基于胞映射理论的岩体动力系统可预测尺度模型
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摘要
岩体混沌动力系统演化过程的可预测尺度是非线性预测理论研究的重要内容。在利用传统的理论和方法分析实际问题时 ,常常由于观测资料不足而无法计算岩体动力系统的可预测尺度。为了解决这一问题 ,基于胞映射理论提出了一种新的岩体动力系统可预测尺度的计算模型。该模型基于系统的非线性动力学方程和随机过程理论 ,将点到点的映射转化成胞到胞的映射 ,以系统演化达到极限状态概率分布前的时段作为系统的可预测尺度 ,消除了初值观测误差和系统离散化对系统造成的影响 ,从而可以更精确地描述系统的混沌性本质。实例的应用也表明了这一点
Predictable time scale of the evolution of chaotic rock mass dynamic systems is one of the most important parameters in nonlinear forecasting theory. However, the predictable time scale of most rock mass dynamic systems can't be calculated because of lack of the observing data. In order to solve this problem, a new model to calculate the predictive time scale of rock mass dynamic system was proposed using the cell mapping theory. The model transforms the point to point mapping to cell to cell mapping using the nonlinear dynamic equation of system and stochastic process theory, and considers period of time before evolution of system reaches to the limit probability distribution as the predictable time scale of system. The model eliminates the influences of error of initial conditions and dispersal on the evolution of system, so chaotic essence of system can be characterized more accurately which is also proved by the example. Case study indicates these advantages.
Predictable time scale of the evolution of chaotic rock mass dynamic systems is one of the most important parameters in nonlinear forecasting theory. However, the predictable time scale of most rock mass dynamic systems can't be calculated because of lack of the observing data. In order to solve this problem, a new model to calculate the predictive time scale of rock mass dynamic system was proposed using the cell mapping theory. The model transforms the point to point mapping to cell to cell mapping using the nonlinear dynamic equation of system and stochastic process theory, and considers period of time before evolution of system reaches to the limit probability distribution as the predictable time scale of system. The model eliminates the influences of error of initial conditions and dispersal on the evolution of system, so chaotic essence of system can be characterized more accurately which is also proved by the example. Case study indicates these advantages.
引文
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[16] HsuCS .Globalanalysisofdynamicsystemsusingposetsanddigraphs[J].IntJofBifurandChaos,1995,5(4):1085-1118
[2] 秦四清,张倬元,王士天,等.非线性工程地质学导引[M ].成都:西南交通大学出版社,1993.109-110. QINSi qing,ZHANGZhuo yuan,WANGShi tian,etal.AnIntroductiontoNonlinearEngineeringGeology[M ].Chengdu:SouthwesternJiaotongUniversityPress,1993.109-110.
[3] XieH ,PariseauWG .Fractalcharacterandmechanismofrockbursts[J].IntJRockMechMinSci,1993,30(4):343-350.
[4] FengXia ting,SetoM .Fractalstructureofthetimedis tributionofmicrofracturinginrocks[J].GeophysJInt,1999,136:257-285.
[5] 陈子林,周硕愚.蕴震系统前兆场的混沌吸引子及分维[J].地震学报,1993(4):463-469. CHENZi lin,ZHOUShuo yu.Chaoticattractorandfractalofearthquakeprecursors[J].JournalofSeism,1993(4):463-469.
[6] 安镇文,王林瑛,姚栋华,等.大震孕育过程中的混沌特征[J].地震学报,1992(4):393-399. ANZhen wen,WANGLin ying,YAODong hua,etal.Chaosintheprocessofgreatearthquake[J].JournalofSeism,1992(4):393-399.
[7] HirataT ,etal.Fractalstructureofspatialdistributionearthquake the two pointcorrelationfunction[J].Geo physJRAstronSoc,1980,62:303-320.
[8] 周 辉.矿震孕育过程中的混沌性及非线性预测理论研究[D].沈阳:东北大学,2000.31-56. ZHOUHui.ChaosandNonlinearForecastingTheoryintheProcessofMineQuake[D].Shenyang:NortheasternUniversity,2000.31-56.
[9] 周 辉,冯夏庭,谭云亮,等.矿震系统的胞映射突变预测模型[J].中国有色金属学报,2002,12(1):155-160. ZHOUHui,FENGXia ting,TANYun liang,etal.Cell mapping catastrophicforecastingmodelofminequakesystem[J].TheChineseJournalofNonferrousMetals,2002,12(1):155-160.
[10] WolfA .Determininglyapunovexponentsfromtimese ries[J].Physica,1988,16D :285.
[11] HsuCS .Atheoryofcell to cellmappingdynamicssys tems[J].ASMEJApplMech,1980,47:931-93[12] HsuCS ,GuttaluRS .Anuntravellingalgorithmforglobalanalysisofdynamicalsystems:anapplicationofcell to cellmappings[J].ASMEJourApplMech,1980,47:940-948.
[13] HsuCS .Generalizedtheoryofcell to cellmappingfornonlineardynamicalsystems[J].JourApplMech,1981,49:634-642.
[14] HsuCS ,GuttaluRS ,ZhuWH .Amethodofanalyz inggeneralizedcellmappings[J].ASMEJourApplMech,1982,49:885-894.
[15] HsuCS .Aprobabilistictheoryofnonlineardynamicalsystemsbasedoncellstatespaceconcept[J].ASMEJourApplMech,1982,49:895-902.
[16] HsuCS .Globalanalysisofdynamicsystemsusingposetsanddigraphs[J].IntJofBifurandChaos,1995,5(4):1085-1118
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