Song Hongwei, Wu Xianqian, Huang Chenguang, Wei Yangpeng, Wang Xi
Key Laboratory for Hydrodynamics and Ocean Engineering, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
Rev Sci Instrum. 2012 Jul;83(7):073301. doi: 10.1063/1.4731014.
Despite the increasing popularity of photonic Doppler velocimetry (PDV) in shock wave experiments, its capability of capturing low particle velocities while changing rapidly is still questionable. The paper discusses the performance of short time Fourier transform (STFT) and continuous wavelet transform (CWT) in processing fringe signals of fast-changing low velocities measured by PDV. Two typical experiments are carried out to evaluate the performance. In the laser shock peening test, the CWT gives a better interpretation to the free surface velocity history, where the elastic precursor, main plastic wave, and elastic release wave can be clearly identified. The velocities of stress waves, Hugoniot elastic limit, and the amplitude of shock pressure induced by laser can be obtained from the measurement. In the Kolsky-bar based tests, both methods show validity of processing the longitudinal velocity signal of incident bar, whereas CWT improperly interprets the radial velocity of the shocked sample at the beginning period, indicating the sensitiveness of the CWT to the background noise. STFT is relatively robust in extracting waveforms of low signal-to-noise ratio. Data processing method greatly affects the temporal resolution and velocity resolution of a given fringe signal, usually CWT demonstrates a better local temporal resolution and velocity resolution, due to its adaptability to the local frequency, also due to the finer time-frequency product according to the uncertainty principle.
尽管光子多普勒测速技术（PDV）在冲击波实验中越来越受欢迎，但其捕捉快速变化的低粒子速度的能力仍存在疑问。本文讨论了短时傅里叶变换（STFT）和连续小波变换（CWT）在处理由PDV测量的快速变化的低速条纹信号时的性能。进行了两个典型实验来评估性能。在激光冲击喷丸试验中，CWT能更好地解释自由表面速度历程，其中弹性前驱波、主塑性波和弹性释放波能够清晰识别。从测量中可以获得应力波速度、胡克弹性极限以及激光诱导的冲击压力幅值。在基于科尔斯基杆的试验中，两种方法都证明了处理入射杆纵向速度信号的有效性，然而CWT在初始阶段对受冲击样品的径向速度解释不当，这表明CWT对背景噪声敏感。STFT在提取低信噪比波形方面相对稳健。数据处理方法极大地影响给定条纹信号的时间分辨率和速度分辨率，通常CWT由于其对局部频率的适应性，以及根据不确定性原理具有更精细的时频乘积，展现出更好的局部时间分辨率和速度分辨率。
