Nonlinear Grey Bernoulli model NGBM (1, 1)'s parameter optimisation method and model application

In the grey prediction, the nonlinear Grey Bernoulli model NGBM (1, 1) is an important type. The NGBM (1, 1) has good adaptability to data fitting and then small prediction errors, and thus has been applied widely. However, if we improve the modelling method, the prediction precision shall be improved to some extent. The important factors of prediction error are the approximation of background value and the approximation of power exponent. Therefore, the paper tries to combine the optimisation of background value with the optimisation of the power exponent of NGBM (1, 1) model and then improves the model from parameter estimation. The paper gives three methods for the following three cases respectively: the background value in the form of exponential curve, the background value in the form of the polynomial curve and the background value in the form of interpolation function, to combine background value optimisation with power exponent optimisation for parameter optimisation. The final section of the paper builds the NGBM (1, 1) models of China's GDP and energy consumption with three improvement methods. The simulation and prediction results show the three improvement methods all have high precision. The methods given offer good approaches for the in-depth study on nonlinear grey Bernoulli model, enrich the method system of grey modelling and can be applied to the studies on other grey models to promote the study and wide application of the grey model.