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Modal Analysis in the Presence of Harmonic Excitation

The case study presented here demonstrates how the harmonic detection and compensation in the Enhanced Frequency Domain Decomposition algorithm makes it easy to estimate modes from of a ship. It also demonstrate an alternative analysis using the Crystal Clear SSI algorithm.

The measurements and analysis presented here are performed by University of Rostock,
Faculty of Mechanical engineering. Chair of Technical Mechanics.

The ship tested has the following technical specifications:

  • Build at Flensburger Schiffbau Gesellschaft.
  • Dimensions: length over all: 199.8 m
  • Speed: 22.5 kn
  • Main engine: 9L 60 MC-C (MAN B&W, 9 cylinder)
  • Power: 20 070 kW
  • Speed: 123 rpm
  • Working process: two-stroke
  • 4-bladed propeller with controllable pitch

The ship was driven by variable pitch propeller, therefore the rotational speed of the main engine was more or less constant. Several harmonic excitation lines is present in the data because of the dynamic characteristic of the engine.

Estimation of Harmonic Indicators

The automatic detection of harmonics was applied to the data. In the display below the Singular Value Decomposition of the spectral densities of the measurements are shown in the lower window. In the top window the average Kurtosis of projection channels at each discrete frequency is shown as the gray curve. Most Kurtosis values are located around 3, which is the Kurtosis for normally distributed data. However, at the frequencies of the deterministic sinusoidal signal (the harmonic and its over tones) the Kurtosis drops to 1.5, that is the value for randomly sampled sinusoidal data. A threshold, indicated by the blue horizontal line, marks what is considered to be "harmonics". At all frequencies where the Kurtosis is below this threshold a harmonic indicator is activated. This indicator is shown as a green vertical line below. All information at these green frequencies should be disregarded, when modal parameters are being estimated.

Utilizing Harmonic Indicators in the Enhanced Frequency Domain Decomposition

In the Enhanced Frequency Domain Decomposition shown below, it is seen how the green "harmonic" zones are disregarded, when the SDOF spectral density is estimated.

The spike caused by the forced "harmonic" excitation is not included the spectral density estimation, and is therefore not destroying the estimation of the natural frequency and damping ratio.

Estimation using Crystal Clear Stochastic Subspace Identification

An alternative way of estimating modal parameters from measurement including deterministic sinusoidal forces, from e.g. rotating machinery, is to apply the Crystal Clear Stochastic Subspace techniques available in the ARTeMIS Extrator Pro. In this case the "harmonics" are fitted just like all other physical information contained in the data. The "harmonics" can then easily be disregarded by looking at the damping, which typically is unreasonable low, and by the harmonic indicator. See below:

Related Information

S.E. Rosenow, P. Andersen
Operational Modal Analysis of a Wind Turbine Mainframe using Crystal Clear SSI
To be presented at the 28th International Modal Analysis Conference (IMAC) Jacksonville, Florida USA, 2010.

N.J. Jacobsen, P. Andersen, R. Brincker
Applications of Frequency Domain Curve-fitting in the EFDD Technique
Proceedings of the 26th International Modal Analysis Conference (IMAC) Orlando, Florida USA, 2008.

N.J. Jacobsen, P. Andersen, R. Brincker
Using EFDD as a Robust Technique to Deterministic Excitation in Operational Modal Analysis
Proceedings of The 2nd International Operational Modal Analysis Conference (IOMAC) Copenhagen, Denmark, 2007.


Structural Vibration Solutions A/S • Tel: +45 9635 4422 • Fax: +45 9635 4575 • svibs@svibs.com




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