Michael Döhler

Crystal Clear SSI for Operational Modal Analysis of Aerospace Vehicles

In this paper we revisit the problem of the modal analysis of space launchers. We consider the Ariane 5 launcher with its usual equipment during a commercial flight under the natural unknown excitation. The case of space launchers is a typical example of a complex structure with sub-structures strongly and quickly varying in time. This issue becomes especially important in e.g. estimation of damping of aerospace vehicles. The eigenfrequencies are also sliding during the flight but the modeshapes are more stable. Recently, a new implementation of the subspace identification method has been proposed, leading to cleaner and more stable stabilization diagrams. We monitor the behavior of estimated modal parameters by applying this “crystal clear” implementation of the data driven and the covariance driven Stochastic Subspace Identification algorithms. We show the importance of “crystal clear” to monitor successfully frequencies and damping estimates over time in such a non stationary case.

Data Merging for Multi-Setup Operational Modal Analysis with Data-Driven SSI

In Operational Modal Analysis (OMA) of large structures we often need to process sensor data from multiple non-simultaneously 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. In this paper we present system identification results using a merging technique for data-driven Stochastic Subspace Identification (SSI), where the data is merged and normalized prior to the identification step. Like this, the different measurement setups can be processed in one step and do not have to be analyzed separately. We apply this new merging technique to measurement data of the Heritage Court Tower in Vancouver, Canada.

First mode damping ratios for buildings

Expressions for the expected value of the first mode damping ratio are derived by using 122 seismic responses from concrete buildings and 81 from steel. The results include dissipation at the soil-structure interface and are appropriate for situations in which this source of dissipation is not included in the model. Comparisons between models of different complexity indicate the appropriateness of using a single regressor, for which the building height is used. It is shown that the Fisher information about damping increases with the number of response cycles; this result is used to define weights for the residuals of the regression. The effective damping in steel buildings, with the exception of very tall structures, is found to be larger than the 2% typically used in practice, whereas the 5% assigned to concrete proves to be similar to the mean of the data set.

Operational Modal Analysis Using a Fast Stochastic Subspace Identification Method

Stochastic subspace identification methods are an efficient tool for system identification of mechanical systems in Operational Modal Analysis, where modal parameters (natural frequencies, damping ratios, mode shapes) are estimated from measured ambient vibration data of a structure. System identification is usually done for many successive model orders, as the true system order is unknown. Then, identification results at different model orders are compared to distinguish true structural modes from spurious modes in so-called stabilization diagrams. These diagrams are a popular GUI-assisted way to select the identified system model, as the true structural modes tend to be stable for successive model orders, fulfilling certain stabilization criteria that are evaluated in an automated procedure. In Operational Modal Analysis of large structures the number modes of interest as well as the number of used sensors can be very large, thus leading to high model orders that have to be considered for system identification. This also means a big computational burden. Recently, an efficient approach to estimate system matrices at multiple model orders in Stochastic Subspace Identification was proposed. In this paper it is shown how this new “Fast SSI” improves the computation of the stabilization diagrams, leading to much faster system identification results for large systems. The Fast SSI is applied to the system identification of some relevant large scale industrial examples.

Uncertainty quantification for stochastic subspace identification on multi-setup measurements

In Operational Modal Analysis, the modal parameters (natural frequencies, damping ratios and mode shapes), obtained from Stochastic System Identification of structures, are subject to statistical uncertainty from ambient vibration measurements. It is hence necessary to evaluate the uncertainty bounds of these obtained results. To obtain vibration measurements at many coordinates of a structure with only a few sensors, it is common practice to use multiple sensor setups for the measurements. Recently, a multi-setup subspace identification algorithm has been proposed that merges the data from different setups first to obtain one set of global modal parameters. This paper proposes an algorithm that efficiently estimates the uncertainty on modal parameters obtained from this multi-setup subspace identification.

Confidence Intervals of Modal Parameters during Progressive Damage Test

In Operational Modal Analysis, the modal parameters (natural frequencies, damping ratios and mode shapes) obtained from Stochastic Subspace Identification (SSI) of a structure, are afflicted with statistical uncertainty. For evaluating the quality of the obtained results it is essential to know the respective confidence intervals of these figures. In this paper we present algorithms that automatically compute the confidence intervals of modal parameters obtained from covarianceand data-driven SSI of a structure based on vibration measurements. They are applied to the monitoring of the modal parameters of a prestressed concrete highway bridge during a progressive damage test that was accomplished within the European research project IRIS. Results of the covariance- and data-driven SSI are compared.

Fault detection, isolation and quantification from Gaussian residuals with application to structural damage diagnosis

Abstract Despite the general acknowledgment in the Fault Detection and Isolation (FDI) literature that FDI are typically accomplished in two steps, namely residual generation and residual evaluation, the second step is by far less studied than the first one. This paper investigates the residual evaluation method based on the local approach to change detection and on statistical tests. The local approach has the remarkable ability of transforming quite general residuals with unknown or non Gaussian probability distributions into a standard Gaussian framework, thanks to a central limit theorem. In this paper, the ability of the local approach for fault quantification will be exhibited, whereas previously it was only presented for fault detection and isolation. The numerical computation of statistical tests in the Gaussian framework will also be revisited to improve numerical efficiency. An example of vibration-based structural damage diagnosis will be presented to motivate the study and to illustrate the performance of the proposed method.

Damage Detection in Wind Turbine Blade Panels Using Three Different SHM Techniques.

A comparison of three different damage detection methods is made on three nominally identical glass reinforced composite panels, similar to the load carrying laminate in a wind turbine blade. Sensor data were recorded in the healthy state and after the introduction of damage by means of a four–point bending quasi–static test. Acceleration sensors, PZT transducers and the piezoelectric excited Lamb waves were used for the measurements of the panels. All three methods are based on the comparison of the healthy and damaged structure. The first method is statistical covariance–driven damage detection using a subspace–based algorithm, where one damage indicator for all three panels was computed. The second method is based on PZT transducers and the A0 mode of Lamb waves propagating in the panel, making use of the reflection of the signal at damage in the panel. The third method is based on the estimation of modal parameters of the intact and damaged panel using pLSCF and following their deviations. The results from these three damage detection methods are compared and discussed.

Sensitivity Evaluation of Subspace-Based Damage Detection Method to Different Types of Damage

In this paper we investigate a damage detection technique based on the subspace method by applying it to an existing bridge structure model. A reference state of the structure is evaluated using this technique and subsequently its modal parameters are indirectly compared to the current state of the structure. There are no modal parameters estimated in this method. A subspace-based residual between the reference and possibly damaged states is defined independently from the input excitations employing a χ 2 test and then is compared to a threshold corresponding to the reference state. This technique is applied to a model of the bridge structure located in Reibersdorf, Austria. The structure is excited randomly with white noise at different locations and the output data is generated at typical locations instrumented and measured in a bridge. Various damages are simulated in different elements and the sensitivity of the method to each type and ratio of damages is assessed. This evaluation is performed by comparing the prediction of the damage state using this technique and the simulated damage of the structure. It can be inferred from the results that in general the statistical subspace-based damage detection technique recognizes most of the damage cases, except the ones with insignificant change in the global dynamic behaviour.

Multi-Order Covariance Computation for Estimates in Stochastic Subspace Identification Using QR Decompositions

For applications as Operational Modal Analysis (OMA) of vibrating structures, an output-only LTI system with state and measurement noise can be identified using subspace methods. While these identification techniques have been very suitable for the identification of such mechanical, aeronautical or civil structures, covariance expressions of the estimates of the system matrices are difficult to obtain and theoretical results from literature are hard to implement for output-only systems with unknown noise properties in practice. Moreover, the model order of the underlying system is generally unknown and due to noise and model errors, usual statistical criteria cannot be used. Instead, the system is estimated at multiple model orders and some GUI driven stabilization diagram containing the resulting modal parameters is used by the structural engineer. Then, the covariance of the estimates at these different model orders is an important information for the engineer, which, however, would be computationally expensive to obtain with the existing tools. Recently a fast multi-order version of the stochastic subspace identification approach has been proposed, which is based on the use of the QR decomposition of the observability matrix at the largest model order. In this paper, the corresponding covariance expressions for the system matrix estimates at multiple model orders are derived and successfully applied on real vibration data.