A new grey prediction model and its application to predicting landslide displacement

Landslide displacement prediction is an important part of reducing landslide hazard losses. The existing methods to predict landslide displacement are too complicated to be applied to engineering practice. The landslide displacement evolution and the grey model prediction mechanism show a good consistency. However, the existing grey prediction model also has some shortcomings including neglecting time term. A new grey prediction model called the background value optimization nonlinear grey prediction model (BNGM(1,1, t2)) is proposed to overcome the deficiencies. BNGM(1,1, t2) is a univariate prediction model that incorporates the influence of the time term. The integration method is used to determine the background value, and the minimum value method is employed to obtain a constant term of time response functions. Five accuracy test methods for BNGM(1,1, t2) are examined. BNGM(1,1, t2) can show better performances than other multivariate prediction models including the recursive discrete multivariate grey prediction model. BNGM(1,1, t2) is applied to four typical landslide case studies. The results indicate that the BNGM(1,1, t2) has the best prediction accuracy. The complexity of BNGM(1,1, t2) is lower than the nonlinear grey Bernoulli model, the Weibull–Bernoulli grey model, and the fractional accumulation nonlinear grey Bernoulli model. The comparison of comprehensive results demonstrates that the BNGM(1,1, t2)-based method has a wide application potential to predict landslide displacement. •An improved grey prediction model BNGM(1,1, t2) is proposed.•Background value and constant in time response function is obtained by integral and derivative.•BNGM(1,1, t2) performs better than other grey models.•BNGM(1,1, t2) is successfully applied to predicting landslide displacement.