最佳灰色回归组合模型及其在中国火灾预测中的应用

火灾每年给国家和人民生命财产造成巨大损失.火灾现象具有随机性、模糊性,是个复杂的灰色系统行为.研究火灾发生规律及发展趋势,具有实用价值.为此,首先给出最小二乘估计(LSE)意义下的最佳组合预测模型的定义,并求得组合模型的权的公式和证明权的唯一性.其次,用回归分析方法建立多个回归模型,并按以下三条标准:①回归指数(或相关系数)r大、②系统误差s小、③模型精度p高,选定最佳非线性回归模型;用灰色理论建立多个灰色模型,并按以下三条标准:①后验差比值c小、②小误差概率P大、③预测关联度ξ大,选定最佳灰色模型;再用最小二乘法将最佳回归模型与最佳灰色模型有机地结合起来建立的中国火灾最佳灰色回归组合预测模型.最佳灰色回归组合预测模型综合利用前两者提供的不同的有用信息,改善了单一模型的局限性,提高了模型的预测精度,减少了预测误差,使预测效果更佳.组合模型预测中国年火灾起数处于动态增长过程.

An Optimal Grey-Regression Combinatorial Model and Its Applications in China Fire's Forecasting

Every year fire causes enormous losses to people in many Countries.Fire is a complex action of Grey system with random and fuzzy complexity.It is of practical value to study the rule of fire occurrence and its evolutional trend.Therefore,firstly the definition of the optimal combinatorial forecasting model was given in the sense of least square estimate and find out the expression of weight of the above mentioned model,and to prove it to be unique;then the optimal nonlinear regression forecasting model was selected by establishing several regression models by means of regression analysis and in accordance to the following three standards:① index of correlation (the major),② error of system(the minor),③ precision of model(the major),and the optimal gray forecasting model was selected by establishing several gray models by means of gray theory,and in accordance with the following three standards: ① quotient of square error(the least),② probability of residual error(the major),③ forecasting relative degree(the major);and finally an optimal combinatorial forecasting model for fire in China has been established through combining the Grey and regression models by means of linear least square algorithms.The combinatorial forecasting model combines the two sources of information together,thus improving and expanding the corresponding field for Grey model & regression model,and making the results better and accurate.The combinatorial model forecasts that fire in China occurs on a dynamic increase trend year after year.