基于可变集的围岩质量等级识别原理与判别方法
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摘要
基于可变集的对立统一定理,提出围岩质量等级可变集识别原理与方法。导出可变集多指标综合相对隶属度模型。首次将辩证法规律及其数学定理用于工程围岩等级识别。列举了两个应用实例,并与集对分析模型的围岩质量等级识别结果进行了比较与分析,指出它存在的问题。提出的围岩质量等级可变集识别原理与方法可推广应用于土木建筑、水利、水电、岩土工程等不同建筑物围岩质量等级识别,有广宽的应用前景。
A brief introduction to basic mathematical theorem of dialectics law which was introduced by Professor CHEN Shou-Yu is provided.The theory provides the opposite axiom of variable sets and the mathematical theorem of variable sets based on the basic law of materialist dialectics.Based on the qualitative and quantitative change theorem,that shows the standard interval intersection of the relative differences about the quality index of rock mass adjacent grades is zero.And based on the theorem of unity of opposites,that shows the sum of relative membership degree about two adjacent indexes is one.To apply mathematical theorems of dialectics law to engineering,examples of applications to get the comparisons and analysis between variable sets and set pair analysis was enumerated.The examples and comparisons revealed the problems and errors in set pair analysis.And the method is introduced,that can be extended to many academic fields to identify the quality of rock mass different buildings including:civil and architectural engineering,hydraulic and hydro-power engineering,geotechnical engineering,etc.It has a very broad application prospect.
A brief introduction to basic mathematical theorem of dialectics law which was introduced by Professor CHEN Shou-Yu is provided.The theory provides the opposite axiom of variable sets and the mathematical theorem of variable sets based on the basic law of materialist dialectics.Based on the qualitative and quantitative change theorem,that shows the standard interval intersection of the relative differences about the quality index of rock mass adjacent grades is zero.And based on the theorem of unity of opposites,that shows the sum of relative membership degree about two adjacent indexes is one.To apply mathematical theorems of dialectics law to engineering,examples of applications to get the comparisons and analysis between variable sets and set pair analysis was enumerated.The examples and comparisons revealed the problems and errors in set pair analysis.And the method is introduced,that can be extended to many academic fields to identify the quality of rock mass different buildings including:civil and architectural engineering,hydraulic and hydro-power engineering,geotechnical engineering,etc.It has a very broad application prospect.
引文
[1]陆兆溱,王京,吕亚平.模糊模式识别法在围岩稳定性分类上的应用[J].河海大学学报,1991,19(6):97-101.LU Zhao-Zhen,WANG Jin,LU Ya-Ping.Direct method of fuzzy pattern Recoginition and its application to stability classification of surrounding rocks[J].Journal of Hohai University,1991,19(6):97-101.(in Chinese)
[2]陈守煜.模糊最优归类理论模型及其在围岩稳定性分类与场地土类别评定中的应用[J].水利学报,1993,12:26-36.CHEN Shou-Yu.Fuzzy optimal model and its applications to stability classification of surrounding rocks as well as site classification[J].J Hydraul Eng,1993,26-36.(in Chinese)
[3]陈守煜.系统模糊决策理论与应用[M].大连:大连理工大学出版社,1994.CHEN Shou-Yu.System fuzzy decision theorem and application[M].Dalian:Dalian University of Technology Press,1994.(in Chinese)
[4]王迎超,徐兴华,刘永莉,等.公路隧道围岩分级的集对分析模型[J].哈尔滨工业大学学报,2011,43(4):114-119.WANG Ying-Chao,XU Xing-Hua,LIU Yong-Li,et al.Set pait analysis model in surrounding rock classification of hightway tunnel[J].Journal of Harbin Institute of Technology,2011,43(4):114-119.(in Chinese)
[5]赵克勤.集对分析及其初步应用[M].杭州:浙江科学技术出版社,2000.ZHAO Ke-Qin.Set pair analysis and its initial application[M].Hangzhou:Zhejiang Science Technology Press,2000.(in Chinese)
[6]陈守煜,胡吉敏,李敏.水电站导流洞围岩稳定性的可变模糊评价方法[J].北京工业大学学报,2009,35(4):464-469.CHEN Shou-Yu,HU Ji-Min,LI Min.Variable fuzzy evaluation method for analysis of the stability of surrounding rock in diversion tunnel of hydro project[J].Journal of Beijing University of Technology,2009,35(4):464-469.(in Chinese)
[7]陈守煜,韩晓军.围岩稳定性评价的模糊可变集合工程方法[J].岩石力学与工程学报,2006,25(9):1 857-1 861.CHEN Shou-Yu,HAN Xiao-Jun.Engineering method of variable fuzzy set for assessment of surrounding rock stability[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(9):1 857-1 861.(in Chinese)
[8]陈守煜,王子茹,罗宝力,等.可变模糊模式识别方法及在水电站地下厂房岩体稳定性评价中的应用[J].水利学报,2011,42(4):396-402.CHEN Shou-Yu,WANG Zi-Ru,LOU Bao-Li,et al.Method of variable fuzzy pattern recognition and it application to surrounding rock stability of water power station underground building[J].J Hydraul Eng,2011,42(4):396-402.(in Chinese)
[9]陈守煜.模糊可变集合的拓展:可变集合——兼论可拓零界关联函数等于零的错误[C]//数学及其应用.北京:原子能出版社,2007.CHEN Shou-Yu.The expand of the fuzzy variable sets:variable sets-and theory extension zero bound correlation function is equal to zero error[C]//Mathematics and its application.Beijing:Atomic Energy Press,2007.(in Chinese)
[10]陈守煜.可变集—可变模糊集的发展及其在水资源系统中的应用[J].数学的实践与认识,2012,42(1):92-101.CHEN Shou-Yu.Variable Sets-the development of Variable Fuzzy Sets and Application in assessment of water resource[J].Math Pract Theory,2012,42(1):92-101.(in Chinese)
[11]陈守煜.可变集及水资源系统优选决策可变集原理与方法[J].水利学报,2012,43(9):1 066-1 074.CHEN Shou-Yu.Variable sets and the theorem and method of optimal decision making for water resource system[J].J Hydraul Eng,2012,43(9):1 066-1 074.(in Chinese)
[12]陈守煜.可变模糊集理论与模型及其应用[M].大连:大连理工大学出版社,2009.CHEN Shou-Yu.Theory and model of variable fuzzy sets and its application[M].Dalian:Dalian University of Technology Press,2009.(in Chinese)
[13]陈守煜,王定乾.基于可变集的建筑结构地震损伤评估原理和方法[J].黑龙江大学工程学报,2012,3(2):1-6,37.CHEN Shou-Yu,WANG Ding-Qian.Evaluation principle and wethod for earthquake damage of building structure based on variable sets[J].Journal of Engineering of Heilongjiang University,2012,3(2):1-6,37.
[14]ZADEH L A.Fuzzy sets[J].Information and control,1965,8(3):338-353.
[15]CHEN Shou-Yu,XUE Zhi-Chun,LI Min.Variable Sets principle and method for flood classification[J].Science China Technological Sciences,2013,56(9):2 343-2 348.
[16]CHEN Shou-Yu,XUE Zhi-Chun,LI Min,et al.Variable sets method for urban flood vulnerability assessment[J].Science China Technological Sciences,2013,56(12):3 129-3 136.
[17]陈守煜,薛志春,李敏.基于可变集方法的流域防洪工程体系风险评价[J].人民长江,2013,44(11):1-4.CHEN Shou-Yu,XUE Zhi-Chun,LI Min.Risk evaluation of basin flood-control engineering system based on variable sets method[J].Yangtze River,2013,44(11):1-4.(in Chinese)
[18]陈守煜.工程模糊集理论与应用[M].北京:国防工业出版社,1998.CHEN Shou-Yu.Engineering fuzzy set theory and application[M].Beijing:National defense industry press,1998.(in Chinese)
[19]陈守煜,聂相田,王子茹,等.基于可变集的建筑工程评标原理与方法[J].黑龙江大学工程学报,2013,4(3):1-5.CHEN Shou-Yu,NIE Xiang-Tian,WANG Zi-Ru,et al.Evaluation of bid theory and method of construction engineering based on variable sets[J].Journal of Engineering of Heilongjiang University,2013,4(3):1-5.
[20]王文圣,李跃清,金菊良,等.水文水资源集对分析[M].北京:科学出版社,2010.WANG Wen-Sheng,LI Yue-Qing,JIN Ju-Liang,et al.Hydrology and Water Resources Set Pair Analysis[M].Beijing:Science Press,2010.(in Chinese)
[21]陈守煜.水资源系统可变集评价原理与方法[J].水利学报,2013,44(2):134-142.CHEN Shou-Yu.Variable sets assessment theory and method of water resource system[J].J Hydraul Eng,2013,44(2):134-142.(in Chinese)
[22]陈守煜.质量互变定理用于识别可拓学与集对分析的基础性错误[J].中国科技成果,2013,(9):48-51.CHEN Shou-Yu.Application of quality-quantity exchange theorem to the recognition of Extenics and Set Pair Analysis's basic errors[J].China Sci Tech Achieve,2013,(9):48-51.(in Chinese)
[2]陈守煜.模糊最优归类理论模型及其在围岩稳定性分类与场地土类别评定中的应用[J].水利学报,1993,12:26-36.CHEN Shou-Yu.Fuzzy optimal model and its applications to stability classification of surrounding rocks as well as site classification[J].J Hydraul Eng,1993,26-36.(in Chinese)
[3]陈守煜.系统模糊决策理论与应用[M].大连:大连理工大学出版社,1994.CHEN Shou-Yu.System fuzzy decision theorem and application[M].Dalian:Dalian University of Technology Press,1994.(in Chinese)
[4]王迎超,徐兴华,刘永莉,等.公路隧道围岩分级的集对分析模型[J].哈尔滨工业大学学报,2011,43(4):114-119.WANG Ying-Chao,XU Xing-Hua,LIU Yong-Li,et al.Set pait analysis model in surrounding rock classification of hightway tunnel[J].Journal of Harbin Institute of Technology,2011,43(4):114-119.(in Chinese)
[5]赵克勤.集对分析及其初步应用[M].杭州:浙江科学技术出版社,2000.ZHAO Ke-Qin.Set pair analysis and its initial application[M].Hangzhou:Zhejiang Science Technology Press,2000.(in Chinese)
[6]陈守煜,胡吉敏,李敏.水电站导流洞围岩稳定性的可变模糊评价方法[J].北京工业大学学报,2009,35(4):464-469.CHEN Shou-Yu,HU Ji-Min,LI Min.Variable fuzzy evaluation method for analysis of the stability of surrounding rock in diversion tunnel of hydro project[J].Journal of Beijing University of Technology,2009,35(4):464-469.(in Chinese)
[7]陈守煜,韩晓军.围岩稳定性评价的模糊可变集合工程方法[J].岩石力学与工程学报,2006,25(9):1 857-1 861.CHEN Shou-Yu,HAN Xiao-Jun.Engineering method of variable fuzzy set for assessment of surrounding rock stability[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(9):1 857-1 861.(in Chinese)
[8]陈守煜,王子茹,罗宝力,等.可变模糊模式识别方法及在水电站地下厂房岩体稳定性评价中的应用[J].水利学报,2011,42(4):396-402.CHEN Shou-Yu,WANG Zi-Ru,LOU Bao-Li,et al.Method of variable fuzzy pattern recognition and it application to surrounding rock stability of water power station underground building[J].J Hydraul Eng,2011,42(4):396-402.(in Chinese)
[9]陈守煜.模糊可变集合的拓展:可变集合——兼论可拓零界关联函数等于零的错误[C]//数学及其应用.北京:原子能出版社,2007.CHEN Shou-Yu.The expand of the fuzzy variable sets:variable sets-and theory extension zero bound correlation function is equal to zero error[C]//Mathematics and its application.Beijing:Atomic Energy Press,2007.(in Chinese)
[10]陈守煜.可变集—可变模糊集的发展及其在水资源系统中的应用[J].数学的实践与认识,2012,42(1):92-101.CHEN Shou-Yu.Variable Sets-the development of Variable Fuzzy Sets and Application in assessment of water resource[J].Math Pract Theory,2012,42(1):92-101.(in Chinese)
[11]陈守煜.可变集及水资源系统优选决策可变集原理与方法[J].水利学报,2012,43(9):1 066-1 074.CHEN Shou-Yu.Variable sets and the theorem and method of optimal decision making for water resource system[J].J Hydraul Eng,2012,43(9):1 066-1 074.(in Chinese)
[12]陈守煜.可变模糊集理论与模型及其应用[M].大连:大连理工大学出版社,2009.CHEN Shou-Yu.Theory and model of variable fuzzy sets and its application[M].Dalian:Dalian University of Technology Press,2009.(in Chinese)
[13]陈守煜,王定乾.基于可变集的建筑结构地震损伤评估原理和方法[J].黑龙江大学工程学报,2012,3(2):1-6,37.CHEN Shou-Yu,WANG Ding-Qian.Evaluation principle and wethod for earthquake damage of building structure based on variable sets[J].Journal of Engineering of Heilongjiang University,2012,3(2):1-6,37.
[14]ZADEH L A.Fuzzy sets[J].Information and control,1965,8(3):338-353.
[15]CHEN Shou-Yu,XUE Zhi-Chun,LI Min.Variable Sets principle and method for flood classification[J].Science China Technological Sciences,2013,56(9):2 343-2 348.
[16]CHEN Shou-Yu,XUE Zhi-Chun,LI Min,et al.Variable sets method for urban flood vulnerability assessment[J].Science China Technological Sciences,2013,56(12):3 129-3 136.
[17]陈守煜,薛志春,李敏.基于可变集方法的流域防洪工程体系风险评价[J].人民长江,2013,44(11):1-4.CHEN Shou-Yu,XUE Zhi-Chun,LI Min.Risk evaluation of basin flood-control engineering system based on variable sets method[J].Yangtze River,2013,44(11):1-4.(in Chinese)
[18]陈守煜.工程模糊集理论与应用[M].北京:国防工业出版社,1998.CHEN Shou-Yu.Engineering fuzzy set theory and application[M].Beijing:National defense industry press,1998.(in Chinese)
[19]陈守煜,聂相田,王子茹,等.基于可变集的建筑工程评标原理与方法[J].黑龙江大学工程学报,2013,4(3):1-5.CHEN Shou-Yu,NIE Xiang-Tian,WANG Zi-Ru,et al.Evaluation of bid theory and method of construction engineering based on variable sets[J].Journal of Engineering of Heilongjiang University,2013,4(3):1-5.
[20]王文圣,李跃清,金菊良,等.水文水资源集对分析[M].北京:科学出版社,2010.WANG Wen-Sheng,LI Yue-Qing,JIN Ju-Liang,et al.Hydrology and Water Resources Set Pair Analysis[M].Beijing:Science Press,2010.(in Chinese)
[21]陈守煜.水资源系统可变集评价原理与方法[J].水利学报,2013,44(2):134-142.CHEN Shou-Yu.Variable sets assessment theory and method of water resource system[J].J Hydraul Eng,2013,44(2):134-142.(in Chinese)
[22]陈守煜.质量互变定理用于识别可拓学与集对分析的基础性错误[J].中国科技成果,2013,(9):48-51.CHEN Shou-Yu.Application of quality-quantity exchange theorem to the recognition of Extenics and Set Pair Analysis's basic errors[J].China Sci Tech Achieve,2013,(9):48-51.(in Chinese)
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