基于复化Simpson公式改进的灰色神经网络组合模型对国民总收入的预测

The Grey Neural Network Combination Model Based on Complex Simpson Formula is Used to Predict the Gross National Income of China

针对我国国民总收入数据具有非线性、随机性等特点,本文建立复化Simpson公式改进的灰色神经网络组合预测模型来对我国国民总收入进行预测研究。首先,建立了GM(1,1)模型和基于复化Simpson积分公式改进背景值的GM(1,1)模型。其次,建立了BP神经网络预测模型。进一步,将复化Simpson公式改进的GM(1,1)模型和BP神经网络预测模型进行最优线性加权组合,运用最小二乘法思想,误差平方和最小为目标函数,结合遗传算法求解目标函数,得到各模型的加权系数,以提高预测精度。最后,对比分析GM(1,1)模型、复化Simpson公式改建的GM(1,1)模型、BP神经网络模型和复化Simpson公式改进的灰色神经网络模型对国民总收入预测的结果。从预测结果看出,复化Simpson公式改进的灰色神经网络模型对国民总收入的预测明显优于其他预测模型。

Aiming at the non-linearity andrandomness of China's gross national income data, this paper establishes a greyneural network combined forecasting model which is improved by using the complexSimpson formula to predict China's gross national income. Firstly, the GM(1,1)model and the GM(1,1) model based on the complex Simpson integral formula to improvethe background value are established. Secondly, a BP neural network predictionmodel is established. Furthermore, the GM(1,1) model and the BP neural networkprediction model improved by the complex Simpson formula are optimally linearlyweighted, and the objective function is solved by using the genetic algorithmto obtain the objective function with the smallest squared error sum. Weightingfactors are to improve prediction accuracy. Finally, the GM(1,1) model, theGM(1,1) model of the modified Simpson formula, the BP neural network model andthe improved gray neural network model of the modified Simpson formula are usedto compare the results of the gross national income forecast. From theprediction results, the gray neural network model improved by the complex Simpsonformula is significantly better than the GM(1,1) model, the GM(1,1) model ofthe modified Simpson formula and the BP neural network model.