多尺度直线拟合法在时间序列突变点检测中的应用

在电液伺服阀的测量和筛选过程中,为进行伺服阀死区和分辨率的测量,需要检查数据序列中的突变点。目前突变点的主要检测方法有Mann-Kendall算法、累积和控制图(CUSUM)算法、最小均方差(MSE)法、小波变换法等,但这些检测方法均有一定的局限性。为此提出了一种多尺度直线拟合法,采用变换拟合尺度逐步逼近的方式来检测突变点。将时间序列按给出的初始长度计算法划分为若干段,每一段用最小二乘拟合的直线代替。比较相邻拟合线段的斜率,其中斜率变化最大的两段线段之内存在突变点。在该两段线段的范围内缩小拟合尺度,继续使用上述方法进行查找,直至拟合尺度收敛为1,此时斜率变化最大的点即是原时间序列的突变点。将该检测方法同其他方法进行比较,并在伺服阀测试系统和故障检测信号中进行实际应用,验证了该方法在查找突变点时的准确性、针对复杂信号时的有效性和计算效率上的优越性。

Application of Multi-scale Line Fitting Method in Change Point Detection in Time Series

In test and selection processes of electro-hydraulic servo valve, the change point of time series should be checked to measure the dead zone and the resolution ratio. The main detection methods are Mann-Kendall method, cumulative sum charts (CUSUM) method, least mean square error (MSE) method, and wavelet transform method. The methods all have some limitations. A multi-scale line fitting method is proposed, which can be used to detect the change point step-by-step by changing the scale of line fitting. The time series are divided into many segments according to the initial scale calculation method, and every single segment is replaced by a fitting line using least square method. Then the slopes of every neighbor segment are compared to find out the maximum change of the slope, and the change point should be included in these two segments. The scale is changed in the range of the two neighbor segments, and the change points are continously detected using the method until the length of segment is reduced to 1. The final point found out by the method is the change point of original time series.The proposed method is compared with other methods. The proposed method is used for the electro-hydraulic servo testing system and the fault signal detection to verify its accuracy and effectiveness.