Arch Appl Mech (2005) 74: 878–889 DOI 10.1007/s00419-005-0399-0 ORIGINAL Tadeusz Uhl Identification of modal parameters for nonstationary mechanical systems Received: 27 January 2005 / Accepted: 4 May 2005 / Published online: 12 November 2005 © Springer-Verlag 2005 Abstract This paper presents two different approaches to the identification of modal model parameters for nonstationary mechanical systems. The problem is related to model-based structural health monitoring. Dam- age in this approach is detected by tracking modal parameters of the structure during operation. The detected parameter changes can be indicators of structural damage. The recursive method based on the autoregressive moving-average model of signals and wavelet-transform-based algorithms are presented. The methods are tested using simulated data. Case studies of airplane flutter detection are shown using both methods. 1 Introduction Many practical engineering systems change dynamic parameters during operation. Parameters may change as a result of damage. The problem of damage detection can be defined as the identification of parameter changes in a system model. In the literature [1] this approach is called model-based diagnostics. The classical approach to model-based damage detection is formulated [2] on the assumption that a system is stationary during the identification experiment. But nonstationary behavior due to system damage is expected for some experi- ments. In practical cases, however, the system model parameters can be changed during any given experiment, in which case the system should be treated as nonstationary. The identification and analysis of nonstationary systems is more difficult than of stationary systems. One of the most important cases of nonstationary behavior of aviation structures is flutter. Flutter is a complex phenomenon where, in the classical case, two or more structural modes are coupled and excited through aerodynamic loads [3, 4]. The flutter phenomenon is related to a self-excited vibration phenomenon present at a certain forward flow speed. A self-excitation mechanism makes it possible to stimulate flutter even in cases where aerodynamic loading is time independent but is due to feedback between bending and torsion vibration modes. The feedback causes the damping force to decrease with constant excitation forces. For a given combination of flight parameters the vibration damping forces can be very low, even less than zero. In such a case, the amplitude will immediately increase and in certain cases the structure can lose integrity. The modal parameters, which are responsible for increases in the vibration amplitude at a given flight speed, are dampened [5–8]. The damping ratios of the critical modes are commonly used as the index of the flutter stability margin. Damping can change due to variations in air speed or air density during flight for a given aircraft design. If damping is less than zero, then in a system that has lost stability and vibration the amplitude can increase immediately to a very high value, which can be a reason for structural damage. Then vibration modes for which damping is very small should be carefully investigated according to flutter phenomena [9–11]. Modal parameters of the structure can be extracted using experimental modal-anal- ysis techniques, but such techniques are formulated and valid for stationary mechanical systems (with constant T. Uhl University of Science and TechnologyAGH, Krakow, Poland E-mail: tuhl@agh.edu.pl