Section: New Results

System identification

Variance estimation of modal parameters from subspace-based system identification

Participants : Michael Doehler, Laurent Mevel.

This work has been carried out in collaboration with Palle Andersen.

Subspace-based system identification allows the accurate estimation of the modal parameters (natural frequencies, damping ratios, mode shapes) from output-only measurements, amongst others with data-driven methods like the Unweighted Principal Component (UPC) algorithm. Due to unknown excitation, measurement noise and finite measurements, all modal parameter estimates are inherently afflicted by uncertainty. The information on their uncertainty is most relevant to assess the quality of the modal parameter estimates, or when comparing modal parameters from different datasets. A method for variance estimation is presented for the variance computation of modal parameters for the UPC subspace algorithm. Developing the sensitivities of the modal parameters with respect to the output covariances, the uncertainty is propagated from the measurements to the modal parameters from UPC. The resulting variance expressions are easy to evaluate and computationally tractable when using an efficient implementation. In a second step, the uncertainty information of the stabilization diagram is used to extract appropriately weighted global mode estimates and their variance. The method is applied to experimental data from the Z24 Bridge [30].

Bayesian parameter estimation for parameter varying systems using interacting Kalman filters

Participants : Antoine Crinière, Laurent Mevel, Jean Dumoulin, Subhamoy Sen.

This work is in collaboration with F. Cerou of ASPI team at Inria.

Standard filtering techniques for structural parameter estimation assume that the input force either is known exactly or can be replicated using a known white Gaussian model. Unfortunately for structures subjected to seismic excitation, the input time history is unknown and also no previously known representative model is available. A novel algorithm is proposed to estimate the force as additional state in parallel to the system parameters. Two concurrent filters are employed for parameters and force respectively, mixing interacting Particle Kalman filter and another filter employed to estimate the seismic force acting on the structure [38], [49].

From structurally independent local LTI models to LPV model

Participant : Qinghua Zhang.

This work on linear parameter varying (LPV) system identification has been carried out in collaboration with Lennart Ljung (Linköping University, Sweden).

The local approach to LPV system identification consists in interpolating individually estimated local linear time invariant (LTI) models corresponding to fixed values of the scheduling variable. It is shown in this work that, without any global structural assumption of the considered LPV system, individually estimated local state-space LTI models do not contain sufficient information for determining similarity transformations making them coherent. Nevertheless, it is possible to estimate these similarity transformations from input-output data under appropriate excitation conditions [21].

Stability of the Kalman filter for output error systems

Participant : Qinghua Zhang.

The stability of the Kalman filter is classically ensured by the uniform complete controllability regarding the process noise and the uniform complete observability of linear time varying systems. Recently we have studied the stability of the Kalman filter for output error (OE) systems, in which the process noise is totally absent. In this case the classical stability analysis assuming the controllability regarding the process noise is thus not applicable. Our first efforts were focused on continuous time systems, whereas discrete time systems have been studied since last year. It is shown in this work that the uniform complete observability is sufficient to ensure the stability of the Kalman filter applied to time varying OE systems, regardless of the stability of the OE systems [22].

Reduced-order interval-observer design for dynamic systems with time-invariant uncertainty

Participant : Qinghua Zhang.

This work on interval-based state estimation has been carried out in collaboration with Vicenç Puig's team (Universitat Politècnica de Catalunya, Spain). The reported work addresses in particular the design of reduced-order interval-observers for dynamic systems with both time-invariant and time varying uncertainties. Because of the limitations of the set-based approach and the wrapping effect to deal with interval-observers, the trajectory-based interval-observer approach is used with an appropriate observer gain. Due to difficulties to satisfy the conditions for selecting a suitable gain to guarantee the positivity of the resulting observer, a reduced-order observer is designed to increase the degree of freedom when selecting the observer gain and to reduce the computational complexity. Simulation examples illustrates the effectiveness of the proposed approach [37].

Parameter uncertainties quantification for finite element based subspace fitting approaches

Participants : Guillaume Gautier, Laurent Mevel, Michael Doehler.

This work has been carried out in collaboration with Jean-Mathieu Mencik and Roger Serra (INSA Centre Val de Loire).

Recently, a subspace fitting approach has been proposed for vibration-based finite element model updating. The approach makes use of subspace-based system identification, where the extended observability matrix is estimated from vibration measurements. Finite element model updating is performed by correlating the model-based observability matrix with the estimated one. However, estimates from vibration measurements are inherently exposed to uncertainty. A covariance estimation procedure for the updated model parameters is proposed, which propagates the data-related covariance to the updated model parameters by considering a first-order sensitivity analysis. In particular, this propagation is performed through each iteration step of the updating minimization problem, by taking into account the covariance between the updated parameters and the data-related quantities. Simulated vibration signals and experimental data of a beam validate the method [18].