Giampellegrini, L.; (2007) Uncertainty in correlation-driven operational modal parameter estimation. Doctoral thesis , University of London.

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Abstract

Due to the practical advantages over traditional input-output testing, operational or output-only modal analysis is receiving increased attention when the modal parameters of large civil engineering structures are of interest. However, as a consequence of the random nature of ambient loading and the unknown relationship between excitation and response, the identified operational modal parameters are inevitably corrupted by errors. Whether the estimated modal data is used to update a finite element model or different sets of modal parameters are used as a damage indicator, it is desirable to know the extent of the error in the modal data for more accurate response predictions or to assess, if changes in the modal data are indicative of damage or just the result of the random error inherent in the identification process. In this thesis, two techniques are investigated to estimate the error in the modal parameters identified from response data only: a perturbation and a bootstrap based method. The perturbation method, applicable exclusively to the correlation-driven stochastic subspace identification algorithm (SSI/Cov), is a two stage procedure. It operates on correlation functions estimated from a single set of response measurements and, in a first step, the perturbations to these correlation function estimates need to be determined. A robust, data-driven method is developed for this purpose. The next step consists in propagating these perturbations through the algorithm resulting in an estimate of the sensitivities of the modal data to these perturbations. Combining the sensitivities with the perturbations, an estimate of both the random and bias errors in the SSI/Cov-identified modal parameters is found. The bootstrap technique involves creating pseudo time-series by resampling from the only available set of response measurements. With this additional data at hand, a modal identification is performed for each set of data and the errors in the modal parameters are determined by sample statistics. However, the bootstrap itself introduces errors in the computed sample statistics. Three bootstrapping schemes are investigate in relation to operational modal analysis and an automated, optimal block length selection is implemented to minimise the error introduced by the bootstrap. As opposed to the perturbation method, the bootstrap technique is more versatile and it is not restricted to correlation-driven operational modal analysis. Its applicability to the data-driven stochastic subspace identification algorithm (SSI/Data) for error prediction of the SSI/data-identified modal data is explored. The performance of the two techniques is assessed by simulation on simple systems. Monte-Carlo type error estimates are used as a benchmark against which the predicted errors in the modal parameters computed from a single response history from both techniques are validated. Both techniques are assessed in terms of their accuracy and stability in predicting the uncertainty in the operational modal parameters and their computational efficiency is compared. Also, the performance of the bootstrap and the perturbation theoretic method is investigated in hostile ambient excitation conditions such as non-stationarity and the presence of deterministic components and the limitations of both methods are clearly exposed.

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