Measuring nonlinear distortions: from test case to an F-16 Fighter
What are the similarities and differences between the behavior of a small vibrating test system and an F-16 fighter? To find it out, we compare measurements of the test system to measurements from the bolted connection of the wing and the missile of a F-16 Fighter Falcon from the Belgian air force. These measurements were done during a ground vehicle test (GVT) campaign. Essentially, the behavior of these systems match, even though the test system is only the heart of a self-study kit for nonlinear system identification and the F-16 is a complex real life mechanical structure. This clearly shows the added value of an experiment driven nonlinear educational system identification package. It provides safe small-scale toy examples for hands-on excersises that react like real systems. We believe that this practical approach lowers the gap between learning system identification concepts and applying it on real systems.
Figure 1: FRF Measurement with increasing amplitude (dark to light grey) UP: Test case System; Down: F-16 Fighter
The mechanical systems are first excited by a multisine signal with a low measured amplitude. The frequency response function (FRF) is a rather smooth curve with resonance frequencies. When the amplitude is slightly increased, the FRF does not change. The system behaves like a typical linear time invariant (LTI) system (Figure 1, dark grey). Increasing the amplitude of the input signal further makes the FRF depart from this value for both systems as the nonlinear distortions pop up.
An example where this knowledge is of great importance is in the case of GVT campaigns. In GVT mostly, LTI-based methods are used to identify the resonance frequencies and predict flutter of an aircraft. If the system contains odd nonlinear distortions, this becomes very dangerous to asses dampings as the dynamics of the system is changed.
Figure 2: Detect, quantify and qualify nonlinear distortions of an F-16 Fighter: black: FRF, blue: even NL, red: odd NL, Green:noise
An F-16 and the test system look pretty much alike indeed, the kit prepares practitioners to tackle real-world problems.
 R. Pintelon and J. Schoukens (2012) System Identification, a Frequency Approach. IEEE Press, New York
 J. Schoukens, R. Pintelon and Y. Rolain (2012) Mastering system identification in 100 Exercises. IEEE Press, New York