Abstract: A novel multi-variable MGM(1,m) self-memory coupled system model is presented for use in multi-variable systems with interactional relationship under the condition of small sample size. The proposed model can uniformly describe the relationships among system variables and improve the modeling accuracy. The model combines the advantages of the self-memory principle of dynamic system and traditional MGM(1,m) model through coupling of the above two prediction methods. The weakness of the traditional grey prediction model, i.e., being sensitive to initial value, can be overcome by using multi-time-point initial field instead of only single-time-point initial field in the system's self-memorization equation. As shown in the case study of foundation pit deformation prediction, the novel model can take full advantage of the system's multi-time historical data and accurately predict the system's evolutionary trend. And it prominently possesses higher accuracy of simulation and prediction than the traditional multi-variable MGM(1,m) model. The results show that the proposed model enriches and perfects grey prediction theory, and can be applied to other similar multi-variable engineering systems.

Key words: multi-variable system, MGM(1,m) model, self-memory principle, coupled system, foundation pit deformation