Research On LDV Doppler Frequency Algorithm Based On Mixed-Radix FFT And Its Introduced Uncertainty Evaluation

Laser Doppler Velocimetry(LDV)is a single-point velocity measurement instrument which has high-precision and non-contact properties.This paper aims to solve the problem of traceability of high-speed measurement results of LDV,and to clarify the applicability of low-speed calibration results of LDV by the spinning-disc facility under high-speed conditions.The main work of this paper includes:(1)A practical Doppler frequency algorithm composed of the mixed-radix FFT algorithm and the phase difference correction method was proposed;by comparing DFT,radix-2 FFT,mixed-radix FFT and its fast algorithm in terms of computational burden,time complexity and simulation results,the feasibility of using mixed-radix FFT and phase difference correction method to correct the spectrum was discussed,verifying the rationality of the Doppler frequency algorithm in the LDV data processing system.(2)GUIs were designed both in MATLAB and Python environments for signal simulation and visualization.A Doppler frequency calculation system based on the two-channel data collection system named Handyscope HS5-540 XM from the Netherlands company Tie Pie engineering was built;the signal generator inside was controlled by the algorithm to output the Doppler signal which was received through data channel and then was calculated and displayed on the oscilloscope in the environment of Python 3.7.9.(3)The method of Monte Carlo Method(MCM)propagating probability distribution was proposed to evaluate and express the uncertainty of Doppler frequency caused by Doppler algorithm at different velocity.By comparing the uncertainty at different velocity,it was found that the relative uncertainty of Doppler frequency caused by the algorithm fluctuated around 0.04%,were all less than 0.05%and remained basically unchanged within the range of velocity from 0.1 to 340 m/s.And the budget of the change of the Doppler frequency measurement uncertainty at different velocity on the velocity measurement results was less than 0.0011%,which verified the applicable accuracy range of the Doppler frequency algorithm.Therefore,the LDV calibration results at low velocity can be reasonably applied at high velocity measurement and then the traceability problem of the high velocity measurement of LDV has been solved.