Output-only Modal Analysis of a Beam Via Frequency Domain Decomposition Method Using Noisy Data

Document Type : Original Article


1 Department of Civil Engineering, Payame Noor University (PNU), Tehran, Iran

2 Faculty of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran


The output data from a structure is the building block for output-only modal analysis. The structure response in the output data, however, is usually contaminated with noise. Naturally, the success of output-only methods in determining the modal parameters of a structure depends on noise level. In this paper, the possibility and accuracy of identifying the modal parameters of a simply supported beam in the presence of noise has been discussed. The output-only modal analysis method with frequency domain decomposition was used and output data with various noise levels were considered. Initially, finite element modal analysis was used to determine the modal parameters for the beam which were afterwards enforced as the reference modal parameters. Then, appropriate input was applied to the beam and the acceleration signals of different nodes were produced through finite element transient analysis. In order to simulate noisy data, noises with different power levels were generated and added to the signals. Finally, the modal parameters were obtained by frequency domain decomposition method. The results showed that the modal parameters corresponding to the first vibration mode could only be identified with acceptable validity at low to moderate noise levels, whereas for higher modes, the modal parameters can be correctly obtained even at high noise levels.


 1. Giraldo, D. F., Song, W., Dyke, S. J. and Caicedo, J. M.,
“Modal identification through ambient vibration:
comparative study”, Journal of Engineering Mechanics, Vol.
135, No. 8, (2009), 759-770. 
2. Brincker, R. and Kirkegaard, P. H., “Special issue on
Operational Modal Analysis”, Mechanical Systems and
Signal Processing, Vol. 24, No. 5, (2010), 1209-1212. 
3. Brincker, R., Zhang, L. and Andersen, P., “Modal
identification of output-only systems using frequency
domain decomposition”, Smart Materials and Structures, Vol.
10, No. 3, (2001), 441-445. 
4. Batel, M., “Operational modal analysis-Another way of
doing modal testing”, Sound and Vibration, (2002), 22-27. 
5. Andersen, P., Brincker, R., Goursat, M. and Mevel, L.,
“Automated modal parameter estimation for operational
modal analysis of large systems”, in 2nd International
Operational Modal Analysis Conference, 299-308, (2007). 
6. Davoodi, M. R., Navayi Neya, B., Mostafavian, S. A.,
Nabavian, S. R. and Jahangiri, GH. R., “Determining
minimum number of required accelerometer for output -only
structural identification of frames”, in 7th International
Operational Modal Analysis Conference, 279-284, 2017. 
7. Mellinger, P., Döhler, M. and Mevel, L., “Variance estimation of
modal parameters from output-only and input/output subspace-based
system identification”, Journal of Sound and Vibration, Vol. 379, (2016), 1–27.

8. Stephan, C., “Sensor placement for modal identification”,
Mechanical Systems and Signal Processing, Vol. 27, (2012)
9. Wang, L., Song, R., Wu, Y. and Hu, W.  “Statistically Filtering
Data for Operational Modal Analysis under Ambient Vibration in
Structural Health Monitoring Systems”, in 3rd International
Conference on Industrial Engineering and Applications (ICIEA)
MATEC Web Conference 2016, Vol. 68, 14010, (2016). 
10. Makki Alamdari, M., Li, J. and Samali, B., “FRF-based damage
localization method with noise suppression approach”, Journal
of Sound and Vibration, Vol. 333, No. 14, (2014), 3305–3320. 
11. Peeters, B., Cornelis, B.,  Janssens, K. and  Van Der Auweraer,
H.,  “Removing Disturbing Harmonics in Operational Modal
Analysis”, in 2nd International Operational Modal Analysis
Conference, 185-192, (2007). 
12. Ingle, R. and Awale, R., “A unique approach of noise elimination
from electroencephalography signals between normal and
meditation state”, International Journal of EngineeringTransactions B: Applications, Vol. 31, No. 5, (2018), 719-728.
13. Bonness, W. K. and Jenkins, D. M., “Removing Unwanted Noise
from Operational Modal Analysis Data”, Topics in Modal
Analysis, Vol. 10, (2015), 115–122. 
14. Feng, L. and Lin, L., “Comparative analysis of image denoising
methods based on wavelet transform and threshold functions”, 
International Journal of Engineering-Transactions B:
Applications,  Vol. 30, No. 2, (2017), 199-206. 
15. Khoshnood, A. M., Khaksari, H., Roshanian, J. and Hasani, S. M.,
“Active noise cancellation using online wavelet based control
system: numerical and experimental study”, International
Journal of Engineering-Transactions A: Basics, Vol. 30, No. 1,
(2017), 120-126. 
16. Reynders, E. and De Roeck, G., “Reference-based combined
deterministic-stochastic subspace identification for experimental
and operational modal analysis”, Mechanical Systems and
Signal Processing, Vol. 22, No. 3, (2008), 617–637. 
17. Shi, Y., Li, Z. and Chang, C.C., “Output-only subspace
identification of structural properties and unknown ground
excitation for shear-beam buildings”, Advances in Mechanical
Engineering, Vol. 8, No. 11, (2016), 1–15. 
18. Yi, J.H. and Yun, C.B., “Comparative study on modal
identification methods using output-only information”,
Structural Engineering and Mechanics, Vol. 17, No. 3-4,
(2004), 445–466. 
19. Tamura, Y., “Damping in buildings and estimation techniques”,
in 6th Asia-Pacific Conference on Wind Engineering (APCWEVI),
20. Brincker, R., Zhang, L. and Andersen, P., “Output-Only Modal
Analysis by Frequency Domain Decomposition”, in 25th
International Conference on Noise and Vibration Engineering,
717-723, (2000). 
21. Gade, S., Møller, N. B., Herlufsen, H. and Konstantin-Hansen H.,
“Frequency Domain Techniques for Operational Modal
Analysis”, in 1st International Operational Modal Analysis
Conference, 1-10, (2005). 
22. Zhang, J., Prader, J., Grimmelsman, K. A., Moon, F., Aktan, A.
E. and Shama, A., “Experimental Vibration Analysis for
Structural Identification of a Long-Span Suspension Bridge”,
Journal of Engineering Mechanics, Vol.139, No.6, (2013), 748–
23. Proakis, J.G. and Salehi, M., “Digital communications”,
McGraw-Hill, Fifth edition, (2008). 

24. Moaveni, B., Barbosa, A. R., Conte, J. P. and Hemez, F. M., 
“Uncertainty analysis of system identification results obtained for
a seven-story building slice tested on the UCSD-NEES shake
table”, Structural Control and Heath Monitoring, Vol. 21, No.4,
(2014), 466–483. 
25. Perry, M. J. and Koh, C. G., “Output-only structural identification
in time domain: Numerical and experimental studies”,
Earthquake Engineering and Structural Dynamics, Vol. 37,
No.4, (2008), 517–533. 
26. Makki Alamdari, M., Samali, B., Li, J., Kalhori, H. and Mustapha,
S., “Spectral-Based Damage Identification in Structures under
Ambient Vibration”, Journal of Computing in Civil
Engineering, Vol. 30, No. 4, (2016), 4015062. 
27. He, J. and Fu, Z. F., “Modal Analysis”, Dehli: Butterworth
HeinteMann, (2001). 
28. Mostafavian, S. A., Davoodi, M. R. and Vaseghi Amiri, J., “Ball
joint behavior in a double layer grid by dynamic model updating”,
Journal of Constructional Steel Research, Vol. 76, (2012), 28– 38. 
29. Adeli, H. and Jiang, X., “Dynamic Fuzzy Wavelet Neural
Network Model for Structural System Identification”, Journal of
Structural Engineering, Vol. 132, No. 1, (2006), 102–111. 
30. Moaveni, B. and Asgarieh, E., “Deterministic-stochastic subspace
identification method for identification of nonlinear structures as
time-varying linear systems”, Mechanical Systems and Signal
Processing, Vol. 31, (2012), 40–55. 
31. Gkoktsi, K., Giaralis, A. and TauSiesakul, B., “Sub-Nyquist
signal-reconstruction-free operational modal analysis and damage
detection in the presence of noise”, in Proceeding of Sensors and
Smart Structures Technologies for Civil, Mechanical, and
Aerospace Systems 2016, 980312, (2016). 
32. Pastor, M., Binda, M. and HarĨarik, T., “Modal Assurance
Criterion”, Procedia Engineering, Vol. 48, (2012), 543-548. 
33. Allemang, R.J., “The modal assurance criterion - Twenty years of
use and abuse”, Sound and Vibration, Vol. 37, No. 8, (2003) 14–21.