基于小波与灰色模型的滑坡时间预测预报

i摘要我国是世界上滑坡灾害最为严重的国家之一。滑坡灾害往往会造成严重的经济损失，威胁人民生命安全。据统计，我国有70多个城市，460多个县收到滑坡灾害的威胁及危害，每年平均至少造成15亿—23亿元的经济损失，由于近年来自然灾害增多，滑坡也相应增加。如果我们能够知道滑坡发生的时间，积极采取应对措施，就可以将滑坡危害降到最低，减少不必要的人员伤亡和经济损失。因此对滑坡时间进行预测预报研究具有十分重要的意义。本文基于以上目的，针对滑坡预测预报中存在的问题进行时间预测预报研究。本文主要通过对小波理论和灰色模型的介绍和研究，将小波降噪和灰色模型应用于滑坡时间预测预报。主要研究内容如下：（1）对滑坡时间预测预报及其发展趋势做了简单的介绍。介绍了滑坡监测技术和滑坡预测模型。（2）时间预测预报之前需要对观测的位移时间数据进行处理，去除噪声，以提高预测精度。本文选用小波的方法对滑坡观测的位移数据进行去噪处理。在此之前介绍了小波理论，小波函数和小波阈值的选取规则。后面通过选用不同的阈值来对滑坡数据进行降噪处理，并利用信噪比来比较降噪效果。（3）简单介绍灰色系统模型，利用matlab编写相应的程序。并利用灰色模型对已经降噪处理的数据进行时间预测，并分析结果。（4）把小波阈值降噪方法和灰色模型应用到新滩滑坡，对观测数据进行降噪处理并预测时间，并将结果与真实值进行对比分析。关键词：滑坡小波分析小波阈值灰色模型降噪时间预测iiAbstractChinaisoneofthecountrieswhichhavethemostseriouslandslidecalamityintheworld。Landslidecalamitycanalwayscauseseriouseconomiclosses,whichthreatensthesafetyofpeople'slife.Accordingtothestatistics,about70citiesand460countiesinourcountryhavebeenthreatenedanddamagedbythelandslidehazard.Asaresult,theeconomicusuallysuffersfromalossbetweenatleast1.5billionand2.3billioneveryyear.Asthenaturaldisastersincreaserecently,thelandslidesalsoincreaseaccordingly.Ifweknowthatthelandslideoccurredatcertaintimeandtakeactions,thenthelandslidehazardcanbereducedatmost,besideswecanreduceunnecessarycasualtiesandeconomiclosses.Consequently,researchofforecastingLandslide-timeissignificant.Basedonthepurposeabove,inthispaper,fortheproblemsinthepredictionoflandslide,wewillmakeadetailedresearch.AccordingtotheintroductionandstudyofwavelettheoryandGreymodel,waveletnoisereductionandGreymodelcanbeappliedtolandslideprediction.Themainresearchcontentsareasfollows:（1）Asuccinctintroductionofthelandslide-timepredictionanddevelopmenttendency,includingthelandslidemonitoringtechnologyandlandslidepredictionmodel.（2）BeforetheTimeprediction,Inordertoimprovepredictionaccuracy,itisnecessarytoprocessobserveddisplacementtimedataandremovenoise.Inthispaper,thetechniqueofwaveletisappliedtoremovethenoiseintheobservedlandslidedisplacementdata.Wavelettheory,waveletfunctionandtheselectionrulesofwaveletthresholdareproposedbefore,Thenconductnoisereductionforlandslidedatabydifferentthresholdvalues,besides,throughthesignaltonoiseratiotocomparetheresultofnoisereduction.（3）ProposingGreymodelsuccinctly,programmingbyMATLABandusingGreymodeltoestimatethetimeofthenoisereductivedata,thenanalyzingtheresults.（4）ApplythenoisereductionmethodforwaveletthresholdandGreymodeltothenewbeachlandslide,conductnoisereductionfortheobserveddataandestimateiiithetime,thencomparetheresultstothetruevalue.Keyword:Landslide;waveletanalysis;waveletthreshold;Greymodel;waveletdenosing;Timepredictioniv目录第一章绪论.................................................................................................................................11.1论文的研究背景...........................................................................................................11.2滑坡灾害时间预测预报及其发展趋势..................................................................21.3滑坡预测预报研究目的和意义...............................................................................41.4论文的主要内容............................................................................................................5第二章滑坡监测技术与预测模型.........................................................................................62.1滑坡监测技术...............................................................................................................62.2滑坡预报模型...............................................................................................................6第三章小波理论........................................................................................................................83.1小波变换..........................................................................................................................83.2小波变换原理与分类..................................................................................................93.2.1小波变换原理....................................................................................................93.2.2小波变换分类....................................................................................................93.3多分辨率分析.............................................................................................................133.4Mallat算法....................................................................................................................153.4.1Mallat算法综述...............................................................................................153.4.2Mallat分解算法...............................................................................................163.4.3Mallat合成算法...............................................................................................173.5常用的小波函数.........................................................................................................183.6小波变换用于信号降噪的原理.............................................................................223.6.1基本降噪模型与原理....................................................................................223.7非线性小波变换阈值法...........................................