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为了便于测试,作者将元器件进行了系统集成,装入长宽高为400 mm×260 mm×400 mm的箱体中。测量的移动目标为固定电动位移台上的黑色金属板,通过控制器设定电动位移台的运动状态。实验装置和目标物如图 3所示。
为了便于数据分析,本次实验中所用的采集卡为德国SPECTRUM公司研发的高速数据采集卡M4i.4480-x8,最高采样率可以达到400 MHz,独立模数转换的双通道提供14 bit分辨率可以满足用户高质量的信号采集需求。该采集卡附带有可以实时查看和存储采样数据的软件SBench 6。
实验在成都信息工程大学第二实验楼与信息楼连接的过道上进行。首先在测量起点处放置实验装置,在终点处放置电动位移台,经测距仪测量两者距离为124 m。调整装置与电动位移台的位置,使光斑可以准确落在电动位移台的黑色金属平板上。设定好平移速度后,打开激光测量,由于导轨长度有限而且加速到指定速度需要一定时间,再考虑到对讲机的时间延迟,需要等到金属板移动到平移导轨滑轨中间时再测量。
在测量中,首先将电动位移台固定,采集信号后计算系统固定的频移,通过多次测量后取均值,得到由于系统的不稳定性带来的误差。实验中,分别设定电动位移台的平移速率为-0.04 m/s,-0.06 m/s,-0.08 m/s,负号表示电动位移台朝远离实验装置的方向运动。
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实验中采集的目标散射的外差相干信号如图 4所示。信号长度为230点,在计算中采用的FFT计算长度为512点。
采用WDR & FFT方法和FFT方法分别对静止目标信号计算的频率结果,如图 5a和图 5b所示。图中展示了1000个脉冲的计算结果,横坐标为脉冲数,纵坐标为计算的频率。分别采用WDR & FFT方法和FFT方法以目标静止的1000个脉冲计算的频率累加后的均值为各自的零速度基准,计算了对应平移速率为-0.04 m/s,-0.06 m/s,-0.08 m/s的脉冲信号频率,并作1000次结果累加平均,平均后频率值减去基准频率,最后换算为速度。速度计算结果如表 1所示。
表 1 速度计算结果对比
Table 1. Comparison of speed calculation results
set speed/(m·s-1) WDR & FFT/(m·s-1) FFT/(m·s-1) stationary 0 0 -0.04 -0.0434 -0.0278 -0.06 -0.0625 -0.0446 -0.08 -0.0779 -0.0592 比较图 5可知,WDR & FFT方法计算的结果中偏离均值的频率结果远多于FFT方法计算的结果。但是比较表 1可知,WDR & FFT方法测量结果的准确性高于FFT方法。WDR & FFT方法测量的速度与设置速率的最大偏差为4 mm/s,而FFT方法测量的速率与设置速率的最大偏差为21 mm/s。
表 2 去奇异值计算结果
Table 2. De-singular value calculation results
set speed/(m·s-1) -0.04 -0.06 -0.08 remove speed deviation greater than ±0.03 m/s results/(m·s-1) -0.0435 -0.0614 -0.0782 remove speed deviation greater than ±0.05 m/s results/(m·s-1) -0.0449 -0.0618 -0.0782 remove speed deviation greater than ±0.07 m/s results/(m·s-1) -0.0456 -0.0619 -0.0780 remove speed deviation greater than ±0.09 m/s results/(m·s-1) -0.0469 -0.0619 -0.0771 remove speed deviation greater than ±0.2 m/s results/(m·s-1) -0.0476 -0.0638 -0.0787 为了说明WDR & FFT方法计算结果的准确性与计算结果中较多的偏离值的关系,将1000个脉冲测量的频率值中偏离均值较多的结果作为奇异值去掉,分析其对测量结果的影响,结果如表 2所示。由表 2数据可知,WDR & FFT方法计算的目标速度准确性和分辨率受计算的奇异值影响较小,误差小于8 mm/s。
去除速率偏差大于±0.03 m/s的奇异值后,各脉冲对应的频率值如图 6所示。由图可知,WDR & FFT方法可准确的分辨速率变化为0.02 m/s的目标。
图 6 WDR & FFT法去奇异值之后的频率计算结果
Figure 6. Frequency calculation results by WDR & FFT method and remove singular values
对于计算中较多奇异点的问题,分析原因为:硬靶目标本身振动会造成一定的速度误差[29]加之小波分解与重构中会造成频谱混叠现象;此外作者用频带最高的信号频谱减去频带第二高的信号频谱,并未完全抵消频谱混叠,因此存在目标多普勒频率点的错误识别[30]。
以转盘为高速运动的目标,发现在测量转盘的径向速度时,光束照射的角度测量不准确和转盘本身的振动都将带来较大的误差,无法作为稳定的高速高分辨率的目标进行测量,因此未开展相关实验。
基于WDR联合FFT方法的脉冲相干测速精度研究
Research on the precision of pulse coherent velocimetry based on WDR combined FFT method
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摘要: 为了提高远距离测速精度, 采用一种基于小波分解与重构(WDR)联合快速傅里叶变换(FFT)的信号处理方法(WDR & FFT), 进行了理论分析与实验验证, 取得了不同速度下的硬目标脉冲相干测速数据。结果表明, WDR & FFT方法可准确地分辨速率变化为0.02 m/s的目标。该研究为远距离低速目标的高分辨率测速提供了参考。Abstract: In order to improve the accuracy of long-distance speed measurement, a signal processing method based on wavelet decomposition reconstruction (WDR) combined with fast Fourier transform (FFT) was adopt in this paper. Theoretical analysis and experimental verification were carried out, and the pulse coherent velocimetry data of hard targets at different speeds were obtained. The results show that the targets with a velocity change of 0.02 m/s can be accurately resolved by using the WDR & FFT method. This research provides a reference for the high-resolution velocity measurement of long-distance and low-velocity targets.
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表 1 速度计算结果对比
Table 1. Comparison of speed calculation results
set speed/(m·s-1) WDR & FFT/(m·s-1) FFT/(m·s-1) stationary 0 0 -0.04 -0.0434 -0.0278 -0.06 -0.0625 -0.0446 -0.08 -0.0779 -0.0592 表 2 去奇异值计算结果
Table 2. De-singular value calculation results
set speed/(m·s-1) -0.04 -0.06 -0.08 remove speed deviation greater than ±0.03 m/s results/(m·s-1) -0.0435 -0.0614 -0.0782 remove speed deviation greater than ±0.05 m/s results/(m·s-1) -0.0449 -0.0618 -0.0782 remove speed deviation greater than ±0.07 m/s results/(m·s-1) -0.0456 -0.0619 -0.0780 remove speed deviation greater than ±0.09 m/s results/(m·s-1) -0.0469 -0.0619 -0.0771 remove speed deviation greater than ±0.2 m/s results/(m·s-1) -0.0476 -0.0638 -0.0787 -
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