Decentralized modal identification using sparse blind source separation

Abstract

Popular ambient vibration-based system identification methods process informationcollected from a dense array of sensors centrally to yield the modal properties. In suchmethods, the need for a centralized processing unit capable of satisfying largememory and processing demands is unavoidable. With the advent of wirelesssmart sensor networks, it is now possible to process information locally at thesensor level, instead. The information at the individual sensor level can then beconcatenated to obtain the global structure characteristics. A novel decentralizedalgorithm based on wavelet transforms to infer global structure mode informationusing measurements obtained using a small group of sensors at a time is proposedin this paper. The focus of the paper is on algorithmic development, while theactual hardware and software implementation is not pursued here. The problem ofidentification is cast within the framework of under-determined blind source separationinvoking transformations of measurements to the time–frequency domain resultingin a sparse representation. The partial mode shape coefficients so identified arethen combined to yield complete modal information. The transformations areundertaken using stationary wavelet packet transform (SWPT), yielding a sparserepresentation in the wavelet domain. Principal component analysis (PCA) is thenperformed on the resulting wavelet coefficients, yielding the partial mixing matrixcoefficients from a few measurement channels at a time. This process is repeated usingmeasurements obtained from multiple sensor groups, and the results so obtained from eachgroup are concatenated to obtain the global modal characteristics of the structure.