Modal Analysis from Random and Compressed Samples

Explore modal analysis techniques for structural health monitoring in this 52-minute lecture from the Alan Turing Institute. Delve into sampling and compression strategies for wireless sensor networks, focusing on SVD-based methods and atomic norm minimization for mode shape and frequency recovery. Examine theoretical bounds on sample complexity and recovery accuracy, and compare various sampling/compression approaches. Learn about applications in civil and structural engineering, signal processing, and applied mathematics. Gain insights from speaker Michael B. Wakin, an accomplished researcher in compressive sensing and signal processing, as he presents case studies, experimental results, and discusses open questions in the field.

Intro
Motivation
Data collection
Equations of motion
Free vibration
Modal analysis techniques
Sampling model
Joint sparse frequency estimation
Classical spectral estimation
Method #1: Proper Orthogonal Decomposition
SVD of data matrix
POD considerations
Minimum separation condition
Uniform time sampling
Experiment: Telegraph Bridge data
Experiment, ctd
Method #2: Atomic norm minimization
Synchronous random sampling
Random temporal compression
Random spatial compression
Benefits of compression
Sampling rate scaling
Orthogonality
Synchronous vs. asynchronous
More sensors
Open questions