基于降维分析的大坝安全特征提取方法及其应用研究
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摘要
为有效提取大坝安全的低维特征,将特征正交分解、等概率粗粒化、主成分/核主成分分析等降维方法与大坝安全特征提取方法相结合,提出了基于POD的分位数回归分析法、基于实测资料复杂网络分析法、基于PCA/KPCA的预警指标提取法以及基于POD的多场耦合强度折减法等4种新方法,研究表明,上述4种方法能提取高维实测数据或无穷维大坝安全的低维特征,使得大坝安全性态分析和判断可以在低维空间进行,典型工程实例检验了新方法的有效性。
In order to extract the low-dimensional features of dam safety effectively, dimensionality reduction methods, such as the dimensionality reduction method, the equal probability coarse granulation and the principal component/kernel principal component analysis, are combined with the dam safety feature extraction method to propose four new methods of quantile regression analysis based on POD, complex network analysis method based on measured data, early warning index extraction method based on PCA/KPCA and multi-Field coupling strength reduction method based on POD. The research shows that the above four methods can extract the high-dimensional measured data or the low-dimensional characteristics of infinite dimensional dam safety, so that the analysis and judgment of dam safety state can be carried out in low-dimensional space. The typical engineering verifies the effectiveness of the new methods.
In order to extract the low-dimensional features of dam safety effectively, dimensionality reduction methods, such as the dimensionality reduction method, the equal probability coarse granulation and the principal component/kernel principal component analysis, are combined with the dam safety feature extraction method to propose four new methods of quantile regression analysis based on POD, complex network analysis method based on measured data, early warning index extraction method based on PCA/KPCA and multi-Field coupling strength reduction method based on POD. The research shows that the above four methods can extract the high-dimensional measured data or the low-dimensional characteristics of infinite dimensional dam safety, so that the analysis and judgment of dam safety state can be carried out in low-dimensional space. The typical engineering verifies the effectiveness of the new methods.
引文
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[14]李政锴.基于复杂网络的水坝实测数据分析方法研究[D].南京:河海大学,2016.
[15]张娜.基于KPCA的均质土坝渗流溃坝阈值研究[D].南京:河海大学,2015.
[2]张斌.基于能量原理的有限元强度折减法分析边坡稳定[D].上海:同济大学,2008.
[3]DONOHO D L.High-dimensional data analysis:The curses and blessings of dimensionality[C].AMS math challenges lecture,2000:32.
[4]MAATEN L J P,POSTMA E O,HERIK H J.Dimensionality reduction:a comparative review[J].IEEE Transaction on Pattern Analysis and Machine Intelligence,2007,10(2):1-35.
[5]方卫华.大坝安全监控:问题、观点与方法[M].南京:河海大学出版社,2013.
[6]李琳.基于特征正交分解和分位数回归的大坝实测数据分析方法研究[D].南京:河海大学,2016.
[7]吴中如.水工建筑物安全监控理论及其应用[M].北京:高等教育出版社,2003.
[8]谷艳昌,何鲜峰,郑东健.基于蒙特卡罗方法的高拱坝变形监控指标拟定[J].水利水运工程学报,2008(1):14-19.
[9]金秋,刘贝贝,张磊.古田溪大坝典型坝段水平位移监控指标的拟定[J].人民黄河,2010,32(2):122-123.
[10]周涛,柏文洁,汪秉宏,等.复杂网络研究概述[J].物理,2005(1):31-36.
[11]陈国庆,黄润秋,石豫川,等.基于动态和整体强度折减法的边坡稳定性分析[J].岩石力学与工程学报,2014,33(2):243-256.
[12]胡金秀,高效伟.变系数瞬态热传导问题边界元格式的特征正交分解降阶方法[J].物理学报,2016,65(1):265-281.
[13]罗振东,陈静,孙萍,等.抛物性方程基于POD方法的时间二阶精度CN有限元降维格式[J].中国科学A辑,2011,41(2):447-460.
[14]李政锴.基于复杂网络的水坝实测数据分析方法研究[D].南京:河海大学,2016.
[15]张娜.基于KPCA的均质土坝渗流溃坝阈值研究[D].南京:河海大学,2015.