P. Verboven

Force identification by means of in-operation modal models

In-operation modal analysis has become a valid alternative for structures where a classic forced-vibration test would be difficult if not impossible to conduct. The modelling of output-only data obtained from naturally excited structures is particularly interesting because the test structure remains in its normal in-operation condition during the test. One of the drawbacks of in-operation analysis is that part of the modal parameters can no longer be estimated. Consequently, the applicability of in-operation modal models remains somewhat restricted. For some in-operation applications, interest lies in the identification of forces that gave rise to measured response signals. In order to solve this ill-conditioned problem, a complete modal model of the structure is required. Recently, a sensitivity-based method was proposed for the normalization of operational mode shape estimates on a basis of in-operation modal models only. This method allows the reconstruction of complete modal models from output-only data. In this contribution, the possibility of using such re-completed in-operation modal models for the identification of localized forces is explored.

An automatic frequency domain modal parameter estimation algorithm

In this article, a frequency-domain modal parameter estimation method is proposed. The algorithm automatically separates physical poles from mathematical ones. An important issue in the automatization of the algorithm is the inclusion of noise information to estimate the standard deviations of the poles. These standard deviations are used (together with other features) as the inputs of a fuzzy clustering algorithm. The clustering algorithm then classifies the poles into the mathematical and physical ones. The method requires no user interaction, and a parameter is available quantifying the success of the classification.

Identification of modal parameters including unmeasured forces and transient effects

In this paper, a frequency-domain method to estimate modal parameters from short data records with known input (measured) forces and unknown input forces is presented. The method can be used for an experimental modal analysis, an operational modal analysis (output-only data) and the combination of both. A traditional experimental and operational modal analysis in the frequency domain starts respectively, from frequency response functions and spectral density functions. To estimate these functions accurately sufficient data have to be available. The technique developed in this paper estimates the modal parameters directly from the Fourier spectra of the outputs and the known input. Instead of using Hanning windows on these short data records the transient effects are estimated simultaneously with the modal parameters. The method is illustrated, tested and validated by Monte Carlo simulations and experiments. The presented method to process short data sequences leads to unbiased estimates with a small variance in comparison to the more traditional approaches.

Modal parameter estimation and monitoring for on-line flight flutter analysis

The clearance of the flight envelope of a new airplane by means of flight flutter testing is time consuming and expensive. Most common approach is to track the modal damping ratios during a number of flight conditions, and hence the accuracy of the damping estimates plays a crucial role. However, aircraft manufacturers desire to decrease the flight flutter testing time for practical, safety and economical reasons by evolving from discrete flight test points to a more continuous flight test pattern. Therefore, this paper presents an approach that provides modal parameter estimation and monitoring for an aircraft with a slowly time-varying structural behaviour that will be observed during a faster and more continuous exploration of the flight envelope. The proposed identification approach estimates the modal parameters directly from input/output Fourier data. This avoids the need for an averaging-based pre-processing of the data, which becomes inapplicable in the case that only short data records are measured. Instead of using a Hanning window to reduce effects of leakage, these transient effects are modelled simultaneously with the dynamical behaviour of the airplane. The method is validated for the monitoring of the system poles during flight flutter testing.

Increased reliability of reference-based damage identification techniques by using output-only data

Abstract During the past few years, a considerable number of damage identification techniques have been proposed and successfully tested on vibration data obtained from mechanical structures. Most vibration-based methods identify damage by interpreting measured changes in modal parameters. In practice, damage identification problems can occur due to minor changes in the boundary conditions of the test set-up especially if classic input–output vibration measurements are required for the diagnosis of a lightweight structure. In this contribution, a comparison is made between an input–output and output-only damage identification set-up for an aluminum beam structure suffering from fatigue-induced crack formation.

User-assisting tools for a fast frequency-domain modal parameter estimation method

Abstract Recently, the least-squares complex frequency-domain (LSCF) estimator has been developed for modal analysis applications. This contribution elaborates in more detail the fast derivation of stabilisation charts and uncertainty bounds for the estimated poles. An alternative representation for the stabilisation chart as well as a robust cluster algorithm to identify clusters of poles using the chart information is presented. Based on the clusters, uncertainty bounds for the poles and an automation of the pole selection process are derived. The relation of these “variances” with the stochastic variances (or confidence bounds) introduced by the noise on the measurements is compared by means of Monte-Carlo simulations. The use of alternative representation for the stabilisation chart in combination with the robust cluster analysis as well as the availability of uncertainty bounds for the modal parameters, assist the user with the performance of an accurate modal parameter estimation.

On-line detection of fatigue cracks using an automatic mode tracking technique

Experimental fatigue tests usually require large testing times. In addition to the resulting increased time-to-market, the large fatigue test time also implies that any structural health monitoring technique that is used should be automatic. When using the modal parameters as damage indicators, an important amount of user interaction is still needed to separate physical poles from computational ones. In this paper, an experimental framework will be developed to automatically track the health of the structure on-line with the performance of fatigue tests. The modal parameters are tracked using a combination of the maximum likelihood estimator and an auto-regressive model. Since confidence levels on the modal parameter are available it is possible to detect if damage is present. In addition, the quasi-static stiffness with computed confidence levels is also used as a damage indicator. The proposed techniques are demonstrated on a steel beam with a propagating fatigue crack.

Fourier fringe processing by use of an interpolated Fourier-transform technique

Recently a powerful Fourier transform technique was introduced that was able to extract the phase from only one image. However, because the method is based on the two-dimensional Fourier transform, it inherently suffers from leakage effects. A novel procedure is proposed that does not exhibit this distortion. The procedure uses localized information and estimates both the unknown frequencies and the phases of the fringe pattern (using an interpolated fast Fourier transform method). This allows us to demodulate the fringe pattern without any distortion. The proposed technique is validated on both computer simulations and the profile measurements of a tube.

Multivariable frequency-response curve fitting with application to modal parameter estimation

This paper presents a computational approach for the frequency-domain identification of multivariable, discrete-time transfer function models based on a cost function minimization. The algorithm is optimized for the parametric characterization of complex high-order multivariable systems requiring a large number of model parameters, including sparse matrix methods and QR-projections for the reduction of computation time and memory requirements. The algorithm supports a multivariable frequency-dependent weighting, which generally improves the quality of the transfer function model estimate. The overall approach is successfully demonstrated for a typical case encountered in experimental structural dynamics modelling (using modal analysis) and compared with related algorithms in order to assess the gain in computational efficiency.

An automatic position calibration method for the scanning laser Doppler vibrometer

When using a scanning Doppler laser vibrometer (SLDV) an important amount of user interaction is required to perform a calibration between the required scanning mirror angles and the coordinates of the grid points which are to be measured. Apart from the possibility of leading to incorrect (or inaccurate) laser beam positioning, the user interaction is a problem when the SLDV is used in-line (for instance as a quality control tool in the production process). In this paper, a method is developed to perform the position calibration in a fully automatic manner. The method is validated with the aid of two SLDV measurement examples: a sheet with a rectangular mesh, and an electronic circuit board.