Proceedings of the 7th International Symposium on NDT in Aerospace (2015)

A state space approach for the non-destructive evaluation of CFRP with ultrasonic testing

C. Brandt, P. Maaß

The subject of this presentation is a new approach for the evaluation of porosity in Carbon Fibre Reinforced Polymers (CFRP) with ultrasonic testing. The standard procedure for Airbus parts is a pulse echo inspection. This is based on the evaluation of the so-called back-wall echo (BWE), i.e. the echo coming back from the surface opposite to the probe.
However, in situations with complex geometry, like sandwich or bonded parts, this BWE does not exist or cannot be properly evaluated. A new approach is presented based on a “state space” or “phase space” representation of the ultrasonically tested CFRP part regarded as a dynamical system. The final target of the work is to determine a “back-wall echo equivalent” out of the intermediate echoes (that start after the surface echo and end before the BWE). This shall be employable for data from standard commercially available UT equipment that is capable to record full A-scans.
A dynamical system is an (engineering, economical...) system evolving over time, which is represented by its state variables. For a simple system like a pendulum the, in that case 2, state variables are the angle and the angle velocity, which define this system completely. The plane in which the possible values of these two variables are represented is in this case the state space.
A key for evaluation is the reconstruction of the representation in state space via a so-called delay embedding out of one scalar variable. In the present case, the intermediate echoes out of the A-scan are taken as this scalar variable. This method for reconstruction, set up and proven 1981 by the mathematician Floris Takens, is briefly outlined. A feature is extracted out of Recurrence Plots, which are generated out of the representation of the dynamical system (the part under ultrasonic test) in reconstructed state space. This approach is known as Recurrence Quantification Analysis.
First results for correlating a feature out of Recurrence Plots, the determinism DET, with the BWE height are shown. The best correlation was achieved with a parameter setting generally not recommended for RQA and giving a reverse correlation than expected. Future work will elaborate this on samples of other material and with “natural” porosity.

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