Edwin Reynders

Output-only structural health monitoring in changing environmental conditions by means of nonlinear system identification

Structural health monitoring relies on the repeated observation of damage-sensitive features such as strains or natural frequencies. A major problem is that regular changes in temperature, relative humidity, operational loading, and so on also influence those features. This influence is in general nonlinear and it affects different features in a different way. In this article, an improved technique based on kernel principal component analysis is developed for eliminating environmental and operational influences. It enables the estimation of a general nonlinear system model in a computationally very efficient way. The technique is output-only, which implies that only the damage-sensitive features need to be measured, not the environmental parameters. The nonlinear output-only model is identified by fitting it to the damage-sensitive features during a phase in which the structure is undamaged. Afterwards, the structure is monitored by comparing the model predictions with the observed features. The technique is validated with natural frequency data from a three-span prestressed concrete bridge, which was progressively damaged at the end of a one-year monitoring period. It is demonstrated that capturing the regular variations of the features requires a nonlinear model. Monitoring the misfit between the predictions made with this model and the observed data allows a very clear discrimination between validation data in undamaged and damaged conditions.

Combined Experimental-Operational Modal Testing of Footbridges

In combined vibration testing, an artificial, measured force is used in operational conditions. This requires the identification of a system model that takes both the measured and the operational excitation into account. Advantages with respect to the classical operational modal analysis approach are the possibility of obtaining mass-normalized mode shapes and the increase of the excitation level and its frequency content. An advantage with respect to the classical experimental modal analysis approach, where the ambient excitation is not modeled, but considered as disturbing noise, is the possibility of using excitation levels that are of the same amplitude, or even smaller, than the ambient excitation levels. In this paper, combined modal testing of footbridges is explored using two case studies: a steel arch footbridge with spans of 75.2 m and 30.3 m and a concrete stress-ribbon footbridge with spans of 30 m and 28 m. The comparison of the modal parameters (eigenfrequencies, damping ratios, mode shapes,...

Response probability distribution of built-up vibro-acoustic systems.

The vibro-acoustic response of built-up structures, consisting of stiff components with low modal density and flexible components with high modal density, is sensitive to small imperfections in the flexible components. In this paper, the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way, i.e., carrying a diffuse wave field, and by subsequently computing the response probability density function. The master systems mean squared response amplitude follows a singular noncentral complex Wishart distribution conditional on the subsystem energies. For a single degree of freedom, this is equivalent to a chi-square or an exponential distribution, depending on the loading conditions. The subsystem energies follow approximately a chi-square distribution when their relative variance is smaller than unity. The results are validated by application to plate structures, and good agreement with Monte Carlo simulations is found.

Pre- and Post-identification Merging for Multi-Setup OMA with Covariance-Driven SSI

In Operational Modal Analysis (OMA) of large structures we often need to process sensor data from multiple nonsimultaneously recorded measurement setups. These setups share some sensors in common, the so-called reference sensors that are fixed for all the measurements, while the other sensors are moved from one setup to the next. To obtain the modal parameters of the investigated structure, it is necessary to process the data of all the measurement setups and normalize it as the unmeasured background excitation of each setup might be different. For this we compare three different approaches in this paper which differ in the order of the data merging, normalization and system identification step: The classical PoSER (identification-normalization-merging), the PoGER (merging-identification-normalization) and the PreGER (normalization-merging-identification). Special care was taken with the PreGER method and its efficiency has been tested with respect to the two other methods. The system identification is done with the SSI-cov/ref method. We apply these methods to the extraction of the modal parameters (natural frequencies, damping ratios and mode shapes) of the Luiz I arch bridge in Porto, Portugal, compare them and evaluate the different methods.

Parametric uncertainty quantification of sound insulation values

A probabilistic framework is developed for quantifying the combined effect of uncertain parameters in sound insulation measurements, such as test sample dimensions, room properties, and loudspeaker positions, on the sound insulation values. The joint probability distribution of the uncertain parameters is constructed from the available information by means of a maximum entropy approach. The resulting sound insulation predictions are fully compatible with the available information but otherwise maximally conservative, so that the robustness of the predictions is guaranteed. Fundamental insight in the inherent uncertainty of the measurement procedure for airborne sound insulation is obtained by combining the method with detailed numerical simulations of the measurement procedure for single and double walls. The resulting uncertainty levels are very large, especially in the lowest frequency bands, and agree with experimental results. Furthermore, the probability distribution of the band-averaged sound reduction index of modally sparse walls can be of bimodal form.

Measurement of modal curvatures using optical fiber strain sensors and application to damage identification using vibration monitoring

Vibration monitoring is a well-known technique to determine wether a civil engineering structure is damaged or not. From the vibration tests, natural frequencies, modal displacements, damping ratios and modal curvatures can be determined using system identification methods. These modal parameters are subsequently used for damage identification. If a structure is damaged, the changes in modal curvatures tend to be more local than the changes in modal displacements, so modal curvatures are more useful for damage localization. The possibility of directly measuring modal curvatures using optical fibre strain sensors, instead of calculating them from modal displacements using a numerical integration procedure, is a big step forward in the exploitation of modal curvatures for damage identification. As a practical application, the damage identification at the Tilff bridge is discussed.

Automated interpretation of stabilization diagrams

Modal parameter estimation requires a lot of user interaction, especially when parametric system identification methods are used and the modes are selected in a stabilization diagram. In this paper, a fully automated, three-stage clustering approach is developed for interpreting such a diagram, that does not require any user-specified parameter or threshold value. The three stages correspond to the three stages in a manual analysis: setting stabilization thresholds for clearing out the diagram, detecting columns of stable modes, and selecting a representative mode from each column. A validation study, where nine real-life noisy operational modal bridge data sets are both automatically and manually analyzed, illustrates the accuracy and robustness of the proposed automatization strategy.

Consistent Impulse-Response Estimation and System Realization From Noisy Data

A novel method for the estimation of a finite part of the impulse response is presented. The method is consistent in case the measured output data are prone to colored noise. The combination of Kungs realization algorithm yields a consistent system identification algorithm that is particularly useful for the identification of systems with uncoupled deterministic and stochastic dynamics. This algorithm is called IREAR. A detailed linear sensitivity analysis of the impulse response estimation and Kungs realization algorithms yields novel error and covariance formulae for the estimated impulse response and system matrices and the poles and frequency-response functions that result from the identified system description.

OMAX testing of a steel bowstring footbridge

A recent development in operational modal analysis (OMA) is the possibility of using measured, artificial loads in addition to the unmeasured, ambient excitation, while the ratio between forced and ambient excitation can be low compared to classical experimental modal analysis (EMA). Most of these so-called OMAX algorithms lack the intuitiveness of their EMA and OMA counterparts, since they fit a system model that takes both the measured and the operational excitation into account directly to the measured signals. A more physically intuitive subspace algorithm for OMAX, that starts with an accurate decomposition of the measured joint response in a forced and an ambient part, was recently introduced. In this paper, the performance of this algorithm, which is called CSI-ic/ref, is assessed by means of a case study, where a two-span steel arch footbridge is tested in operational conditions, with and without using additional actuators. From a comparison of the modal parameters with results from a finite elementmodel, an OMA algorithm, and an alternative OMAX algorithm, it can be concluded that CSI-ic/ref yields accurate modal parameter estimates.

Subspace identification for operational modal analysis

This chapter deals with the estimation of modal parameters from measured vibration data using subspace techniques. An in-depth review of subspace identification for operational modal analysis is provided. In addition, two recent developments are emphasised: the estimation of the probability density function of the modal parameters, and the use of an exogenous force in addition to the unmeasured operational excitation.