B. Cauberghe

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.

Maximum likelihood identification of non-stationary operational data

Abstract In-operation modal analysis has become a valid alternative for structures where a classic input–output test would be difficult if not impossible to conduct. Due to practical considerations, measurements are sometimes performed in patches (roving sensor setups) instead of covering the entire structure at once. In practice, one is often confronted with non-stationary ambient excitation sources (e.g., wind, traffic, waves, etc.). Since the scaling of operational mode shape estimates depends on the unknown level of the ambient excitation, an extra effort is required in order to correctly merge the different parts of the mode shapes. In this contribution, two different approaches, for merging operational mode shapes from non-stationary data, are proposed. Both methods are based upon a single maximum likelihood estimation procedure. For comparison and validation, both techniques were applied to non-stationary data sets obtained by scanning laser vibrometry as well as the Z24 bridge bench mark data.

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.

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.

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.

IDENTIFICATION OF CONTINUOUS-TIME NOISE MODELS

Abstract Current methods identify the physical parameters of continuous-time ARMA(X) processes via discrete-time approximations. Based on a frequency domain maximum likelihood estimator described in Ljung (1999), this paper proposes an exact continuous-time noise modeling approach. The theory is illustrated on real measurement examples.

Elimination of background disturbances from measurement spectra

Performing measurements (as for instance vibration measurements) in harsh industrial environments can be a tough task. In contrast to controlled laboratory conditions, important disturbing background vibrations can be present. Since these disturbances are often very high in amplitude, the measurements can be useless, even if the frequency of the disturbance is separated from the actual frequency band of interest of the structure under investigation. Indeed, because of spectral leakage a single-frequency component can spread out its energy over a large frequency range. In this paper, a technique is proposed to eliminate background disturbances from measurements (although vibration measurements are considered in the paper the technique also works for general signals). The technique developed uses two periods of a periodic signal as the excitation signal. The odd frequency lines of the discrete Fourier transform of two periods are used to estimate a parametric model of the disturbance. This model is then used to correct the measurement. The proposed technique is validated on both simulations and vibration measurements of a car door.

Combined Deterministic-Stochastic Frequency-Domain Subspace Identification for Experimental and Operational Modal Analysis

Until recently frequency-domain subspace algorithms were limited to identify deterministic models from input/output measurements. In this paper, a combined deterministic-stochastic frequency-domain subspace algorithm is presented to estimate models from input/output spectra, frequency response functions or power spectra for application as experimental and operational modal analysis. The relation with time-domain subspace identification is elaborated. It is shown by both simulations and real-life test examples that the presented method outperforms traditional frequency-domain subspace methods.Copyright