小波变换在混合系统时间序列离散事件检测中的应用

Application of wavelet transform in discrete event detection of hybrid system time series

为了检测混合系统的时间序列,使用小波分析方法。离散事件的检测是混合系统辨识的一个重要步骤,而小波变换是一种适合于混合系统时间序列分析的方法。将两种小波分析技术相结合,得到了在弱噪声条件下检测转换点的方法。在此背景下,重点讨论了将理论结果用于实时序列离散事件检测时的效果。当系数振幅的评估仅限于较粗尺度时,将基于系数最大值的检测与基于小波的去噪过程相结合,从而允许在转换点附近进行局部细化并减少噪声,使离散事件的失真降至最低。

In order to detect discrete time,wavelet analysis is used to analyze the time series of hybrid system containing both discrete and continuous dynamics.Discrete event detection is an important step of hybrid system identification,and wavelet transform is a suitable method for hybrid system time series analysis.By combining the two wavelet analysis techniques,a method to detect the transition point in the weak noise condition is obtained.In this context,the problems that arise when the theoretical results are applied to discrete event detection of real-time sequences are discussed emphatically.When the evaluation of the coefficient amplitudes is limited to the effects that occur at coarse-scale,combining the maximum coefficient based detection with the wavelet based denoising process allows local thinning and noise reduction near the transition point,minimizing the distortion of discrete events.