泥石流数学模型构建及危险性评价研究
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摘要
泥石流是一种常见的自然灾害现象,具有爆发时间短、破坏力强、群发性高等特点,不仅直接威胁到人民的生命和财产安全,而且严重地阻碍了社会的进步和经济的可持续发展。本文基于水动力学基本理论来建立泥石流数学模型,并基于粗糙集理论构建泥石流危险性评价模型,用所建立的模型来预测泥石流的发生情况以及对泥石流危险度等级进行判定,可以为泥石流预警预报提供技术支持,具有重要的理论意义和实际应用价值。
本文以实时降雨过程为前提,基于水动力学基本理论,以降雨、地表汇流、河道径流等因素作为泥石流形成的驱动力,以泥沙起动理论作为泥石流发生的起动条件,以广西五个市(县)的行政区域为地域边界,建立了综合考虑地形条件、地质条件、气候水文条件、植被情况、人口分布等影响因子的泥石流数学模型。模型中通过程序实现计算区域网格自动化划分,通过GIS技术和差值模式进行地形的数字化处理,利用不同编码进行地质条件的模化,通过河道、网格及通道的切割形成网格的数字化河网等。将数学模型的计算结果与同一时期计算区域内的实际地质灾害图进行分析比较,验证了泥石流数学模型的可行性。
本文以粗糙集理论中的知识及知识库、不可分辨关系、上下近似集、属性约简、属性值约简、知识依赖度、属性重要度等概念为理论基础,将范例推理技术、相似系统相似度与粗糙集理论相结合,以云南37条泥石流沟的统计资料作为源数据,构建了基于粗糙集理论的泥石流危险性评价模型。模型中将一次泥石流可能最大冲出量、泥石流发生频率、流域面积等十个因素作为评价的影响因子,给出了一种综合权重的方式计算影响因子权值的方法,利用范例相似度最大原则来探讨目标范例与源范例的关系。应用所建立的模型来确定待评定的泥石流沟危险度等级,通过计算结果与实际值的分析比较,验证危险性评价模型的可行性。最后将综合权重计算的方法引入到数学模型中确定影响因子权值,通过计算结果与实际值的比较来验证权值的修正情况。
Debris flow is a kind of natural disaster that burst in a short time with powerful damage. It occurs frequently in mountain areas after heavy rain. Debris flow directly threatens the security of human’s lives and properties and seriously impedes the sustainable development of the social economic. This article presents a mathematical model of debris flow based on the basic hydrodynamic theory and a risk assessment model of debris flow based on rough set theory. The mathematical model is used for forecasting the debris flow and the risk assessment model is adopted to predicate the danger degree of the debris flow,which are both have important theoretical significance and practical application value.
The hydrodynamic mathematical model is established based on the basic hydrodynamic theory and the real time rainfall process. In this model, the theory of incipient motion of sediment is considered as the motion conditions of debris flow and five cities' administrative areas of Guangxi province are considered as the region boundary. Many factors such as geography, geology, climate and hydrology, vegetation and population are also considered in this mathematical model. Fortran programming generates the calculating meshes, GIS technique digitizes the geography information, various coding methods are applied to simulate the geology condition, and the river channels are combined together with the mesh channels. By comparing the simulated results with those obtained from geology disaster distribution chart, the mathematical model is proved to be credible.
This article builds a risk assessment model of debris flow not only based on many concepts of the rough set theory such as knowledge and knowledge base, indiscernibility relation, upper and lower approximation, reduction, reduction of values, dependency graph of knowledge, importance of attribute, but also based on case based reasoning, similarity degree of similarity system. In this model, data comes from statistical data of thirty-seven debris flow ditch of Yunnan. The amount of debris flow, frequency of debris flow, valley covers, and other three impact factors are considered as the influencing factors of debris flow in this article. The paper calculates the weights of impact factors based on rough set theory. By comparing the simulated results with those obtained from the measured value, the risk assessment model is proved to be credible. Finally,the calculation method of synthesized weights is introduced to mathematical model to calculate the weight of impact factors,comparing calculated results and actual value to verify the correction weights.
本文以实时降雨过程为前提,基于水动力学基本理论,以降雨、地表汇流、河道径流等因素作为泥石流形成的驱动力,以泥沙起动理论作为泥石流发生的起动条件,以广西五个市(县)的行政区域为地域边界,建立了综合考虑地形条件、地质条件、气候水文条件、植被情况、人口分布等影响因子的泥石流数学模型。模型中通过程序实现计算区域网格自动化划分,通过GIS技术和差值模式进行地形的数字化处理,利用不同编码进行地质条件的模化,通过河道、网格及通道的切割形成网格的数字化河网等。将数学模型的计算结果与同一时期计算区域内的实际地质灾害图进行分析比较,验证了泥石流数学模型的可行性。
本文以粗糙集理论中的知识及知识库、不可分辨关系、上下近似集、属性约简、属性值约简、知识依赖度、属性重要度等概念为理论基础,将范例推理技术、相似系统相似度与粗糙集理论相结合,以云南37条泥石流沟的统计资料作为源数据,构建了基于粗糙集理论的泥石流危险性评价模型。模型中将一次泥石流可能最大冲出量、泥石流发生频率、流域面积等十个因素作为评价的影响因子,给出了一种综合权重的方式计算影响因子权值的方法,利用范例相似度最大原则来探讨目标范例与源范例的关系。应用所建立的模型来确定待评定的泥石流沟危险度等级,通过计算结果与实际值的分析比较,验证危险性评价模型的可行性。最后将综合权重计算的方法引入到数学模型中确定影响因子权值,通过计算结果与实际值的比较来验证权值的修正情况。
Debris flow is a kind of natural disaster that burst in a short time with powerful damage. It occurs frequently in mountain areas after heavy rain. Debris flow directly threatens the security of human’s lives and properties and seriously impedes the sustainable development of the social economic. This article presents a mathematical model of debris flow based on the basic hydrodynamic theory and a risk assessment model of debris flow based on rough set theory. The mathematical model is used for forecasting the debris flow and the risk assessment model is adopted to predicate the danger degree of the debris flow,which are both have important theoretical significance and practical application value.
The hydrodynamic mathematical model is established based on the basic hydrodynamic theory and the real time rainfall process. In this model, the theory of incipient motion of sediment is considered as the motion conditions of debris flow and five cities' administrative areas of Guangxi province are considered as the region boundary. Many factors such as geography, geology, climate and hydrology, vegetation and population are also considered in this mathematical model. Fortran programming generates the calculating meshes, GIS technique digitizes the geography information, various coding methods are applied to simulate the geology condition, and the river channels are combined together with the mesh channels. By comparing the simulated results with those obtained from geology disaster distribution chart, the mathematical model is proved to be credible.
This article builds a risk assessment model of debris flow not only based on many concepts of the rough set theory such as knowledge and knowledge base, indiscernibility relation, upper and lower approximation, reduction, reduction of values, dependency graph of knowledge, importance of attribute, but also based on case based reasoning, similarity degree of similarity system. In this model, data comes from statistical data of thirty-seven debris flow ditch of Yunnan. The amount of debris flow, frequency of debris flow, valley covers, and other three impact factors are considered as the influencing factors of debris flow in this article. The paper calculates the weights of impact factors based on rough set theory. By comparing the simulated results with those obtained from the measured value, the risk assessment model is proved to be credible. Finally,the calculation method of synthesized weights is introduced to mathematical model to calculate the weight of impact factors,comparing calculated results and actual value to verify the correction weights.
引文
[1]张丙午译.世界自然灾害事件统计[J].新疆气象,1995,18(6):57-58.
[2]高建国,聂高众.1990~1995年世界各国(地区)自然灾害对比[J].地学前缘,1996,3(1-2):219-229.
[3]郑远长.防灾减灾的基础研究及应用研究进展概况[J].自然灾害学报,1996,5(4):1-5.
[4]郑远长.全球自然灾害概述[J].中国减灾,2000,10(1):14-19.
[5]孟晖,胡海涛.我国主要人类工程活动引起的滑坡、崩塌和泥石流灾害[J]. 1996,4(4):69-74.
[6]张伟东,姚建义,田野,等.我国近二十年自然灾害回顾分析[J].中国热带医学,2009,9(6):1111-1112.
[7]朱东海,任爱珠,江见鲸.浅论灾害科学的研究现状[J].灾害学,2000,15(1):67-72.
[8]王伟奇.中国泥石流现状及浅析[J].科技信息,2009,(29):597-598.
[9]叶耀先.推广适用防灾技术在“国际减灾十年”做出新贡献[J].工程抗震,1989,(3):4-10.
[10]钟敦伦,谢洪.泥石流与人类经济活动[J].长江流域资源与环境,1999,8(3):327-333.
[11]康志成,李焯芬,马蔼乃,等.中国泥石流研究[M].北京:科学出版社,2004.
[12]谭万沛.中国泥石流危害的现状[J].水土保持通报,1989,9(6):10-14.
[13]张杰坤.泥石流研究综述[J].中国地质灾害与防治学报,1994,5(4):1-8.
[14]姚德基译.泥石流[M].北京:科学出版社,1986.
[15]高建国.1998年世界自然灾害概述[J].中国减灾,1999,9(1):52-58.
[16]谢洪,钟敦伦,韦方强等.我国山区城镇泥石流灾害及其成因[J].山地学报,2006,24(1):79-87.
[17]崔鹏.中国2004年泥石流灾害特点及其对减灾的启示[J].山地学报,2005,23(4):437-441.
[18] Takahashi.T, Tsujimoto.H. Delineation of the Debris Flow Hazardous Zone by A Numerical Simulation Method[C]// Proceeding of International Symposium on Erosion, Debris Flow and Disaster Prevention. Tsukuba: Japan of Erosion Comtrol Engineering Society, 1985: 457-462.
[19] Mizuyama.T, Yazawa.A. Computer Simunation of Debris Flow Depositional Processes[C]// Erosion and Sedimentation in the Pacific Rim. Wallingford: IAHS Press, 1987: 179-190.
[20] O’Brien.J.S, Julien.P.Y, Fullerton.W.T. Two-Dimensional Water Flood and Mudflow Simulation [J]. Journal of Hydraulic Engineering, 1993, 119 (2): 244-261.
[21] Morris.J.P, Zhu.Y, Fox.P.J. Parallel Simulation of Pore-scale Flow Through Porous Media[J]. Computers and Geotechnics, 1999, 25(4): 227–246.
[22] Brufau.P, García-Navarro.P, Ghilardi.P, etal. 1D Mathematical Modelling of Debris Flow[J]. Journal of Hydraulic Research/De Recherches Hydrauliques, 2000, 38(6): 435-446.
[23] De Joode.A, Van Steijn.H. A GIS-Based Simulation Model for Debris-Flow Hazard Prediction[C]. International Conference on Debris-Flow Hazards Mitigation, 2003, 2: 1173-1184.
[24] McDougall Scott, Hungr Oldrich. A Model for the Analysis of Rapid Landslide Motion Across Three-Dimensional Terrain[J]. Canadian Geotechnical Journal, 2004, 41(6): 1084-1097.
[25] Bui.H.H, Sako.K, Fukagawa.R. Numerical Simulation of Soil-Water Interaction Using Smoothed Particle Hydrodynamics (SPH) method [C]// Proceedings of the 15th International Conference of the ISTVS. Japan: Hayama, 2005, 9: 1–15.
[26] Martinez.C, Miralles-Wilhelm.F, Garcia-Martinez.R. Verification of A 2D Finite Element Debris Flow Model Using Bingham and Cross Rheological Formulations[J]. WIT Transactions on Engineering Sciences, 2008, 60: 61-69.
[27] Martinez.C, Miralles-Wilhelm.F, Garcia-Martinez.R. Debris Flow Modelling Accounting for Large Boulder Transport[J]. WIT Transactions on Engineering Sciences, 2010, 67: 29-40.
[28]匡尚富.天然坝溃决的泥石流形成机理及其数学模型[J].泥沙研究,1993,(4):42-57.
[29]解明曙,王玉杰,张洪江,等.沟道松散堆积物形成泥石流的水动力条件分析及其数学模型[J].北京林业大学学报,1993,15(4):1-11.
[30]范椿.一维定常泥石流的数学模型[J].力学与实践,1994,16(1):50-52.
[31]唐川.泥石流堆积泛滥过程的数值模拟及其危险范围预测模型的研究[J].水土保持学报,1994,8(1):45-50.
[32]余斌.美国纽约州立大学布法罗分校火山碎屑流和泥石流数学模型研究近况[J].山地学报,2005,23(1):126-128.
[33]章书成,陈英燕,袁晓凤,等.粘性泥石流一维运动数学模型[J].自然灾害学报,1996,5(4):68-76.
[34]刘学,王兴奎,王光谦.GIS与二维泥石流数学模型集成系统研究[J].中国图象图形学报,1998,3(12):1037-1041.
[35]王纯祥,白世伟,江崎哲郎,等.泥石流的二维数学模型[J].岩土力学,2008,28(6):1237-1241.
[36]刘儒勋,舒其望.计算流体力学的若干新方法[M].北京:科学出版社,2003.
[37]高学平.高等流体力学[M].天津:天津大学出版社,2005.
[38]李义天,赵明登,曹志芳.河道平面二维水沙数学模型[M].北京:中国水利水电出版社,2001.
[39]陶建华.水波的数值模拟[M].天津:天津大学出版社,2005.
[40]李德元,徐国荣,水鸿寿,等.二维非定常流体力学数值方法[M].北京:科学出版社,1998.
[41]谭维炎.计算浅水动力学-有限体积法的应用[M].北京:清华大学出版社,1998.
[42]王福军.计算流体动力学分析-CFD软件原理与应用[M].北京:清华大学出版社,2004.
[43]钱宁,万兆惠.泥沙运动力学[M].北京:科学出版社,2003.
[44] Fayyad.U.M, Piatetsky.S, Smyth.P. The KDD Process for Extracting Useful Knowledge from Volumes of Data[J]. Comunications of the ACM, 1996, 39(11): 27-34.
[45] L.A.Zadeh. Fuzzy Sets[J]. Information and Control, 1965, (8): 338-353.
[46] Z.Pawlak. Rough Sets[J]. International Journal of Computer and Information Sciences. 1982, 11(5):341-356.
[47] Z.Pawlak. Rough Sets: Theoretical Aspects of Reasoning About Data[M]. Netherlands: Kluwer, 1991.
[48] Slowinshi.R. Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory[M]. Dordrecht: Kluwer Academic Publishers, 1992.
[49] R.Golan, W.Ziarko. Methodology for Stock Market Analysis Utilizing Rough Set Theory[J]. Proc. of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, New Jersey, 1995, 22: 32-40.
[50]刘甲伟.基于粗糙集的绩优股票预测系统研究[D].硕士学位论文:大连交通大学,2009.
[51] G.Alvatore, M.Bentto, S.Roman. Rough Set Theory for Multi Criteria Decision Analysis[J]. European Journal of Operational Research, 2001, 129:1-47.
[52] Slowinshi.R. Rough Set Approach to Decision Analysis[J]. AI Expert, 1995, (3): 19-25.
[53] Alvatore.G, Benito.M, Roman.S. Rough Set Theory for Muli-criteria Decision Analysis[J]. European Journal of Operational Research, 2001, 129: 1-47.
[54]杨婷,陈海涛.粗糙集理论在水资源管理群决策中的应用[J].华北水利水电学院学报,2010,31(6):39-42.
[55] Pawlak.Z. Rough Sets[J]. Communications of ACM, 1995, 38(11): 89-95.
[56]李男,邱天爽,刘惠,等.基于粗糙集的数据挖掘技术及其在临床医学诊断中的应用[J].上海生物医学工程,2002,23(2):3-7.
[57]李运贤,杜瑞卿,王相东,等.粗糙集理论在酒精性肝病诊断中的应用研究[J].北京生物医学工程,2006,25(3):307-311.
[58] Teghem.J. Use of Rough Sets Method to Draw Premonitory Factors for Earthquakes by Emphasizing Gas Geochemistry[M]. Dordrecht: Kluwer Academic Publishers, 1992.
[59]安利平,吴育华,仝凌云.基于粗糙集理论的冲突分析和谈判模型[J].北京科技大学学报,2002,24(1):91-95.
[60] Pawlak.Z. Rough Sets, Rough Relations and Rough Functions[J]. Fundamenta Informaticae, 1996, 27(2): 103-108.
[61] Mrozek.A. Rough Sets and Dependency Analysis Among Attributes in Conrputer Implementations of Exper’s Inference Models[J]. International Journal of Man-machine Studies, 1989,30(4): 457-473.
[62]牛丽仙,苑津莎,张英慧.基于粗糙集和支持向量机的电力系统短期负荷预测[J].电力科学与工程,2010,26(2):32-35.
[63] Pawlak.Z. Vagueness and Uncertainty-A Rough Set Prespective[J]. Computational Intelligence, 1995, 11(2): 227-232.
[64]韩祯祥,张琦,文福拴.粗糙集理论与其应用综述[J].控制理论与应用,1999,26(2):153-157.
[65]程钧谟,綦振法,徐福缘,等.粗糙集理论与其它不确定理论的比较分析[J].山东理工大学学报,2004,18(4):7-10.
[66] Banerjee.M, Pal.S.K. Roughness of A Fuzzy Set[J]. Information Sciences, 1996, 93(3): 235-246.
[67]王珏.粗糙集理论及其应用研究[D].博士学位论文:西安电子科技大学,2005.
[68]王清印,刘志勇.集合概念的扩张与完善[J].数学的实践与认识,2005,35(7):224-231.
[69]曾黄麟.粗集理论及其应用-关于数据推理的新方法[M].重庆:重庆大学出版社,1996.
[70]王国胤.Rough集理论与知识获取[M].西安:西安交通大学出版社,2001.
[71]曾黄麟.智能计算-关于粗集理论、模糊逻辑、神经网络的理论及其应用[M].重庆:重庆大学出版社,2004.
[72]张国军.基于粗糙集的相对属性约简算法及决策方法研究[D].博士学位论文:华中科技大学,2010.
[73]张腾飞,肖健梅,王锡淮.粗糙集理论中属性相对约简算法[J].电子学报,2005,33(11):2080-2083.
[74]范霄文.基于粗糙集的定性数据分析方法研究[D].博士学位论文:厦门大学,2008.
[75]王国胤,姚一豫,于洪.粗糙集理论与应用研究综述[J].计算机学报,2009,32(7):1229-1246.
[76]刘永超.粗糙集理论在数据预处理中的应用研究[D].硕士学位论文:大连理工大学,2007.
[77]Φhrn.A. Discernibility and Rough Sets in Medicine: Tools and Applications[D]. PhD: Norwegian University of Science and Technology, 1999.
[78]Φhrn.A. Rosetta Technical Reference Manual[M]. Norwegian: Norwegian University of Science and Technology, 2001.
[79]张政超,关欣,何友,等.粗糙集理论数据处理方法及其研究[J].计算机技术与发展,2010,20(4):12-16.
[80] Hu Xiaohua, N.Cercone. Learning in Relational Database: A Rough Set Approach[J]. Computational Intelligence, 1995, 11(2): 323-337.
[81]谭炳炎.泥石流沟严重程度的数量化综合评判[J].铁道学报,1986,8:74-82.
[82]韩朝超,黄树彩,武婧.一种基于属性值状态的指标权重确定方法[J].昆明理工大学学报,2010,35(2):106-109.
[83]李德顺,许开立,李春晨.基于集值迭代的多专家主观权重确定方法的研究[J].金属矿山,2009,(9):42-43.
[84]魏春荣.煤矿安全模糊评价的一种指标权重确定方法[J].矿山机械,2008,36(6):33-35.
[85]常建娥,蒋太立.层次分析法研究权重的研究[J].武汉理工大学学报,2007,29(1):153-156.
[86]李绍勤,吴琦,王大伟.基于最优传递矩阵层次分析法的改进及应用[J].武警工程学院学报,2006,22(2):14-18.
[87]郑雪茹,何健敏.基于层次分析法的电力需求评价指标权重确定方法[J].现代管理科学,2006,(8):8-9.
[88]足立胜治,德山久仁夫,中筋章人,等.土石流发生危险度の判定にフやて.新砂防,30(3),1977,7-16.
[89]池谷浩,米尺谷诚悦.土石流危险区域の设定に关する研究(第二报).土木技术资料,21(9),1979,46-50。
[90] Hollingsworth.R, Kovacs G.S. Soil Slumps and Debris Flows: Prediction And Protection [J]. Bulletin of the Association of Engineering Geologists, 1981, 38(1): 17-28.
[91]高桥堡.中川一佐.藤宏章,扇状地における图砂泛滥灾害危险度の评价.京都大学防灾研究所年报,31(B-2),1988,655-676。
[92] Fannin.R.J, Wise.M.P, Wilkinson.J.M.T, etal. Debris flow hazard assessment in British Columbia[C]. International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, Proceedings, 1997: 197-206.
[93] Calvo.B, Savi.F, A real-world application of Monte Carlo procedure for debris flow risk assessment[J]. Computers and Geosciences, 2009, 35(5): 967-977.
[94]唐晓春,唐邦兴.我国灾害地貌及其防治研究中的几个问题[J].自然灾害学报,1988,3(1):70-74.
[95]刘希林.泥石流危险度判定的研究[J].灾害学,3(3),1988,10-15.
[96]岳天祥,艾南山,张英保.论流域系统稳定性的判别指标-超熵[J].水土保持学报,1989,3(2):20-28.
[97]蒋忠信.泥石流流域系统的超熵[J].中国地质灾害与防治学报,1992,3(1):33-40.
[98]刘希林,唐川.泥石流危险性评价[M].北京:科学出版社,1995.
[99]崔鹏,杨坤,韦方强,等.泥石流灾情综合评估模式[J].自然灾害学报,2002,11(1):20-27.
[100] Liu.Y, Guo.H.C, Zou.R, etal. Neural network modeling for regional hazard assessment of debris flow in Lake Qionghai Watershed, China[J]. Environmental Geology, 2006, 49(7): 968-976.
[101]程礼来,吴俊峰.大渡河左岸小河沟泥石流特征及其危险性评估研究[J].水土保持研究,2011,18(1):87-96.
[2]高建国,聂高众.1990~1995年世界各国(地区)自然灾害对比[J].地学前缘,1996,3(1-2):219-229.
[3]郑远长.防灾减灾的基础研究及应用研究进展概况[J].自然灾害学报,1996,5(4):1-5.
[4]郑远长.全球自然灾害概述[J].中国减灾,2000,10(1):14-19.
[5]孟晖,胡海涛.我国主要人类工程活动引起的滑坡、崩塌和泥石流灾害[J]. 1996,4(4):69-74.
[6]张伟东,姚建义,田野,等.我国近二十年自然灾害回顾分析[J].中国热带医学,2009,9(6):1111-1112.
[7]朱东海,任爱珠,江见鲸.浅论灾害科学的研究现状[J].灾害学,2000,15(1):67-72.
[8]王伟奇.中国泥石流现状及浅析[J].科技信息,2009,(29):597-598.
[9]叶耀先.推广适用防灾技术在“国际减灾十年”做出新贡献[J].工程抗震,1989,(3):4-10.
[10]钟敦伦,谢洪.泥石流与人类经济活动[J].长江流域资源与环境,1999,8(3):327-333.
[11]康志成,李焯芬,马蔼乃,等.中国泥石流研究[M].北京:科学出版社,2004.
[12]谭万沛.中国泥石流危害的现状[J].水土保持通报,1989,9(6):10-14.
[13]张杰坤.泥石流研究综述[J].中国地质灾害与防治学报,1994,5(4):1-8.
[14]姚德基译.泥石流[M].北京:科学出版社,1986.
[15]高建国.1998年世界自然灾害概述[J].中国减灾,1999,9(1):52-58.
[16]谢洪,钟敦伦,韦方强等.我国山区城镇泥石流灾害及其成因[J].山地学报,2006,24(1):79-87.
[17]崔鹏.中国2004年泥石流灾害特点及其对减灾的启示[J].山地学报,2005,23(4):437-441.
[18] Takahashi.T, Tsujimoto.H. Delineation of the Debris Flow Hazardous Zone by A Numerical Simulation Method[C]// Proceeding of International Symposium on Erosion, Debris Flow and Disaster Prevention. Tsukuba: Japan of Erosion Comtrol Engineering Society, 1985: 457-462.
[19] Mizuyama.T, Yazawa.A. Computer Simunation of Debris Flow Depositional Processes[C]// Erosion and Sedimentation in the Pacific Rim. Wallingford: IAHS Press, 1987: 179-190.
[20] O’Brien.J.S, Julien.P.Y, Fullerton.W.T. Two-Dimensional Water Flood and Mudflow Simulation [J]. Journal of Hydraulic Engineering, 1993, 119 (2): 244-261.
[21] Morris.J.P, Zhu.Y, Fox.P.J. Parallel Simulation of Pore-scale Flow Through Porous Media[J]. Computers and Geotechnics, 1999, 25(4): 227–246.
[22] Brufau.P, García-Navarro.P, Ghilardi.P, etal. 1D Mathematical Modelling of Debris Flow[J]. Journal of Hydraulic Research/De Recherches Hydrauliques, 2000, 38(6): 435-446.
[23] De Joode.A, Van Steijn.H. A GIS-Based Simulation Model for Debris-Flow Hazard Prediction[C]. International Conference on Debris-Flow Hazards Mitigation, 2003, 2: 1173-1184.
[24] McDougall Scott, Hungr Oldrich. A Model for the Analysis of Rapid Landslide Motion Across Three-Dimensional Terrain[J]. Canadian Geotechnical Journal, 2004, 41(6): 1084-1097.
[25] Bui.H.H, Sako.K, Fukagawa.R. Numerical Simulation of Soil-Water Interaction Using Smoothed Particle Hydrodynamics (SPH) method [C]// Proceedings of the 15th International Conference of the ISTVS. Japan: Hayama, 2005, 9: 1–15.
[26] Martinez.C, Miralles-Wilhelm.F, Garcia-Martinez.R. Verification of A 2D Finite Element Debris Flow Model Using Bingham and Cross Rheological Formulations[J]. WIT Transactions on Engineering Sciences, 2008, 60: 61-69.
[27] Martinez.C, Miralles-Wilhelm.F, Garcia-Martinez.R. Debris Flow Modelling Accounting for Large Boulder Transport[J]. WIT Transactions on Engineering Sciences, 2010, 67: 29-40.
[28]匡尚富.天然坝溃决的泥石流形成机理及其数学模型[J].泥沙研究,1993,(4):42-57.
[29]解明曙,王玉杰,张洪江,等.沟道松散堆积物形成泥石流的水动力条件分析及其数学模型[J].北京林业大学学报,1993,15(4):1-11.
[30]范椿.一维定常泥石流的数学模型[J].力学与实践,1994,16(1):50-52.
[31]唐川.泥石流堆积泛滥过程的数值模拟及其危险范围预测模型的研究[J].水土保持学报,1994,8(1):45-50.
[32]余斌.美国纽约州立大学布法罗分校火山碎屑流和泥石流数学模型研究近况[J].山地学报,2005,23(1):126-128.
[33]章书成,陈英燕,袁晓凤,等.粘性泥石流一维运动数学模型[J].自然灾害学报,1996,5(4):68-76.
[34]刘学,王兴奎,王光谦.GIS与二维泥石流数学模型集成系统研究[J].中国图象图形学报,1998,3(12):1037-1041.
[35]王纯祥,白世伟,江崎哲郎,等.泥石流的二维数学模型[J].岩土力学,2008,28(6):1237-1241.
[36]刘儒勋,舒其望.计算流体力学的若干新方法[M].北京:科学出版社,2003.
[37]高学平.高等流体力学[M].天津:天津大学出版社,2005.
[38]李义天,赵明登,曹志芳.河道平面二维水沙数学模型[M].北京:中国水利水电出版社,2001.
[39]陶建华.水波的数值模拟[M].天津:天津大学出版社,2005.
[40]李德元,徐国荣,水鸿寿,等.二维非定常流体力学数值方法[M].北京:科学出版社,1998.
[41]谭维炎.计算浅水动力学-有限体积法的应用[M].北京:清华大学出版社,1998.
[42]王福军.计算流体动力学分析-CFD软件原理与应用[M].北京:清华大学出版社,2004.
[43]钱宁,万兆惠.泥沙运动力学[M].北京:科学出版社,2003.
[44] Fayyad.U.M, Piatetsky.S, Smyth.P. The KDD Process for Extracting Useful Knowledge from Volumes of Data[J]. Comunications of the ACM, 1996, 39(11): 27-34.
[45] L.A.Zadeh. Fuzzy Sets[J]. Information and Control, 1965, (8): 338-353.
[46] Z.Pawlak. Rough Sets[J]. International Journal of Computer and Information Sciences. 1982, 11(5):341-356.
[47] Z.Pawlak. Rough Sets: Theoretical Aspects of Reasoning About Data[M]. Netherlands: Kluwer, 1991.
[48] Slowinshi.R. Intelligent Decision Support-Handbook of Applications and Advances of the Rough Sets Theory[M]. Dordrecht: Kluwer Academic Publishers, 1992.
[49] R.Golan, W.Ziarko. Methodology for Stock Market Analysis Utilizing Rough Set Theory[J]. Proc. of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, New Jersey, 1995, 22: 32-40.
[50]刘甲伟.基于粗糙集的绩优股票预测系统研究[D].硕士学位论文:大连交通大学,2009.
[51] G.Alvatore, M.Bentto, S.Roman. Rough Set Theory for Multi Criteria Decision Analysis[J]. European Journal of Operational Research, 2001, 129:1-47.
[52] Slowinshi.R. Rough Set Approach to Decision Analysis[J]. AI Expert, 1995, (3): 19-25.
[53] Alvatore.G, Benito.M, Roman.S. Rough Set Theory for Muli-criteria Decision Analysis[J]. European Journal of Operational Research, 2001, 129: 1-47.
[54]杨婷,陈海涛.粗糙集理论在水资源管理群决策中的应用[J].华北水利水电学院学报,2010,31(6):39-42.
[55] Pawlak.Z. Rough Sets[J]. Communications of ACM, 1995, 38(11): 89-95.
[56]李男,邱天爽,刘惠,等.基于粗糙集的数据挖掘技术及其在临床医学诊断中的应用[J].上海生物医学工程,2002,23(2):3-7.
[57]李运贤,杜瑞卿,王相东,等.粗糙集理论在酒精性肝病诊断中的应用研究[J].北京生物医学工程,2006,25(3):307-311.
[58] Teghem.J. Use of Rough Sets Method to Draw Premonitory Factors for Earthquakes by Emphasizing Gas Geochemistry[M]. Dordrecht: Kluwer Academic Publishers, 1992.
[59]安利平,吴育华,仝凌云.基于粗糙集理论的冲突分析和谈判模型[J].北京科技大学学报,2002,24(1):91-95.
[60] Pawlak.Z. Rough Sets, Rough Relations and Rough Functions[J]. Fundamenta Informaticae, 1996, 27(2): 103-108.
[61] Mrozek.A. Rough Sets and Dependency Analysis Among Attributes in Conrputer Implementations of Exper’s Inference Models[J]. International Journal of Man-machine Studies, 1989,30(4): 457-473.
[62]牛丽仙,苑津莎,张英慧.基于粗糙集和支持向量机的电力系统短期负荷预测[J].电力科学与工程,2010,26(2):32-35.
[63] Pawlak.Z. Vagueness and Uncertainty-A Rough Set Prespective[J]. Computational Intelligence, 1995, 11(2): 227-232.
[64]韩祯祥,张琦,文福拴.粗糙集理论与其应用综述[J].控制理论与应用,1999,26(2):153-157.
[65]程钧谟,綦振法,徐福缘,等.粗糙集理论与其它不确定理论的比较分析[J].山东理工大学学报,2004,18(4):7-10.
[66] Banerjee.M, Pal.S.K. Roughness of A Fuzzy Set[J]. Information Sciences, 1996, 93(3): 235-246.
[67]王珏.粗糙集理论及其应用研究[D].博士学位论文:西安电子科技大学,2005.
[68]王清印,刘志勇.集合概念的扩张与完善[J].数学的实践与认识,2005,35(7):224-231.
[69]曾黄麟.粗集理论及其应用-关于数据推理的新方法[M].重庆:重庆大学出版社,1996.
[70]王国胤.Rough集理论与知识获取[M].西安:西安交通大学出版社,2001.
[71]曾黄麟.智能计算-关于粗集理论、模糊逻辑、神经网络的理论及其应用[M].重庆:重庆大学出版社,2004.
[72]张国军.基于粗糙集的相对属性约简算法及决策方法研究[D].博士学位论文:华中科技大学,2010.
[73]张腾飞,肖健梅,王锡淮.粗糙集理论中属性相对约简算法[J].电子学报,2005,33(11):2080-2083.
[74]范霄文.基于粗糙集的定性数据分析方法研究[D].博士学位论文:厦门大学,2008.
[75]王国胤,姚一豫,于洪.粗糙集理论与应用研究综述[J].计算机学报,2009,32(7):1229-1246.
[76]刘永超.粗糙集理论在数据预处理中的应用研究[D].硕士学位论文:大连理工大学,2007.
[77]Φhrn.A. Discernibility and Rough Sets in Medicine: Tools and Applications[D]. PhD: Norwegian University of Science and Technology, 1999.
[78]Φhrn.A. Rosetta Technical Reference Manual[M]. Norwegian: Norwegian University of Science and Technology, 2001.
[79]张政超,关欣,何友,等.粗糙集理论数据处理方法及其研究[J].计算机技术与发展,2010,20(4):12-16.
[80] Hu Xiaohua, N.Cercone. Learning in Relational Database: A Rough Set Approach[J]. Computational Intelligence, 1995, 11(2): 323-337.
[81]谭炳炎.泥石流沟严重程度的数量化综合评判[J].铁道学报,1986,8:74-82.
[82]韩朝超,黄树彩,武婧.一种基于属性值状态的指标权重确定方法[J].昆明理工大学学报,2010,35(2):106-109.
[83]李德顺,许开立,李春晨.基于集值迭代的多专家主观权重确定方法的研究[J].金属矿山,2009,(9):42-43.
[84]魏春荣.煤矿安全模糊评价的一种指标权重确定方法[J].矿山机械,2008,36(6):33-35.
[85]常建娥,蒋太立.层次分析法研究权重的研究[J].武汉理工大学学报,2007,29(1):153-156.
[86]李绍勤,吴琦,王大伟.基于最优传递矩阵层次分析法的改进及应用[J].武警工程学院学报,2006,22(2):14-18.
[87]郑雪茹,何健敏.基于层次分析法的电力需求评价指标权重确定方法[J].现代管理科学,2006,(8):8-9.
[88]足立胜治,德山久仁夫,中筋章人,等.土石流发生危险度の判定にフやて.新砂防,30(3),1977,7-16.
[89]池谷浩,米尺谷诚悦.土石流危险区域の设定に关する研究(第二报).土木技术资料,21(9),1979,46-50。
[90] Hollingsworth.R, Kovacs G.S. Soil Slumps and Debris Flows: Prediction And Protection [J]. Bulletin of the Association of Engineering Geologists, 1981, 38(1): 17-28.
[91]高桥堡.中川一佐.藤宏章,扇状地における图砂泛滥灾害危险度の评价.京都大学防灾研究所年报,31(B-2),1988,655-676。
[92] Fannin.R.J, Wise.M.P, Wilkinson.J.M.T, etal. Debris flow hazard assessment in British Columbia[C]. International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, Proceedings, 1997: 197-206.
[93] Calvo.B, Savi.F, A real-world application of Monte Carlo procedure for debris flow risk assessment[J]. Computers and Geosciences, 2009, 35(5): 967-977.
[94]唐晓春,唐邦兴.我国灾害地貌及其防治研究中的几个问题[J].自然灾害学报,1988,3(1):70-74.
[95]刘希林.泥石流危险度判定的研究[J].灾害学,3(3),1988,10-15.
[96]岳天祥,艾南山,张英保.论流域系统稳定性的判别指标-超熵[J].水土保持学报,1989,3(2):20-28.
[97]蒋忠信.泥石流流域系统的超熵[J].中国地质灾害与防治学报,1992,3(1):33-40.
[98]刘希林,唐川.泥石流危险性评价[M].北京:科学出版社,1995.
[99]崔鹏,杨坤,韦方强,等.泥石流灾情综合评估模式[J].自然灾害学报,2002,11(1):20-27.
[100] Liu.Y, Guo.H.C, Zou.R, etal. Neural network modeling for regional hazard assessment of debris flow in Lake Qionghai Watershed, China[J]. Environmental Geology, 2006, 49(7): 968-976.
[101]程礼来,吴俊峰.大渡河左岸小河沟泥石流特征及其危险性评估研究[J].水土保持研究,2011,18(1):87-96.