Abstract
For the development of innovative materials, construction types or maintenance strategies, experimental investigations are inevitable to validate theoretical models in praxis. Numerical simulations are alternatives to expensive experimental investigations. The statistical properties of the response in the frequency domain obtained from continuously measured data are often the basis for many approaches, such as the optimization of damage indicators for structural health monitoring systems. Two straightforward numerical simulation methods exist to derive the statistics of a response due to random excitation. One method is the sample-based technique, wherein for each excitation sample a time integration solution is needed. This can be computationally very expensive if a high accuracy of the statistical properties is of interest. The other method consists in using Fourier transforms and frequency response functions, wherein an infinite weakly stationary process is assumed. In this paper, a novel method is proposed that overcomes the limitation of both straightforward methods, by providing a fast probabilistic framework to determine accurately the statistics of the response for short time series. The influences of signal processing techniques, such as windowing, are considered as well. The performance of the algorithm is demonstrated on a three-degree-of-freedom system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bathe KJ (1996) Finite element procedures. Prentice Hall, Englewood Cliffs
Brehm M, Massart TJ, Deraemaeker A (2012) Application of an updated notched beam model using an implicit gradient cracking approach for the purpose of damage detection based on modal strains. In: Proceedings of international conference on noise and vibration engineering (ISMA), Leuven, Belgium, 17–19 September 2012
Brehm M, Zabel V, Bucher C (2013) Optimal reference sensor positions using output-only vibration test data. Mech Syst Signal Process 41(1–2):196–225
Deraemaeker A, Reynders E, De Roeck G, Kullaa J (2008) Vibration based structural health monitoring using output-only measurements under changing environment. Mech Syst Signal Process 22(1):34–56
Mao Z, Todd M (2013) Statistical modeling of frequency response function estimation for uncertainty quantification. Mech Syst Signal Process 38(2):333–345
Natke HG (1989) Baudynamik, 3rd edn. B.G. Teubner Stuttgart, Germany
Natke HG (1992) Einführung in die Theorie und Praxis der Zeitreihen- und Modalanalyse, 3rd edn. Vieweg & Sohn, Braunschweig/Wiesbaden, Germany
Oppenheim AV, Schafer RW, Buck JR (1999) Discrete-time signal processing, 2nd edn. Prentice-Hall, Englewood Cliffs
Preumont A (1982) Frequency domain analysis of time integration operators. Earthquake Eng Struct Dyn 10:691–697
Stein M (1987) Large sample properties of simulations using Latin hypercube sampling. Technometrics 29(2):143–151
Tondreau G (2013) Damage localization in civil engineering structures using dynamic strain measurements. Ph.D. thesis, Université libre de Bruxelles, Belgium
Tondreau G, Deraemaeker A (2013) Local modal filters for automated data-based damage localization using ambient vibrations. Mech Syst Signal Process 39(1–2):162–180
Zhang F (2011) Matrix theory: basic results and techniques. Springer, Berlin
Acknowledgements
The research presented in this article was carried out within the postdoctoral project “Dynamic Strain Sensing for SHM” funded through an incentive grant for scientific research by the Belgian funding organization F.R.S.-FNRS to which the authors like to express their gratitude for financial support.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Brehm, M., Deraemaeker, A. (2014). An Efficient Method for the Quantification of the Frequency Domain Statistical Properties of Short Response Time Series of Dynamic Systems. In: Atamturktur, H., Moaveni, B., Papadimitriou, C., Schoenherr, T. (eds) Model Validation and Uncertainty Quantification, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04552-8_30
Download citation
DOI: https://doi.org/10.1007/978-3-319-04552-8_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04551-1
Online ISBN: 978-3-319-04552-8
eBook Packages: EngineeringEngineering (R0)