Research on the prediction model of agricultural drought hazard considering the time-delayed cumulative effect and system development characteristics.

Agricultural drought hazard is a complex time-delayed system affected by multiple hazard factors. The ability to estimate agricultural drought hazard accurately is crucial for guaranteeing food security. A TDMGM(1,m,N) prediction model coupling the time-delayed cumulative driving effect of multi-factor and the development characteristics of multi-system is constructed by introducing the time-delayed driving term and simultaneous formula with the goal of solving the problem of multivariate time-delayed prediction modeling of agricultural drought hazard. The definition form and derivation form of the TDMGM(1,m,N) model are given under the two cases of small and large variations of relevant variables, and the nonlinear solutions of the optimal delay parameters are given by using the fmincon function in Matlab. The solution method for model parameter estimation is also provided. It is proved that GM(1,1), GM(1,N), time-delayed GM(1,N), MGM(1,m) and MGM(1,m,N) are all special forms of TDMGM(1,m,N) model. The effect of multiplier transformation on model parameters, simulation prediction value, and model accuracy is also investigated. Finally, the TDMGM(1,m,N) model is applied to predict agricultural drought hazard in Henan Province. The findings demonstrate that the model can address the prediction problem of multiple system characteristic variables when multiple relevant variables exhibit time-delayed properties with good fitting and prediction accuracy.