Measuring and testing – Vibration – Sensing apparatus
Reexamination Certificate
2002-05-03
2004-08-24
Williams, Hezron (Department: 2856)
Measuring and testing
Vibration
Sensing apparatus
C073S660000, C073S662000
Reexamination Certificate
active
06779404
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for vibration analysis according to the preamble of claim
1
.
2. Background of the Invention
Modal identification is the process of estimating modal parameters from vibration measurements obtained from different locations of a structure. The modal parameters of a structure include the mode shapes, natural (or resonance) frequencies and the damping properties of each mode that influence the response of the structure in a frequency range of interest.
Modal parameters are important because they describe the inherent dynamic properties of the structure. Since these dynamics properties are directly related to the mass and the stiffness, experimentally obtained modal parameters provide information about these two physical properties of a structure. The modal parameters constitute a unique information that can be used for model validation, model updating, quality control and health monitoring.
In traditional modal analysis the modal parameters are found by fitting a model to the Frequency Response Function relating excitation forces and vibration response. In output-only modal analysis, the modal identification is performed based on the vibration responses only and a different identification strategy has to be used.
Output-only modal testing and analysis is used for civil engineering structures and large mechanical structures or structures m operation that are not easy to excite artificially.
Large civil engineering stares are not easily excited and they are often loaded by natural (ambient) loads that cannot easily be controlled or measured. Examples of such loads include wave loads on offshore structures, wind loads on buildings and traffic loads on bridges in such cases it is an advantage just to measure the natural (or ambient) responses and then estimate the modal parameters by performing an output-only modal identification. For civil structures the technique is often referred to as ambient response testing and ambient response analysis.
Application of output-only modal identification instead of traditional modal identification gives the user some clearly defined benefits in case of large structures and natural loading. Rather than loading the structure artificially and considering the natural loading as an unwanted noise source, the latter is used as the loading source. The main advantages of this technique are:
Testing is less time consuming since equipment for exciting the structure is not needed.
Testing does not interrupt the operation of the structure.
The measured response is representative of the real operating conditions of the structure.
When performing output-only modal identification of a structure, the user can perform the identification in the time domain or in the frequency domain. For output only identification, the time domain techniques have been rather dominating since no accurate techniques for frequency domain identification exists. However, since the frequency domain supports the physical intuition of the system, i.e. the user can observe the spectral densities and, thus, directly have an idea of the modes of the system by regarding the spectral peaks, simple and rather approximate techniques have been widely accepted for preliminary analysis. The most well-known frequency domain technique is the so-called classical approach, also denoted the basic frequency method, or the peak picking method, where the user simply chooses one of the frequency lines in the spectrum at the appearing peak as the natural (resonance) frequency and then estimates the corresponding mode shape as one of the columns of the spectral density matrix.
The classical approach is based on simple signal processing using the Discrete Fourier Transform, and is using the fact that well-separated modes can be estimated directly from the spectral density matrix at the peak, as shown in by Julius S. Bendat and Allan G. Piersol in “Engineering Applications of Correlation and Spectral Analysis”, John Wiley & Sons, 1993.
Other implementations of the technique make use of the coherence between channels as described by A. J. Felber in “Development of a Hybrid Bridge Evaluation System”, Ph.D. thesis, Department of Civil Engineering, University of British Columbia, Vancouver, Canada, 1993. The term channel is commonly used for the output data of a sensor.
The main advantage of the classical approach compared to other approaches, such as two-stage time domain identification technique, or the one-stage time domain identification techniques, for example the Stochastic Subspace Identification algorithms is its user-friendliness. It is fast, simple to use, and gives the user a “feeling” of the data he or she is dealing with.
The two-stage time domain has been described by H. Vold, J. Kundrat, G. T. Rocklin, and R. Russel in “A Multi-Input Modal Estimation Algorithm For Mini-Computer”, SAE Technical Paper Series, No. 820194, 1982; by S. R. Ibrahim and E. C. Milkulcik in “The Experimental Determination of Vibration Test Parameters From Time Responses”, The Shock and Vibration Bulletin, Vol. 46, No. 5, 1976, pp. 187-196; and by J.-N. Juang and R. S. Papa in “An Eigensystem Realization Algorithm For Modal Parameter Identification And Modal Reduction”, J. of Guidance, Control and Dynamics, Vol. 8, No. 5, 1985, pp. 620-627. The Stochastic Subspace Identification algorithms is described by P. Van Overschee and B. De Moor in “Subspace Identification for Linear Systems”, Kluwer Academic Publishers, 1996,
The classical technique gives reasonable estimates of natural frequencies and mode shapes if the modes are well-separated. However, in the case of close modes, it can be difficult to detect the close modes, and even in the case where close modes are detected, estimates becomes heavily biased by simple estimation of the mode shapes from one of the columns of the spectral matrix.
Further, the frequency estimates are limited by the frequency resolution of the spectral density estimate, and in all cases, damping estimation is uncertain or impossible.
SUMMARY OF THE INVENTION
It is the purpose of the invention to provide a frequency domain method for vibration analysis, i.e. output-only modal analysis, without these disadvantages, but where the user-friendliness is preserved.
This purpose is achieved by a method as mentioned by way of introduction and characterised as described in the characterising part of claim
1
.
The invention significantly reduces the uncertainty in the estimation of vibrational modes of an object. Due to its user friendliness and fast obtainable results, the invention is a substantial improvement for output-only modal analysis, where the only major difference between modal parameters estimated from traditional modal testing and output-only modal analysis is that the output-only modal analysis yields unscaled mode shapes.
In the invention, it is assumed that the object has been excited over a broad frequency range by a signal, which has the same intensity at all frequencies. This kind of excitation is called white noise. As a consequence of the assumption with regard to the input excitation as white noise, the analysis according to the invention is directed to the response of the object and uses therefore the well-known term called output-only modal analysis.
A number of techniques are used in the invention. One is the so called Frequency Domain Decomposition (FDD) which is known from, among others, traditional modal analysis, where the structure is loaded by a known input However, in the case of traditional modal analysis the system matrix that is decomposed is not the spectral density matrix describing the responses, but the frequency response function (FRF) matrix relating input and output of the system.
As a second technique, the present invention uses the so-called Singular Value Decomposition (SVD) to perform the frequency domain decomposition of the spectral matrix. The SVD is known from numerical mathematics and is used in a number of different applications. However, the main application of thi
Andersen Palle
Brincker Rune
Creighton Wray James
Narasimhan Meera P.
Saint-Surin Jacques M.
Williams Hezron
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