Damage monitoring of aircraft structures made of composite materials using wavelet transforms

The present article is dedicated to the study of the acoustic properties of composite materials and the application of non-destructive testing methods to aircraft components. A mathematical model of a wavelet transformed signal is presented. The main acoustic (vibration) properties of different composite material structures were researched. Multiple vibration parameter dependencies on the noise reduction factor were derived. The main steps of a research procedure and new method algorithm are presented. The data obtained was compared with the data from a three dimensional laser-Doppler scanning vibrometer, to validate the results. The new technique was tested in the laboratory and on civil aircraft at a training airfield.


Introduction
As a result of a significant growth in the use of composite materials in aviation structural components there is a strong need for increased capability for the operational monitoring and inspection of such components. The main impact of this research lies in the management and operation of future composite aircraft components. The data, which was obtained, can help to develop a universal nondestructive testing method, and as a result, improve aviation safety. The condition monitoring of modern passenger aircraft with complex composite material components, and the prediction of the operational state of such components, will be one of the major aviation operational tasks of the next decades.
During the preliminary research it was concluded that wavelet analysis is the most effective and appropriate tool for the vibration analysis for the determination of the modal parameters of free oscillations, especially in the integral control of a composite structural aircraft component, during the operational inspection. Wavelets can be combined, using a "reverse, shift, multiply and integrate" technique called convolution, with portions of a known signal to extract information from the unknown signal. The present research represents a "shift" technique with the use of the variable list of the wavelet family, such as Morlet, Gabor and Daubechies wavelets [1].
Other diagnostic and NDT methods, materials and results have been studied in detail to verify the correctness of the chosen research method [2][3][4][5][6][7][8]. The aircraft components of interest in the research were: propeller blades (figure 1); Yak-42 aircraft spoilers (figure. 2); and different types of honeycomb construction. Propeller blades with different surface conditions and geometry were tested. The fully composite blade with an Aluminum alloy ring at the attachment point is a perfect example of a modern hybrid composite structure. Each blade was made from pre-preg material using different types of epoxy resin. These blades are commonly used in small civil aviation aircraft, especially in hydro-aeroplanes, trikes, trainer aircrafts, etc.. The life of each blade, according to passport data, is, on average, no more than 600 flight hours. Yak-42 aircraft spoilers, made from a three layer reinforced honeycomb construction, were also tested in lab and on the training airfield.

Theoretical basis
The wavelet transform can be regarded as a three-dimensional spectrum, where time is given on the X -axis, frequency on the Y -axis, and the Z -axis represents the amplitude of harmonics with a given frequency at a given time. There are two main features that make the continuous wavelet transform (CWT) particularly attractive. First, in most cases, the vibration modes are automatically separated, thus providing the natural frequencies. This means that the values of the instantaneous frequencies and damping parameters can be easily obtained. Second, the most significant information is preserved in the CWT line highs and ridges (the high amplitude areas of the CWT figure). It should be noted that for the appropriate choice of the wavelet family, CWT wavelets can serve as a filter for separation of free oscillations.
To illustrate the proposed method, we analyze a simple case of a linear system with two degrees of freedom ( figure 3). This shows the principle for obtaining instantaneous frequency and damping parameters through the use of CWT (calculated only for ranges).
with 0 = 5. Figures 3 (b) and (c) show two a 2D and a 3D view of the CWT, from which the modes of oscillation can be clearly identified; however, the proposed method does not require a complete calculation of the CWT. It is only necessary to perform the calculation for a fixed time, 0 , figure 3 (d), and evaluate the scales 1 and 2 for the maximum deformation:

Methodology and experimental results
The data obtained was validated by comparison with data from a Polytec PSV-400 scanning Vibrometer ( figure 4). The method of the procedure contains several iterations combining direct Fourier transformation and CWT, (figure 5). Using a direct Fourier transform -first iteration, (figure 6), to check the dependence of the vibratory acceleration on the frequency, can be used to indicate the presence of a defect. Figures 7, 8 and 9 illustrate the features of the CWT before and after the appearance of the artificially created defect in the reference honeycomb structure. There is a clear difference between the CWT result for the object before and after the appearance of the defect. The differences marked in yellow highlight the changes in particular areas.  The area of the defect in the reference honeycomb construction was gradually increased, from approximately 1% to 5% of the internal honeycomb construction space. To create the defect, water was injected water, and subsequently frozen, to cause the delamination between the honeycomb core and the layers. After that, the water was vaporized, and the sample was weighed to ensure that there was no remaining water in the construction.

Discussion
As might be anticipated, the new testing experimental procedure, carried out on the reference honeycomb structure, showed a reduction in the value of each natural frequency and an increase in damping at resonance as a result of the presence of damage. Visual features of the CWT 3d and scalogram indicate changes in the overall vibration picture of the signal, which can directly attributed to the integral damage condition of the object under investigation.
The aircraft components for which this procedure would be most applicable include spoilers, propeller blades and different types of honeycomb constructions. It was found that the master blade mode shapes at resonant frequencies are practically the same in comparison with a blade following an operating time of 500-600 flight hours (figure 10).  Vibration speed and vibratory displacement are presented ( figure 11). It is shown that there is an increase in the vibration speed on some certain frequencies.

Conclusion
This research indicates that wavelet based NDT analysis could provide a basis for determining damage levels in structural composite aerospace components, and thus a means to decide whether a component is still fit to be operational. The method presented has the potential for critical life-cycle parameter identification, with a view to enabling life extension certification, based on acoustical structure health monitoring. It should be ACMTAA IOP Publishing IOP Conf. Series: Materials Science and Engineering 153 (2016) 012016 doi:10.1088/1757-899X/153/1/012016 8 mentioned that hardware and software can be used both for searching for defect signatures, and also for structural control. The data obtained during the test series indicated that the maintenance process is sufficiently frequent for predicting time to failure based on observed damage.