American Institute of Aeronautics and Astronautics
Wavelet-Based Techniques for Improved
On-Line Systems Identification
Peter M. Thompson, Ph.D.
, Edward N. Bachelder, Ph.D.
, David H. Klyde
Systems Technology, Inc., Hawthorne, CA, 90250
Chuck Harris, Ph.D.
412 TW/ENTT, Air Force Flight Test Center, Edwards AFB, CA, 93524
Martin J. Brenner
NASA Dryden Flight Research Center, Edwards AFB, CA, 93523
Wavelet transform methods can be used to rapidly identify the frequency response of
aerospace vehicles using on-line time series for selected input/output pairs. These methods
are an alternative to windowed Fourier transforms, the main difference being that wavelet
transforms more rapidly identify changes in the vehicle response at high frequency, and thus
are more suited to problems such as failure detection, loss of control detection, and flutter
detection. Identification methods based on wavelet transforms can improve flight safety and
increase the efficiency of on-line flight test analysis methods. Two wavelet-based methods are
described in this paper, with examples and a discussion of how they are implemented. In the
first method the frequency response is estimated using ratios of wavelet transforms, and is
recommended for use when the input spectrum is broadband and for piloted input during
normal operations. In the second method the wavelets are used as a front end to the
Eigensystem Realization Algorithm, and is recommended for system identification when
using short duration, discrete inputs such as steps and doublets. Windowed Fourier
transform methods remain the recommended choice for longer duration, discrete inputs
such as frequency sweeps.
he objective of recent work at Systems Technology, Inc. has been to develop wavelet-based methods for system
identification and then to apply these methods to a broad range of refractory automatic and manual control
system problems. These control problems are those that escape detection by typical design criteria and
methodologies, surface under unusual or rare circumstances, and threaten flight safety. Examples include hardware
failures, unexpected transitions in multimode flight control software, the onset of flutter, and other loss of control
In work conducted for NASA Dryden as part of a Phase II Small Business Innovation Research (SBIR) project,
wavelet transform methods were developed for loss of control detection. The time varying frequency response
identification methods were implemented and demonstrated in a real-time, flight control system hardware-in-the-
loop, piloted simulation. This simulation included many of the realistic problems that are always part of test data,
such as noise, multiple sample rates, and time skews. The variance of the identified frequency response was reduced
using cross-spectra with smoothing in the time and frequency domain. Stability metrics were identified from the
frequency response, including airplane bandwidth parameters, as they varied in time. The supporting software
Chief Scientist, AIAA Member.