Traditional structural health monitoring (SHM) based on contact sensors has drawbacks, such as high cost, susceptibility to interference, and narrow coverage. Digital twins (DTs) present an effective intelligent solution. However, the real-time monitoring of all structural components remains challenging due to high computational cost of high-order models in underlying framework. Additionally, the vast number of spatial structures globally and their long service time indicate the potential necessity of introducing SHM based on DT. In this context, this study proposed a reduced-order model-based DT framework for spatial structures. By compressing the experimental design samples, the multidimensional high-order physical models were reduced to several approximate low-order models for constructing a DT model, thereby achieving real-time calculation covering all components. The proposed framework was applied and validated through an experiment on a scale model of cable dome structure, and real-time interactive visualisation of monitoring data was displayed on a self-developed platform. The results demonstrate that the DT model enabled real-time presentation of calculation results (the calculation speed of <0.5 s/time), the mean relative error of cable tension monitoring was <3.85%, the strut stress monitoring could be controlled within 7.5%, and the mean absolute error of nodal displacement could be maintained at around 1 mm.