The application of compressed sensing to detecting damage in structures

Detecting damage in a large scale structure such as a bridge or dam requires the collection of data at multiple time and length scales. The collection of these data generally requires the structure under observation to be instrumented with a variety of sensors, each with a unique sampling rate. One of the principal challenges to the structural health monitoring (SHM) community is to take this large, heterogeneous set of data, and extract information that allows the estimation of the remaining service life of a structure. Another important challenge is to collect relevant data from a structure in a manner that is cost effective, and respects the size, weight, cost, energy consumption, and bandwidth limitations placed on the system. Both of these challenges have proven to be formidable hurdles to the wide-scale implementation of SHM systems. In this work we explore the suitability of compressed sensing to address both challenges. Recently compressed sensing has presented itself as a candidate solution for directly collecting relevant information from sparse, high-dimensional measurements. The main idea behind compressed sensing is that by directly collecting a relatively small number of coefficients it is possible to reconstruct the original measurement. The coefficients are obtained from linear combinations of (what would have been the original direct) measurements. At first glance it would appear that this should not be possible because it would require solving an underdetermined linear system of equations. However, it has been shown that if the solution is sparse in some basis, it is possible to find the solution using l 1 norm regularization. Conveniently, most signals found in nature are indeed approximately sparse (in some basis) with the notable exception of random noise. Therefore, the findings of the compressed sensing community hold great potential for changing the way SHM data is collected. In this work a digital version of a compressed sensor is implemented on-board a microcontroller similar to those used in embedded SHM sensor nodes. The sensor node is tested in a surrogate SHM application requiring acceleration measurements. Currently the prototype compressed sensor is capable of collecting compressed coefficients from measurements and sending them to an off-board processor for reconstruction using L1 norm minimization. A compressed version of the matched filter known as the smashed filter, has also been implemented on-board the sensor node, and its suitability for detecting structural damage will be discussed.