灰色预测模型及其在电力需求中的应用

西安建筑科技大学硕士论文灰色预测模型及其在电力需求中的应用专业：应用数学硕士生：刘苗指导老师：燕列雅副教授摘要灰色系统理论是中国著名学者邓聚龙教授创立的，以部分信息已知、部分信息未知的不确定性系统为研究对象.灰色预测模型是灰色系统理论的重要内容之一，已被广泛应用于经济、工业、农业等各领域.因此，对灰色预测模型的研究有着重要的意义.本文以灰色系统理论为基础，以GM(1,1)模型为核心，进而对灰色预测模型进行研究.一方面，在原模型背景值优化的基础上，进一步对其残差模型进行优化，通过实例比较，优化的残差GM(1,1)模型可以有效地提高预测精度；另一方面，鉴于马尔科夫模型和灰色预测模型都可直接应用于相关时间序列的预测，将马尔科夫模型与灰色预测模型结合，既发挥了灰色预测模型少数据、短时间、小波动的优势，又体现了马尔科夫模型适用于随机波动较大问题的特点，在此基础上，考虑到原GM(1,1)模型中背景值的构造会影响模型的预测精度，本文采用改进背景值的GM(1,1)模型与马尔科夫模型组合，以期提高模型精度，从而实现不同模型之间的互补.作为该方法的应用，本文对陕西省全社会及居民生活用电需求进行了预测，结果表明，将改进背景值的GM(1,1)模型与马尔科夫模型组合后，预测精度比较高，且计算过程较简单，其结果可以为陕西省未来几年的电力需求提供一定的参考依据.电力需求会受到国内生产总值、电价等诸多因素的影响.本文通过灰色关联分析，从外在因素和内部结构两个角度对陕西省电力需求结构及其影响因素进行了剖析，具有实际意义，可供电力部门参考.关键词：GM(1,1)模型；马尔科夫链；背景值；灰马尔科夫模型；灰色关联分析西安建筑科技大学硕士论文西安建筑科技大学硕士论文GreyForecastingModelandItsApplicationinElectricPowerDemandsSpeciality:AppliedmathematicsName:LiuMiaoInstructor:A.P.YanLieyaABSTRACTThegreysystemtheoryisfoundedbyProfessorDengJulongwhoisthefamousscholarinChina.，theresearchobjectofwhichistheuncertaintysystemthatpartialinformationisknownandsomeisunknown.Greyforecastingmodelisoneoftheimportantcontentinthegreysystemtheory,whichhasbeenwidelyappliedintheeconomy,industry,agriculture,biologicalandsoon.Therefore,thestudyofthegreyforecastingmodelhasimportantsignificance.Inthispaper,thegreyforecastingmodelwasstudiedwithGM(1,1)modelasthecoreandbasedongreysystemtheory.Ontheonehand,theresidualmodelwasoptimizedbasedonthebackgroundvalueoptimizationoftheoriginalmodel.Bycomparingtheexample,theaccuracyofthepredictioncanbeimprovedbytheoptimizationoftheresidualGM(1,1)modeleffectively.Meanwhile,inviewofthegreyforecastingmodelandMarkovamodelcanbeusedinpredictionofrelatedtimeseriesdirectly,thecombinationsofthegreyforecastmodelandMarkovanotonlyplayedtheadvantageofalittlegraypredictionmodeldata,ashortperiodoftime,smallfluctuations,butalsoembodiesthecharacteristicsthatMarkovmodelisapplicabletorandomfluctuations.Basedonthissituation,takingintoaccountthestructureofthebackgroundvalueintheoriginalGM(1,1)modelaffectedtheprecisionofthemodel,thecombinationofGM(1,1)modelthatimprovedthebackgroundvalueofandtheMarkovmodelwasstudiedinthispaper,inordertoimprovethemodelprecision,soastoachievecomplementaritybetweenthedifferentmodels.Astheapplicationofthemethod,electricitydemandofthewholesocietyofShaanxiProvinceandtheresidentialwasforecastedinthispaper,theresultsshowedthatthepredictionaccuracyofimprovedgrayMarkovmodelisrelativelyhigh,andthecalculationprocessisrelatively西安建筑科技大学硕士论文simple.TheresultscanprovidesomereferenceforelectricitydemandofShaanxiProvince,inthenextfewyears.ThepowerdemandwillbeaffectedbytheGDP,thepriceandotherfactors.Inthispaper,electricitydemandofShaanxiProvinceanditsinfluencingfactorswereanalyzedbythegrayrelationalanalysis,fromtwoanglesontheexternalfactorsandinternalstructure.Thestudyhaspracticalsignificanceandcanprovidesomereferencefortheelectricitydemand.Keywords:GM(1,1)model;Markovachain;thebackgroundvalue;thegreyMarkovamodel;greycorrelationanalysis西安建筑科技大学硕士论文I目录1绪论..............................................................................................................................11.1研究背景及意义................................................................................................11.2研究历史及研究现状........................................................................................11.3本文研究的主要目的与内容............................................................................42灰色系统基本理论......................................................................................................52.1灰色系统的基本概念与原理............................................................................52.1.1概念...........................................................................................................52.1.2基本原理...................................................................................................52.2GM(1,1)模型的建模过程...................................................................................62.2.1建模思想...................................................................................................62.2.2GM(1,1)模型的建立..................................................................................62.3残差GM(1,1)模型.............................................................................................72.4GM(1,1)模型的探讨...........................................................................................92.4.1GM(1,1)模型的的适用范围......................................................................92.4.2模型的检验分析.......................................................................................92.5灰色关联分析..................................................................................................112.5.1灰色关联分析概述.................................................................................112.5.2灰色关联分析方法.................................................................................112.5.3优势分析.................................................................................................123灰色预测模型.....................................................