System and method for automated extraction of high resolution structural dynamics from video

1. A method for automatically extracting vibrational modes of a structure, the method comprising:

receiving, by a processor, a plurality of video frames, each of the video frames comprising a plurality of pixels;

decomposing, by the processor, each of the video frames on a plurality of spatial scales in accordance with complex steerable pyramid filters to obtain a filter response for each of the spatial scales;

computing, by the processor, a plurality of local phases of the pixels of each frame;

removing, by the processor, a temporal mean from each frame to obtain a plurality of factored vibration motion functions;

performing, by the processor, principal component analysis on the factored vibration motion functions to obtain principal components;

blind source separating, by the processor, the principal components to compute a plurality of modal coordinates;

magnifying an ith modal coordinate of the modal coordinates by:

scaling the ith modal coordinate by a positive coefficient to compute a scaled ith modal component;

scaling each non-ith modal coordinate other than the ith modal coordinate by a negative coefficient to compute one or more non-ith scaled modal coordinates; and

applying an inverse transform on the scaled ith modal coordinate and the one or more non-ith scaled modal coordinates to compute an ith-mode magnified vibration motion function;

computing, by the processor, frequency and damping ratios in accordance with the modal coordinates; and

outputting, by the processor, the computed frequency and damping ratios.

2. The method of claim 1 , further comprising outputting the ith-mode magnified vibration motion function as a factored vibration motion function.

3. The method of claim 1 , further comprising reconstructing a plurality of ith mode magnified images based on the ith mode magnified vibration motion function.

4. The method of claim 3 , further comprising outputting the ith magnified images as a video.

5. The method of claim 3 , further comprising:

performing edge detection on the ith mode magnified image to generate magnified ith mode shapes; and

outputting the magnified ith mode shapes.

6. The method of claim 5 , further comprising outputting the magnified ith mode shapes as a video.

7. The method of claim 1 , wherein the video frames are received from a video camera, the video frames being captured by the video camera at a rate of at least 240 frames per second.

8. The method of claim 1 , wherein the video frames are received from a video camera, the video frames being captured by the video camera at a rate of at least 24 frames per second.

9. A system for automatically extracting vibrational modes of a structure comprising:

a processor; and

memory coupled to the processor, the memory having instructions stored there on that, when executed by the processor, cause the processor to:

receive a plurality of video frames, each of the video frames comprising a plurality of pixels;

decompose each of the video frames on a plurality of spatial scales in accordance with complex steerable pyramid filters to obtain a filter response for each of the spatial scales;

compute a plurality of local phases of the pixels of each frame;

remove a temporal mean from each frame to obtain a plurality of factored vibration motion functions;

perform principal component analysis on the factored vibration motion functions to obtain principal components;

blind source separate the principal components to compute a plurality of modal coordinates;

magnify an ith modal coordinate of the modal coordinates by:

scaling the ith modal coordinate by a positive coefficient to compute a scaled ith modal component;

scaling each non-ith modal coordinate other than the ith modal coordinate by a negative coefficient to compute one or more non-ith scaled modal coordinates; and

applying an inverse transform on the scaled ith modal coordinate and the one or more non-ith scaled modal coordinates to compute an ith-mode magnified vibration motion function;

compute frequency and damping ratios in accordance with the modal coordinates; and

output the computed frequency and damping ratios.

10. The system of claim 9 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to output the ith-mode magnified vibration motion function as a factored vibration motion function.

11. The system of claim 9 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to reconstruct a plurality of ith mode magnified images based on the ith mode magnified vibration motion function.

12. The system of claim 11 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to output the ith magnified images as a video.

13. The system of claim 11 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to:

perform edge detection on the ith mode magnified image to generate magnified ith mode shapes; and

output the magnified ith mode shapes.

14. The system of claim 13 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to output the magnified ith mode shapes as a video.

15. The system of claim 9 , further comprising a video camera, the video camera being configured to capture the video frames at a rate of at least 240 frames per second.

16. The system of claim 9 , further comprising a video camera, the video camera being configured to capture the video frames at a rate of at least 24 frames per second.

17. A system for automatically extracting vibrational modes of a structure, the system comprising:

means for receiving a plurality of video frames, each of the video frames comprising a plurality of pixels;

means for decomposing each of the video frames on a plurality of spatial scales in accordance with complex steerable pyramid filters to obtain a filter response for each of the spatial scales;

means for computing a plurality of local phases of the pixels of each frame;

means for removing a temporal mean from each frame to obtain a plurality of factored vibration motion functions;

means for performing principal component analysis on the factored vibration motion functions to obtain principal components;

means for blind source separating the principal components to compute a plurality of modal coordinates;

means for magnifying an ith modal coordinate of the modal coordinates by:

scaling the ith modal coordinate by a positive coefficient to compute a scaled ith modal component;

scaling each non-ith modal coordinate other than the ith modal coordinate by a negative coefficient to compute one or more non-ith scaled modal coordinates; and

applying an inverse transform on the scaled ith modal coordinate and the one or more non-ith scaled modal coordinates to compute an ith-mode magnified vibration motion function;

means for computing frequency and damping ratios in accordance with the modal coordinates; and

means for outputting the computed frequency and damping ratios.