基于尺度变换的数据转折点检测方法

A Data Break Point Detection Method Based on Scale Transformation

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.