management capability and to support decision-making during the entire system lifecycle. This paper aims to explore the CDT concept and its core elements following a systems engineering approach. A conceptual architecture is designed according to the ISO 42010 standard to support CDT development; and an application framework enabled by knowledge graph is provided to guide the CDT applications. In addition, an enabling tool-chain is proposed corresponding to the framework to facilitate the implementation of CDT. Finally, a case study is conducted, based on simulation experiments as a proof-of-concept.