Enhanced Multivariate Based Approach for SHM Using Hilbert Transform



Published Sep 25, 2011
Rafik Hajrya Nazih Mechbal Michel Vergé


In structural health monitoring, features extraction from measured data plays an important role. In order to enhance information about damage, we propose in this paper, a new damage detection methodology, based on the Hilbert transform and multivariate analysis. Using measurements given by distributed sensors of a smart composite structure, we apply the Hilbert transform to calculate an envelope matrix. This matrix is then treated using multivariate analysis. The subspaces associated to the envelope matrix are used to define a damage index (DI). Furthermore, from perturbation theory of matrices, we propose a bound associated to this DI, by inspecting this bound, decision on the health of the structure is generated. Experimentation on an actual composite smart structure will show the effectiveness of the proposed approach.

How to Cite

Hajrya, R., Mechbal, N. ., & Vergé, M. . (2011). Enhanced Multivariate Based Approach for SHM Using Hilbert Transform. Annual Conference of the PHM Society, 3(1). https://doi.org/10.36001/phmconf.2011.v3i1.1976
Abstract 75 | PDF Downloads 102



Multivariate analysis, Hilbert transform, angle between subspaces, perturbation theory of matrices, singular value decomposition, Smart composite strcuture

Bendat, J. S., and Piersol, A. G. (2000). "Random data: analysis and measurement procedures." New York, NY: Wiley-Interscience.

De Boe, P., and Golinval, J. C. (2003). "Principal component analysis of a piezosensor array for damage localization." Structural Health Monitoring, 2(2), 137-144.
Giurgiutiu, V., Zagrai, A., and Bao, J. J. (2002). "Piezoelectric wafer embedded active sensors for aging aircraft structural health monitoring." Structural Health Monitoring, 1(1), 41-61.

Golub, G. H. V. L. C. F. (1983). "Matrix computation." Johns Hopkins University Press, Baltimore.

Hajrya, R., Mechbal, N., and Vergé, M. (2010). "Active Damage Detection and Localization Applied to a Composite Structure Using Piezoceramic Patches." Conference on Control and Fault-Tolerant Systems. Nice, France.

Hajrya, R., Mechbal, N., and Vergé, M. (2011). "Proper Orthogonal Decomposition Applied to Structural Health Monitoring." IEEE International Conference on Communications, Computing and Control Applications. Hammamet, Tunisia.

Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Snin, H. H., Zheng, Q., Yen, N. C., Tung, C. C., and Liu, H. H. (1998). "The empirical mode decomposition and the Hubert spectrum for nonlinear and non- stationary time series analysis." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454(1971), 903-995.

Kerschen, G., Golinval, J. C., Vakakis, A. F., and Bergman, L. A. (2005). "The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: An overview." Nonlinear Dynamics, 41(1-
3), 147-169.

Staszewski, W. J. (2002). "Intelligent signal processing for damage detection in composite materials." Composites Science and Technology, 62(7-8), 941- 950.

Su, Z., Wang, X., Chen, Z., Ye, L., and Wang, D. (2006). "A built-in active sensor network for health monitoring of composite structures." Smart Materials and Structures, 15(6), 1939-1949.

Wedin, P. (1972). "Perturbation Bounds in Connection with Singular value Decomposition." Numerical Mathematics, 12(1), 99-111.

Yang, J. N., Lei, Y., Lin, S., and Huang, N. (2004). "Hilbert-Huang based approach for structural damage detection." Journal of Engineering Mechanics, 130(1), 85-95.

Yang, J. N., Lei, Y., Pan, S., and Huang, N. (2003a). "System identification of linear structures based on Hilbert-Huang spectral analysis. Part 1: Normal modes." Earthquake Engineering and Structural Dynamics, 32(9), 1443-1467.

Yang, J. N., Lei, Y., Pan, S., and Huang, N. (2003b). "System identification of linear structures based on Hilbert-Huang spectral analysis. Part 2: Complex modes." Earthquake Engineering and Structural Dynamics, 32(10), 1533-1554.

Zang, C., Friswell, M. I., and Imregun, M. (2004). "Structural damage detection using independent component analysis." Structural Health Monitoring, 3(1), 69-83.
Poster Presentations