Data reduction using a regressive discrete Fourier-transform technique

Joris Vanherzeele; Patrick Guillaume; Steve Vanlanduit; Peter Verboven

doi:10.1117/12.579617

22 June 2004 Data reduction using a regressive discrete Fourier-transform technique

Joris Vanherzeele, Patrick Guillaume, Steve Vanlanduit, Peter Verboven

Proceedings Volume 5503, Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications; (2004) https://doi.org/10.1117/12.579617
Event: Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, 2004, Ancona, Italy

Abstract

With the development of optical measurement techniques it was possible to obtain vast amounts of data. In vibrometry applications in particular where FRF-matrices with tens of thousands of rows and an equal number of rows are stored, data reduction has become a point of interest. It has long been known that it is possible to reduce (approximate) the measurement data (e.g. mode shapes) by means of a Fourier decomposition. One of the most common techniques for evaluating optical measurement data is by means of a Fourier analysis. It is well known that for periodic and band-limited sequences the Discrete Fourier Transform (DFT) returns the true Fourier coefficients when exactly 1 period (or a multiple) is processed. Leakage will occur when less than 1 period is considered. This gives rise to non-negligible errors, which can be resolved by using a Regressive Discrete Fourier Transform (RDFT), introduced in this article. The measured signal is represented by a model using sines and cosines. The coefficients of those sines and cosines are then estimated on a global scale by means of a frequency domain system identification technique. By making use of the regressive technique proposed in this paper, it is possible to reduce the data in comparison to the classical Fourier decomposition even further by a sizeable factor. In this article the introduced method will be applied in particular to the reduction of data for (1D) laser vibrometer measurements performed on a composite (IPC) beam, as well as on an aluminum plate (2D). The proposed technique will also be validated on both 1D and 2D simulations of varying complexity.

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Joris Vanherzeele, Patrick Guillaume, Steve Vanlanduit, and Peter Verboven "Data reduction using a regressive discrete Fourier-transform technique", Proc. SPIE 5503, Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, (22 June 2004); https://doi.org/10.1117/12.579617

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KEYWORDS

Fourier transforms

Aluminum

Error analysis

Vibrometry

Distortion

Optical testing

Data modeling

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