TY - GEN

T1 - A compressive sensing based approach for estimating stochastic process power spectra subject to missing data

AU - Comerford, Liam

AU - Kougioumtzoglou, Ioannis A.

AU - Beer, Michael

PY - 2014

Y1 - 2014

N2 - A compressive sensing (CS) based approach for power spectrum estimation of stationary stochastic processes subject to missing data is developed. In general, stochastic process records such as wind and wave excitations can often be represented with relative sparsity in the frequency domain. Relying on this attribute, a CS framework can be applied to reconstruct a signal that contains sampling gaps, possibly occurring for reasons such as sensor failures, data corruption, limited bandwidth/storage capacity, and power outages. Specifically, first a Fourier basis is selected for the recorded signal expansion. Next, an L1-norm minimization procedure is performed for obtaining the sparsest Fourier based representation of the signal. Finally, power spectrum estimates are derived from the determined expansion coefficients directly circumventing reconstruction of the signal in the time domain. The technique is shown to estimate successfully the essential features such as the dominant spectral peaks of the recorded processes' power spectra. Further, it appears to be efficient even in cases with 75% missing data demonstrating superior performance in comparison with alternative existing techniques. A significant advantage of the approach relates to the fact that it performs satisfactorily even in the presence of noise. Several numerical examples demonstrate the versatility and reliability of the approach.

AB - A compressive sensing (CS) based approach for power spectrum estimation of stationary stochastic processes subject to missing data is developed. In general, stochastic process records such as wind and wave excitations can often be represented with relative sparsity in the frequency domain. Relying on this attribute, a CS framework can be applied to reconstruct a signal that contains sampling gaps, possibly occurring for reasons such as sensor failures, data corruption, limited bandwidth/storage capacity, and power outages. Specifically, first a Fourier basis is selected for the recorded signal expansion. Next, an L1-norm minimization procedure is performed for obtaining the sparsest Fourier based representation of the signal. Finally, power spectrum estimates are derived from the determined expansion coefficients directly circumventing reconstruction of the signal in the time domain. The technique is shown to estimate successfully the essential features such as the dominant spectral peaks of the recorded processes' power spectra. Further, it appears to be efficient even in cases with 75% missing data demonstrating superior performance in comparison with alternative existing techniques. A significant advantage of the approach relates to the fact that it performs satisfactorily even in the presence of noise. Several numerical examples demonstrate the versatility and reliability of the approach.

KW - Compressive sensing

KW - Missing data

KW - Power spectrum estimation

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=84994476677&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84994476677

T3 - Proceedings of the International Conference on Structural Dynamic , EURODYN

SP - 2995

EP - 2999

BT - Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

A2 - Cunha, A.

A2 - Ribeiro, P.

A2 - Caetano, E.

A2 - Muller, G.

T2 - 9th International Conference on Structural Dynamics, EURODYN 2014

Y2 - 30 June 2014 through 2 July 2014

ER -