灰色时序组合模型及其在地下水埋深预测中的应用  

Application of Grey AR Combination Model in the Prediction of Ground Water Depth

作　　者：赵文举[1] 马孝义[1] 李军利[2] 张建兴[1] 

机构地区：[1]西北农林科技大学旱区农业水土工程教育部重点实验室,陕西杨凌712100 [2]陕西省泾惠渠管理局,陕西三原713800

出　　处：《数学的实践与认识》2008年第18期70-76,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(50479052);国家科技支撑计划课题(2006BAD11B04);西北农林科技大学青年学术计划资助课题

摘　　要：地下水埋深的变化过程是一个复杂的非线性过程,这种具有复杂的非线性组合特征的序列,使用某一种模型进行预测,结果往往不理想.在分析了灰色GM(1,1)模型、灰色GM(1,1)周期性修正模型和时序AR(n)模型的优点和缺点基础上,提出了一种新的灰色时序组合预报模型.该方法利用了GM预测所需原始数据少、方法简单的优点,用周期修正方法反映其地下水位埋深周期性波动的特征,用AR(n)模型预报其地下水位埋深的随机变化.实例研究表明,这种方法方便简洁实用且预测结果接近于实际观测值,为其它地区的地下水位埋深和相关时间序列的分析研究提供参考与借鉴作用.The change process of ground water table with time is a complex non-linear process, so it makes the load variations to possess complex nonqinear combined character. For such a suite with the character of complex non-linear combination, it is very difficult to get a satisfying forecasting results by any single model. On the base of analyzing the advantage and disadvantage of GM （1,1） model, GM （1,1） periodical modified model and AR（n） model for the failure forecasting, a new grey AR combination forecasting model was put forward by combining these three models. This method utilze the advantages of GM forecasting method, such as it is simple and needs less original data, periodic modified method is used to predict the periodicity character of ground water depth, and the AR（n） model is also adopted to predict the random item of ground water depth. The test results show that this method is convenient and practical, the predicted values are close to the real ones. The method can offer new references for similar researches on ground water depth in other regions and the analysis of other time series.

关 键 词：GM(1 1) 时序模型(AR) 组合预测模型 地下水埋深预测 

分 类 号：P641.7[天文地球—地质矿产勘探] O211.61[天文地球—地质学]