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With regard to the traditional MGM (1, m) model having jumping error in solving process, an MGM (1, m) direct prediction model (denoted as DMGM (1, m) model) is proposed and its solution method is put forward at first. Second, considering the inherent time development trend of system behavior sequence is ignored in the DMGM (1, m) model, the DMGM (1, m) model is optimized by introducing a time polynomial term, and the optimized model can be abbreviated as TPDMGM (1, m,  φ ) model. Subsequently, it is theoretically proved that the TPDMGM (1, m,  φ ) model can achieve mutual transformation with the traditional MGM (1, m) model and the DMGM (1, m) model by adjusting the parameter values. Finally, two case studies about predicting the deformation of foundation pit and Henan’s vehicle ownership have been carried out to validate the effectiveness of proposed models. Meanwhile, the MGM (1, m) model and Verhulst model are established for comparison. Results show that the modeling performance of four models from superior to inferior is ranked as TPDMGM (1, m,  φ ) model, DMGM (1, m) model, MGM (1, m) model, and Verhulst model, which on the one hand testifies the correctness of defect analysis of the MGM (1, m) model and on the other hand verifies that the TPDMGM (1, m,  φ ) model has advantages in predicting the system variables with mutual relation, mutual restriction, and time development trend characteristic.

A Novel Multivariable MGM (1, m) Direct Prediction Model and Its Optimization