Inferring Structural Properties: Graphs and Bridges
Talkat Workshop on Succinct Data Representations and Applications (Simons Institute Big Data 2013) · 2013-09-16..09-19
summary
Wireless sensors sample bridge vibration and modal shapes are recovered by taking an SVD of the time-by-sensor matrix after aggressive sketching. Using Johnson-Lindenstrauss sketching (per-sensor random ±1 linear combinations) the pipeline reduces 3,000 uniform time samples to about 50 measurements per node (reported 18-sensor testbed), and still returns right singular vectors within an O(ε) bound that depends on the spectral gap and minimum modal-frequency separation. FFT peeks estimate modal frequencies; accuracy trades off with sample duration and rank gaps.
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chapters (13)
- 0:00Intro
- 1:17Structural health monitoring
- 5:06Structural Dynamics
- 9:00Data Collection
- 10:59SVD for Modal Analysis
- 17:47Random Sampling
- 24:13Uniform Sampling with Random Matrix Multiplication
- 29:50Simulations: Grove Street Bridge Data
- 32:36Estimating Modal Frequencies
- 33:08Simulations: Synthetic Data
- 34:32Sketching
- 35:14Sketched SVD
- 36:22Sketch of Proof