Subspace Instability Monitoring for Linear Periodically Time-Varying Systems

Ahmed Jhinaoui (1) , Laurent Mevel (1) , Joseph Morlier (2)

1 I4S - Statistical Inference for Structural Health Monitoring
2 ICA - Institut Clément Ader

Most subspace-based methods enabling instability monitoring are restricted to the linear time-invariant (LTI) systems. In this paper, a new subspace method of instability monitoring is proposed for the linear periodically time-varying (LPTV) case. For some LPTV systems, the system transition matrices may depend on some parameter and are also periodic in time. A certain range of values for the parameter leads to an unstable transition matrix. Early warning should be given when the system gets close to that region, taking into account the time variation of the system. Using the theory of Floquet, some symptom parameter of stability- or residual- is defined. Then, the parameter variation is tracked by performing a set of parallel cumulative sum (CUSUM) tests. Finally, the method is tested on a simulated model of a helicopter with hinged blades, for monitoring the ground resonance phenomenon.

Mots clés: Helicopter dynamics; Time-varying systems; Periodic motion; Resonance; Subspace methods; Statistical inference; Fault detection; Stability limits

Domaines: Mécanique des structures [physics.class-ph]

Ahmed Jhinaoui, Laurent Mevel, Joseph Morlier. Subspace Instability Monitoring for Linear Periodically Time-Varying Systems. 16th IFAC Symposium on System Identification, Jul 2012, Brussels, Belgium. pp.380-385. ⟨hal-01853135⟩