基于尺度变换的数据转折点检测方法
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摘要
数据中的数据转折点一般代表某种变化或者异常,因此数据转折点准确查找对于数据分析和处理来说具有重要的作用和意义,在气象,水文,金融,故障诊断等领域有广泛的应用。目前数据转折点的主要检测方法有Mann-Kendall算法,Cumulative Sum Charts(CUSUM)算法,最小方差法,小波变换法等。为了克服以上方法中的准确性和局限性问题,通过不断地变换尺度的方法来缩小计算范围;通过直线拟合的方法不断获取数据中的变化趋势。在比较分割后各小段数据的变化趋势,寻找趋势变化最大的数据段。在该数据段中将原来的尺度缩小为原来的一半,继续进行变化趋势的对比,直至数据长度变为2,最终逼近并找出原始数据中的转折点。通过多种类型的数据对该方法验证,说明了该方法的有效性和准确性。
The turning point in the data generally represents some kind of change or abnormity,so it is very important for data analysis and processing to find data turning points accurately,the detection method is widely used in the fields of meteorology,hydrology,finance,fault diagnosis and so on.The main detection methods are Mann-Kendall method,cumulative sum charts method(CUSUM),mean square error method(MSE),the wavelet transform method and so on.However,all of these methods have some limitations in accuracy or computation cost.In order to overcome these problems,a new detection method is proposed,by constantly changing the scale to narrow the scope of calculation,by the line fitting method to obtain the change trend of the data.After comparing the trend of each data segment,the largest change of data segments will be found out.In this data section,the scale will be reduced to half of the original size,the changing trend continues to be contrasted until the data length becomes 2,finally the turning point of the original data will be found out.At the end of this paper,in order to show the validity and accuracy of the method,a variety of data are used to verify this new method.
The turning point in the data generally represents some kind of change or abnormity,so it is very important for data analysis and processing to find data turning points accurately,the detection method is widely used in the fields of meteorology,hydrology,finance,fault diagnosis and so on.The main detection methods are Mann-Kendall method,cumulative sum charts method(CUSUM),mean square error method(MSE),the wavelet transform method and so on.However,all of these methods have some limitations in accuracy or computation cost.In order to overcome these problems,a new detection method is proposed,by constantly changing the scale to narrow the scope of calculation,by the line fitting method to obtain the change trend of the data.After comparing the trend of each data segment,the largest change of data segments will be found out.In this data section,the scale will be reduced to half of the original size,the changing trend continues to be contrasted until the data length becomes 2,finally the turning point of the original data will be found out.At the end of this paper,in order to show the validity and accuracy of the method,a variety of data are used to verify this new method.
引文
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[2]Cao Y L.Business cycle turning points of the var threshold model and empirical analysis:based on quarterly data 1970-2012 of 12countries and regions[J].Economic Problems,2015(6):29-34.
[3]李丰,高峰,寇鹏.基于分段线性表示和高斯过程分类的股票转折点概率预测[J].计算机应用,2015,35(8):2397-2403.Li F,Gao F,Kou P.Integrating piecewise linear representation and Gaussian process classification for stock turning points prediction[J].Journal of Computer Applications,2015,35(8):2397-2403.
[4]邓宏贵,曹文晖,高小龙,等.基于混沌和小波变换的信号检测方法[J].控制工程,2011,18(6):937-940.Deng H G,Cao W H,Gao X L.Signal detection based on wavelet transform and chaotic theory[J].Control Engineering of China,2011,18(6):937-940.
[5]武玮,徐宗学,李发鹏.渭河关中段水文情势改变程度分析[J].自然资源学报,2012,27(7):1124-1137.Wu W,Xu Z X,Li F P.Hydrologic alteration analysis in Guanzhong reach of the Weihe river[J].Journal of Natural Resources,2012,27(7):1124-1137.
[6]张应华,宋献方.水文气象序列趋势分析与变异诊断的方法及其对比[J].干旱区地理,2015,38(4):652-665.Zhang Y H,Song X F.Techniques of abrupt change detection and trends analysis in hydroclimatic time-series:Advances and evaluation[J].Arid Land Geography,2015,38(4):652-665.
[7]公茂法,夏文华,张晓明,等.基于HHT的抗CT饱和变压器故障识别新方法[J].电力系统保护与控制,2013,41(22):64-70.Gong M F,Xia W H,Zhang X M,et al.New method to identify transformer fault with anti-CT saturation based on HHT[J].Power System Protection and Control,2013,41(22):64-70.
[8]王冕.牵引网故障突变点检测及性质识别算法的研究[D].南昌:东华理工大学,2015.Wang M.Algorithm research of traction fault detection and property identification[D].Nanchang:East China institute of Technology,2015.
[9]廖俊,于雷,罗寰,等.基于趋势转折点的时间序列分段线性表示[J].计算机工程与应用,2010,46(30):50-53.Liao Jn,Yu L,Luo H,et al.Time series piecewise linear representation based on trend transition point[J].Computer Engineering and Applications,2010,46(30):50-53.
[10]Il'Yasov Y,Ivanov A.Computation of maximal turning points to nonlinear equations by nonsmooth optimization[J].Optimization Methods and Software,2015,31(1):1-23.
[11]Touati S,Naylor M,Main I.Detection of change points in underlying earthquake rates,with application to global megaearthquakes[J].Geophysical Journal International,2016,204(2):753-767.
[12]Lee S,Sang U K.Comparison between change point detection methods with synthetic rainfall data and application in South Korea[J].Ksce Journal of Civil Engineering,2016,20(4):1558-1571.
[13]王波.基于多尺度小波的棉花异纤检测算法[J].控制工程,2009(S1):173-175.Wang B.Foreign fiber detection arithmetic based on multi-scale wavelet[J].Control Engineering of China,2009(S1):173-175.
[14]吴凡,熊高君,叶志婵.小波变换在信号突变点检测中的应用[J].计算机与现代化,2008,15(8):133-135.Wu F,Xiong G J,Ye Z C.Applications of wavelet transform on signals catastrophe-points detection[J].Computer and Modernization,2008,15(8):133-135.