Tracking continuously scanning laser doppler vibrometer systems and methods
A one-dimensional (1D) and two-dimensional (2D) scan scheme for a tracking continuously scanning laser Doppler vibrometer (CSLDV) system to scan the whole surface of a rotating structure excited by a random force. A tracking CSLDV system tracks a rotating structure and sweep its laser spot on its surface. The measured response of the structure using the scan scheme of the tracking CSLDV system is considered as the response of the whole surface of the structure subject to random excitation. The measured response can be processed by operational modal analysis (OMA) methods (e.g., an improved lifting method, an improved demodulation method, an improved 2D demodulation method). Damped natural frequencies of the rotating structure are estimated from the fast Fourier transform of the measured response. Undamped full-field mode shapes are estimated by multiplying the measured response using sinusoids whose frequencies are estimated damped natural frequencies.
1. A method comprising:
measuring a response of a rotating structure subject to random excitation with a tracking continuous scanning laser Doppler vibrometer system;
determining a Fast Fourier Transform (FFT) of the response;
applying a bandpass filter to the response with a passband that includes a damped natural frequency of the rotating structure to create a filtered response;
determining a time interval between a minimum value and a maximum value of the filtered response;
multiplying the filtered response in the time interval by sinusoidal signals to create a plurality of processed responses; and
applying a lowpass filter to the plurality of processed responses to obtain an end-to-end undamped mode shape of the rotating structure.
2. The method of claim 1 , wherein the sinusoidal signals include cos(ω d,i t) and sin(ω d,i t), where ω d,i is the damped natural frequency of the rotating structure.
3. The method of claim 1 , wherein the tracking continuous scanning laser Doppler vibrometer system includes a camera, a scanner, and a single-point laser Doppler vibrometer.
4. The method of claim 1 , wherein the rotating structure is rotating at a non-constant speed.
5. The method of claim 1 , wherein the rotating structure is rotating at a constant speed.
6. The method of claim 1 , wherein the time interval is measured by the tracking continuous scanning laser Doppler vibrometer system from a first end of a scan path to a second end.
7. The method of claim 1 , further including determining end-to-end undamped mode shapes of the structure.
8. The method of claim 1 , further including determining a first normalized end-to-end undamped mode shape, a second normalized end-to-end undamped mode shape, and/or a third normalized end-to-end undamped mode shape of the rotating structure.
9. The method of claim 1 , further including determining a first damped natural frequency, a second damped natural frequency, and/or a third damped natural frequency of the rotating structure.
10. The method of claim 1 , wherein measuring the response of the rotating structure includes identifying a mark on the rotating structure.
11. The method of claim 10 , wherein the mark is a black circular mark.
12. The method of claim 1 , wherein measuring includes scanning along a two-dimensional path on the rotating structure.
13. The method of claim 1 , wherein the rotating structure is a wind turbine blade.
14. A method comprising:
measuring a response of a rotating structure subject to random excitation with a tracking continuous scanning laser Doppler vibrometer system;
interpolate positions of the response on a grid to generate a plurality of interpolated positions;
rectifying the plurality of interpolated positions to create a plurality of rectified interpolated positions;
identifying a plurality of zero-crossings from the plurality of rectified interpolated positions;
determine a portion of the plurality of zero-crossings with a time increment; and
interpolate and lift measurements at the portion of the plurality of zero-crossings.
15. The method of claim 14 , wherein rectifying the plurality of interpolated positions includes determining negative absolute values of differences between the plurality of interpolated positions and a position of a virtual measurement point on a scan path.
16. The method of claim 14 , wherein the time increment is equal to the inverse of a scan frequency.
17. The method of claim 14 , wherein the tracking continuous scanning laser Doppler vibrometer system includes a camera, a scanner, and a single-point laser Doppler vibrometer.
18. The method of claim 17 , wherein the method includes capturing images of the rotating structure.
19. The method of claim 14 , further including determining a damped natural frequency, a damping ratio, and/or an undamped mode shape of the rotating structure.
20. The method of claim 14 , wherein the rotating structure is a wind turbine blade.