【摘要】 根据灰色新息优先利用思想,定义新的累加生成,与灰色离散模型结合,构建出新息优先累加生成的灰色离散模型(NIPDGM(1,1))。在四种误差准则下,给出了参数优化方法。进一步利用数值模拟,研究NIPDGM(1,1)模型在不同误差最小化下对信息的重视程度,分析表明在序列累加生成过程中,四种优化形式对信息的重视较为一致。在实证部分,以高速公路软土路基沉降以及江苏省能源消费问题为例,分析NIPDGM(1,1)模型的建模精度,结果表明:在NIPDGM(1,1)实证模型中,不同误差优化方式对信息的重视程度与数值实验结论相符;与GM(1,1,t2)、反向累加GOM(1,1)、倒数累加GRM(1,1)、GM(1,1)、DGM(1,1)、无偏GM幂模型相比,NIPDGM(1,1)对路基沉降的建模精度更优;与RBF神经网络、灰色累加生成RBF神经网络(GRBF)、支持向量机(SVM)、灰色累加生成支持向量机(GSVM)相比,NIPDGM(1,1)对能源消费的模拟误差大些,但预测误差更小,表明新模型具有更好的泛化能力。更多还原

【Abstract】 The accumulated generation is an important part of grey prediction model,which helps mine information and finds the rule in sequence.According to the axiom of new information priority using in grey systems,new accumulated generation operator with parameter is defined,and then the new information priority accumulated grey discrete model(NIPDGM(1,1))is constructed.Based on four kinds of error minimization criterions(mean squared error,mean absolute error,mean relative squared error,and mean absolute percentage error),the parameters optimization steps are presented.Through numerical simulating,the information weight in NIPDGM(1,1)model with different error criterions is studied.The result shows that the four kinds of optimization form for information weight are almost identical in sequence accumulated generation process.In the empirical analysis,expressway soft soil roadbed settlement and energy consumption problems in Jiangsu province are taken as examples,and the NIPDGM(1,1)modeling is used for two cases.In order to compare the modeling accuracy of new model,other grey model and some artificial intelligence models are also adopted for two cases,such as grey model(GM(1,1)),grey opposite model(GOM(1,1)),grey reciprocal model(GRM(1,1)),discrete grey model(DGM(1,1)),radial basis function(RBF)neural network,support vector machine(SVM)and so on.The results show that the information weights(or the parameter in accumulated generation)are not subjected to the different error minimization methods,which is consistent with the numerical simulating experiment.Compared with GOM(1,1)model,GRM(1,1)model,GM(1,1)model,DGM(1,1)model,grey model with time power(GM(1,1,t2)),and unbiased GM(1,1)power model,NIPDGM(1,1)model has a higher modeling precision in simulating and forecasting period for roadbed settlement.Among RBF neural network,grey accumulation generation RBF neural network(GRBF),support vector machine(SVM),grey accumulated generation support vector machine(GSVM)and NIPDGM(1,1)model for energy consumption modeling,the NIPDGM(1,1)model has a lager error in simulating period,but the smaller error in forecasting period,which indicates that the NIPDGM(1,1)model exhibits better generalization ability.The new accumulated generation operator can also be combined with other grey model,so as to enhance the model accuracy.更多还原