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

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.

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.