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, ${\mathit{t}}^2$)) is proposed to overcome the deficiencies. BNGM(1,1, ${\mathit{t}}^2$) 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, ${\mathit{t}}^2$) are examined. BNGM(1,1, ${\mathit{t}}^2$) can show better performances than other multivariate prediction models including the recursive discrete multivariate grey prediction model. BNGM(1,1, ${\mathit{t}}^2$) is applied to four typical landslide case studies. The results indicate that the BNGM(1,1, ${\mathit{t}}^2$) has the best prediction accuracy. The complexity of BNGM(1,1, ${\mathit{t}}^2$) 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, ${\mathit{t}}^2$)-based method has a wide application potential to predict landslide displacement.

滑坡位移预测是减少滑坡灾害损失的重要组成部分。现有的预测滑坡位移的方法过于复杂，无法应用于工程实践。滑坡位移演化与灰色模型预测机制具有很好的一致性。然而，现有的灰色预测模型也存在一些缺点，包括忽略时间项。一种新的灰色预测模型，称为背景值优化非线性灰色预测模型（BNGM（1,1，${\mathit{Ť}}^2$））建议以克服这些缺陷。BNGM（1,1，${\mathit{Ť}}^2$）是包含时间项影响的单变量预测模型。积分法用于确定背景值，而最小值法用于获得时间响应函数的常数项。BNGM（1,1，${\mathit{Ť}}^2$）进行检查。BNGM（1,1，${\mathit{Ť}}^2$）可以显示比其他多元预测模型（包括递归离散多元灰色预测模型）更好的性能。BNGM（1,1，${\mathit{Ť}}^2$）应用于四个典型的滑坡案例研究。结果表明，BNGM（1,1，${\mathit{Ť}}^2$）具有最佳的预测精度。BNGM（1,1，${\mathit{Ť}}^2$）低于非线性灰色伯努利模型，Weibull–Bernoulli灰色模型和分数累积非线性灰色伯努利模型。综合结果的比较表明，BNGM（1,1，${\mathit{Ť}}^2$的方法具有广泛的预测滑坡位移的应用潜力。