Multi-coupled Electromechanical Systems (MES) are the important component of modern industry, their stable operation heavily relies on effective fault diagnosis. With the development of artificial intelligence technique, sufficient fault data plays an important role in MES's fault diagnosis, while is quite difficult to obtain in practices. In this regard, there is urgent need to generate the virtual fault data through the system simulation and improve the fault diagnosis performance, where the Digital Twin technique with superior virtual mapping capabilities for entity characteristics provides the potential opportunity. However, there is a lack of an effective method that can decouple the complicated MES entity and construct its full-system fault Digital Twin model. Aiming at the above target, we propose a hierarchical collaborative Digital Twin modeling method to implement the fault data generation. In order to structurally describe the complicated entity, MES is decoupled and identified as the multidimensional and multimodal triplet representations, namely, element, relationship, and data. Given the element and data, the hierarchical data-model combined technique is proposed to develop the four-level (space, behavior, process, and status) sub-Digital Twin models, to well balance the modeling adaptability and modeling precision during the local virtualization of MES. Thanks for the proposed collaborative orchestration algorithm, these heterogeneous sub-Digital Twin models are further interacted and integrated into the full-system Digital Twin according to the aforementioned relationship representation, which jointly constitutes the global mirror of the MES entity under various fault modes. We conducted the experiments to validate the proposed method by using a multi-coupled electromechanical fault test bench. The experimental results show that our method improved the accuracy of fault diagnosis by an average of 11.95%, which demonstrates its superiority in the fault data generation for the complicated entity such as MES.