Section: New Results

Flutter monitoring and onset detection

Participants : Michèle Basseville, Laurent Mevel, Rafik Zouari.

See modules  3.3 , 3.5 , 4.4 and  7.1 .

Stating the flutter monitoring problem (see modules  4.4 and  7.1 ) as a statistical hypotheses testing problem, in [8] and [30] we have advocated for an on–line test built on a sample-wise temporal data-driven computation for the subspace–based residual (20 ), a non-local approximation for that residual, and the cumulative sum (CUSUM) test [4] . None of these approaches uses any model of the underlying physical phenomenon.

Adaptive online CUSUM tests.

A new empirical approach to kernel computation has been evaluated and presented at the IFAC World Congress [57] . It compares a recursive Hankel matrix computed online for each time instant t , with a recursive computation of its kernel. The kernel is representative of the modal state at some previous instant. If some brutal change arises, a discrepancy appears between the Hankel matrix and its kernel because of the delay between both computations. The test is not performing flutter detection but monitors the brutal variations of the monitored parameter, which will be the flutter phenomena if we assume that flutter corresponds to a brusque variation in the dynamics of the parameter. An application to a large scale simulated aircraft has been performed during the FliTE2 project and presented at EWSHM in Poland. This was done in collaboration with AGH [58] . It involves mixing wavelet filtering and the above CUSUM test. Wavelet filtering allows reducing model order of the monitored system, which help reducing false alarms.

Work is currently ongoing to publish this work.

Subspace based damping monitoring

Tracking the evolutions of modal parameters is not an easy task. In fact, even for stationary systems, identification is a complex task, notwithstanding the computation of confidence intervals. For non stationary systems, such as an aircraft in operation, reaction time and system variability render most identification methods difficult to implement. The CUSUM technique is reused to handle monitoring of slight in-operation modal variations over time. Application to simulation data shows the relevance of the new approach to track damping coefficients of critical modes. The methods involves the computation of a parametrized reference kernel for the CUSUM test, tuned with some signature representative of some predefined threshold corresponding to a confidence interval for the monitored damping. Minmax rejection allows the rejection of the effect of the frequency evaluation due to the mismatch between the modal model defined by the parameterized kernel and the current model associated with the data, resulting from the interaction with the aeroelasticity model. This method of tracking modal parameter variations by a change detection technique defined by some predefined adaptive threshold has been validated on both academic examples and some realistic simulation of an aircraft under acceleration phase provided by Dassault Aviation. This work has been presented at [24] .