Design of Fractional Verhulst Model for Displacement Prediction of Landslide Based on the Optimization of Beetle Antennae Search Algorithm

Landslides significantly impact economic development and public safety. Aiming at the problem of insufficient prediction accuracy of the displacement data series of the traditional grey Verhulst model, this paper proposes a fractional Verhulst model optimized using the beetle tentacle search algorithm. First, based on the grey Verhulst model, a fractional order operator is introduced to accurately adjust the magnitude between cumulative values, constructing a fractional order-based grey Verhulst model. Expanding the accumulative order range improves prediction performance. Second, the fractional operator is optimized. The beetle antennae search algorithm finds the optimal fractional order between 0 and 1 in the grey Verhulst model, minimizing average relative error. Finally, using Heifangtai landslide group displacement data from Gansu Province, simulation experiments verified that the model has higher fitting accuracy and prediction effect than the traditional grey Verhulst model, Huang's improved Verhulst model, GM (1,1) model, cubic exponential smoothing model, and DGM (2,1) model. The average relative error is 2.949 %. Results show that the beetle antennae search algorithm optimized fractional order grey prediction model significantly improves fitting and prediction effect on data. The optimized fractional Verhulst model is more suitable for predicting landslide displacement deformation.