Section: New Results

identification of linear systems

Modular identification and damage detection for large structures

Participants : Michael Döhler, Laurent Mevel.

Subspace identification algorithms are efficient for output-only eigenstructure identification of linear MIMO systems. The problem of merging sensor data obtained from moving and nonsimultaneously recorded measurement setups under varying excitation is considered. To address the problem of dimension explosion, when retrieving the system matrices of the complete system, a modular and scalable approach is proposed. Adapted to a large class of subspace methods, observability matrices are normalized and merged to retrieve global system matrices [12] .

Fast multi order subspace identification algorithm

Participants : Michael Döhler, Laurent Mevel.

Subspace methods have proven to be efficient for the identification of linear time-invariant systems, especially applied to mechanical, civil or aeronautical structures in operation conditions. Therein, system identification results are needed at multiple (over-specified) model orders in order to distinguish the true structural modes from spurious modes using the so-called stabilization diagrams. In this paper, new efficient algorithms are derived for this multi-order system identification with subspace-based identification algorithms and the closely related Eigensystem Realization Algorithm. It is shown that the new algorithms are significantly faster than the conventional algorithms in use. They are demonstrated on the system identification of a large-scale civil structure [11] , [15] .

Evaluation of confidence intervals and computation of sensitivities for subspace methods

Participants : Michael Döhler, Laurent Mevel.

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. Uncertainty computation schemes have been developed.This approach has been validated on large scale examples[16] .

Subspace methods in frequency domain

Participants : Philippe Mellinger, Michael Döhler, Laurent Mevel.

In Operational Modal Analysis (OMA) of large structures it is often needed to process output-only sensor data from multiple non-simultaneously recorded measurement setups, where some reference sensors stay fixed, while the others are moved between the setups. A standard approach to process the data together for global system identification is to transfer the data into frequency domain and merge it there. However, this only works if the unmeasured ambient excitation remains stationary throughout all setups. As the ambient excitation can be different from setup to setup, the amplitude of the measured data can be different as well and the data has to be normalized. Recently, a method has been developed for covariance- and data-driven Stochastic Subspace Identification (SSI) to automatically normalize and merge the data from multiple setups in order to obtain the global modal parameters (natural frequencies, damping ratios, mode shapes), instead of doing the SSI for each setup separately. In this paper, we adapt this approach to multi-setup SSI in frequency domain, where we use spectra data instead of time series data. We demonstrate the advantages of the new merging approach in the frequency domain and apply it to a relevant industrial large scale example, where we compare the estimation results of the modal parameters between the time and frequency domain approaches [24] .

Subspace Identification for Linear Periodically Time-varying Systems

Participant : Ahmed Jhinaoui.

In this paper, an extension of the output-only subspace identification, to the class of linear periodically time-varying (LPTV) systems, is proposed. The goal is to identify a useful information about the system's stability using the Floquet theory which gives a necessary and sufficient condition for stability analysis. This information is retrieved from a matrix called the monodromy matrix, which is extracted by some simultaneous singular value decomposition (SVD) and from a resolution of a least squares criterion. The method is, finally, illustrated by a simulation of a model of a helicopter with hinged-blades rotor and a prototype of the same model. The method is then applied to data from a real wind turbine [22] , [19] , [20] .