An adaptive non-equidistant grey model with four parameters and its applications in deformation monitoring

The processing and analysis of deformation monitoring data, as well as the establishment of effective forecasting models, form the foundation for assessing whether deformation is within a safe range and for selecting appropriate preventive and disaster reduction measures. Conventional forecasting models are difficult to accurately forecast future phenomena by analyzing deformation data with non-equidistant characteristic, so a non-equidistant grey model has emerged. The article optimizes the traditional non-equidistant grey model from three aspects, thus proposing an adaptive non-equidistant grey model with four parameters, which contains nonlinear and linear terms as well as stochastic perturbation term. First, the nonlinear function is used as a new grey action quantity in order to comprehensively reflect the grey information that affects the development of the system. Second, the particle swarm optimization algorithm is used to optimize the background value so that it can be adaptively adjusted according to the sequence characteristics as well as to obtain a mutually matching model structure based on the integral theory. Third, the optimal selection of initial value with the minimum relative error sum of squares as the objective function further enhances the model optimization. Finally, the model is applied to forecast three kinds of deformation monitoring for high-rise building settlement, highway soft soil roadbed settlement, and mining area GNSS settlement. The results show that the performance of the novel model is significantly better than the existing model, thus verifying its effectiveness and superiority.