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