Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization

Nonlinear grey Bernoulli model (NGBM) is a novel grey forecasting model which is a simple modification of GM(1, 1) together with Bernoulli differential equation. This paper presents a new parameter optimization scheme of NGBM using the particle swarm optimization (PSO) algorithm. The power index of Bernoulli differential equation and production coefficient of the background value are considered as decision variables and the forecasting error is taken as the optimization objective. Parameter optimization of NGBM is formulated as the combinatorial optimization problem and would be solved collectively using PSO technique. Once the PSO finds the optimal parameters of NGBM, the model can be optimized. NGBM with this parameter optimization algorithm is then applied in long-term power load forecasting. Results show that NGBM has remarkably improved the forecasting accuracy and PSO is an effective global optimization algorithm suitable for the parameter optimization of NGBM.