Impact damage assessment in composite structures based on multiwavelet analysis of modal shapes

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 22, August 2015, pp Impact damage assessment in composite structures based on multiwavelet analysis of modal shapes A Katunin* Institute of Fundamentals of Machinery Design, Faculty of Mechanical Engineering, Silesian University of Technology, Konarskiego 18A, Gliwice, Poland Received 31 January 2015; accepted 22 July 2015 The low-velocity impact damage of composite structures is an important problem in various industrial branches, especially in the aircraft and aerospace industriess. Due to the nature of impact damage initiation and propagation and its poor ability of detection based on surface inspection, the appropriate non-destructive damage assessment methods need to be developed. One of the extensively developed groups of methods is the technique based on modal testing and further processing of modal shapes using wavelet analysis. Since the wavelet analysis is very sensitive to even small abrupt changes in an analyzed signal, this approach is chosen for extraction of diagnostic information. In the following study, the novel approach based on multiwavelet analysis of modal shapes, achieved from measurements using a laser vibrometer, is applied to the composite plates damaged following various scenarios. Based on the comparative study, the Donovan-Geronimo- Hardin-Massopust multiwavelet is selected as the best for evaluation of damage sites. The proposed algorithm makes possible detection and localization of cracks and accompanying delaminations, resulted from the impact loading, with high precision, which is verified by comparison with ultrasonic C-scans of the analyzed plates. The obtained results allow for application of the presented method in the industrial non-destructive testing as well. Keywords: Non-destructive testing, Composite structures, Impact damage, Modal analysis, Multiwavelet analysis Due to the increasing application of polymeric composites in machine design problems (especially in the aircraft and aerospace industries), these materials are often used for responsible elements of various constructions, and thus should be properly maintained, including carrying out the periodic inspections. Considering present requirements for such structures and the testing methods, the applied methods should be non-destructive and non-invasive, sensitive to the specific types of damage, able to provide inspection in the field conditions and finally, they should be low-cost. Some ofnondestructive methods need the specific conditions of inspection (e.g. the ultrasound testing should be carried out in a liquid medium or a computed tomography needs specific apparatus) and their application is often limited to the laboratory environment. From the practical point of view, the non-destructive testing should be available in various conditions and for various types and dimensions of structures (e.g. the periodic inspections of the aircraft composite elements). The promising methods that are able to fulfill the above-mentioned requirements are the * andrzej.katunin@polsl.pl vibration-based techniques. However, the analysis of raw results of modal experiment, i.e., the changes of natural frequencies and modal shapes, does not provide the relevant diagnostic information. Therefore, the analysis should be extended to application of advanced signal processing techniques in order to assess a condition of a structure. One of the extensively developed techniques of signal processing applied to the non-destructive testing problems is the wavelet analysis of modal shapes. Since the damage identification problems in practice are generally two-dimensional (2D), the analysis should be performed by using the extended 2D wavelet transform. The first studies on application of a spatial wavelet analysis for damage identification problems have been introduced elesewhere 1. Further, the technique has been developed by application of various wavelets in order to increase the detectability of damage: Chang and Chen 2 used the Gabor wavelets, while Douka et al. 3, and Rucka and Wilde 4 applied the reversed biorthogonal wavelets and others. The above-cited studies have formulated algorithms based on the continuous wavelet transform (CWT). The main factors, which influence on the detectability and accuracy of damage localization are the selection

2 452 INDIAN J. ENG. MATER. SCI., AUGUST 2015 of appropriate wavelet transform together with proper wavelets. The results of the Katunin 5 studies on application of the spatial wavelet transform for damage identification indicated that the application of the discrete wavelet transform (DWT) is the most suitable for the discussed problems due to the lowering of redundancy and thus the computation cost. The comparative studies of application of different wavelet transforms and various wavelets were presented by Katunin and Holewik 6. The 2D wavelets applied in the above-cited studies are the separable ones, i.e., the 2D scaling function and three 2D wavelets were obtained from their 1D analogues as a tensor product of all combinations of a 1D scaling and a wavelet function. Such wavelets have several disadvantages like remaining a strong boundary effect and a lack of directional invariance. The improvement of damage detectability and accuracy of localization is possible by application of the 2D discrete multiwavelet transform (DMWT) with appropriate multiwavelets. The multiwavelet transform has found several applications in signal and image processing 7 and technical diagnostics problems 8. For the best of author s knowledge such approach has not previously been used for the structural damage assessment problems and has been introduced during the analysis of numerical models of plates with simulated damage 9. The improvement of the effectiveness of DMWT with respect to DWT, due to the minimized boundary effect and directional invariance, was reported in several studies Due to the fact that in DMWT-based algorithm the scaling and wavelet functions become vectors of functions, the application of these functions produce more resulting sets of coefficients which creates new possibilities of this approach: the multiwavelets might be constructed in such a way that their properties would exactly match the specificity of the investigated problem. Based on the successful results obtained by the author 9 using multiwavelets, it was decided to apply them to the problem of identification of impact damage in polymeric composites based on experimental data. Using the multiwavelet approach the modal shapes of impacted composite plates obtained experimentally during vibrometer scanning were analyzed. The damage sites were precisely detected and localized. The obtained results were compared with the results obtained using various multiwavelet bases and results obtained using DWT-based algorithm. The advantages of the proposed technique were discussed based on the obtained results. For a verification purpose the results obtained using proposed approach were compared with the ultrasonic scans. Experimental Procedure The 12-layered epoxy laminated plates with dimensions of mm and a thickness of 2.5 mm reinforced by E-glass plain weave cloth with the weight of 200 g/m 2 were manufactured and supplied by Izo-Erg S.A., Gliwice. The plates were pre-damaged by the own-designed impact test rig using various shapes of impactors with energy of 40 J. The impact test rig and impactors ends were presented in Fig. 1. The detailed description of a test rig and impactors can be found in ref. 13. The resulted damage sites obtained using transmitted light imaging technique were presented in Fig. 2. In all cases the impact damage was located in the geometrical centers of the plates. The plates were mounted in a steel frame in order to fulfill clamping boundary conditions and were covered by Helling anti-glare spray in order to improve scanning capabilities of Laser Doppler Vibrometer (LDV). Vibration tests were carried out using scanning LDV Polytec PSV-400 with a vibrometer controller OFV-5000 and a point LDV Polytec PDV-100 as a reference (in order to Fig. 1 Impact test rig and considered impactors: A hemispherical R17 mm, hemispherical with decreased radius: B R14 mm, C R11 mm, D R8 mm, E R5 mm, F conic, G arch-ended

3 KATUNIN: IMPACT DAMAGE ASSESSMENT IN COMPOSITE STRUCTURES 453 Fig. 2 The damages caused by various impactors obtained using transmitted light imaging separate vibrations of the clamping frame from the vibration signal measured by the scanning LDV). The frame with a plate was excited by pseudorandom noise signal emitted by TIRA TV electrodynamic shaker and amplified by the power amplifier TIRA BAA-500. The test rig was presented in Fig. 3. The net of equidistant measurement points was spanned on the area of mm. The measurements were performed with a frequency bandwidth in the range of 0-2 khz with a resolution of 1.25 Hz. As a result of scanning the sets of frequency response functions (FRFs) were achieved. An exemplary FRF obtained from measurements for the case G (see Fig. 2) was presented in Fig. 4. Based on FRFs the natural frequencies were determined and the modal shapes corresponded to them were extracted (see Fig. 4). Only the modal shapes, whose maximal magnitudes were higher than 20% of the maximal magnitude of FRF were considered. The selected natural frequencies corresponded with these modal shapes Fig. 3 A test rig during scanning procedure

4 454 INDIAN J. ENG. MATER. SCI., AUGUST 2015 were presented in Table 1. These modal shapes were collected and imported to the MATLAB environment. All of the collected modal shapes were considered during the analysis due to a fact that the resulted detail coefficients are dependent on the magnitudes of velocity of vibration. If a damage is located in the region, where the magnitudes are low, the detectability of a damage is poor, whereas if more than one modal shape is considered the detectability of damage increases. Considering that the detail coefficients may achieve various values (positive and negative) the absolute values were taken into account in order to neutralize the influence of a sign and then added up for a given case. Fig. 4 Exemplary FRF and selected modal shapes for the case G Table 1 atural frequencies of vibration of investigated plates selected for the analysis Case Selected frequencies, Hz A B C D E F G

5 KATUNIN: IMPACT DAMAGE ASSESSMENT IN COMPOSITE STRUCTURES 455 Results and Discussion Multiwavelet analysis The discrete wavelet analysis, as well as the discrete multiwavelet analysis, can be considered as a filtering procedure with a set of low-pass H and highpass G filters related to scaling Φ and wavelet Ψ functions. In the multiwavelet representation these filters become vector-valued since Φ and Ψ are also vector-valued. Strela stated 14 that the number r of scaling and wavelet functions could be arbitrary large in Φ and Ψ, however the commonly used multiwavelets are primarily with r = 2. The two-scale relations for Φ and Ψ have a form: 1 n k = 0 ( ) 2 k ( 2 ) Φ x = H Φ x k (1) 1 n k = 0 ( ) 2 k ( 2 ) Ψ x = G Ψ x k (2) where k k ( ) r Z r 2 H, G l are the r r matrices of filter coefficients of a low-pass filter and a high-pass filter, respectively, for each k. After the decomposition operation of a 2D signal one obtains 16 sets of coefficients, which are further used for damage identification (see Fig. 5). Similarly as in the author s earlier study 9 three multiwavelet bases were considered: Lebrun-Vetterli (LV), Chui-Lian (CL) and Donovan-Geronimo- Hardin-Massopust (DGHM) multiwavelets (Fig. 6). The coefficients of filters corresponded to the mentioned multiwavelets can be found elsewhere 9. During the analysis only three sets of coefficients obtained by low-pass filtering (H 1 H 2, H 2 H 1 and H 2 H see Fig. 5) were selected due to their highest sensitivity to damage. After the decomposition of each modal shape from the investigated cases the absolute values of the obtained sets of coefficients were added up. In this study the resulted coefficients are called D-coefficients. Comparative studies In order to select an appropriate multiwaveletfor the investigated problem of damage detection and localization the first comparative study between the mentioned multiwavelets was performed. The resulted sets of D-coefficients were presented in Fig. 7. The comparative study was performed for the case G. As it can be noticed the DGHM multiwavelet allows for better filtration ability than the two other multiwavelets. It can be observed that the highest values in the case of DGHM multiwavelet are located in the region of a damage and the artifacts obtained during performing DMWT-based algorithm are much lower than those in the damage location. Moreover, the magnitudes of D-coefficients obtained using DGHM multiwavelet are 10 times lower than in the cases of other multiwavelets, what justifies the better filtration ability of DGHM multiwavelet. Therefore it was selected for further studies. In order to emphasize the effectiveness of application of DMWT-based algorithm the results of transform were compared with the results obtained using DWT-based one. The results obtained sing wavelets used in literature for the damage Fig. 5 2D signal sub-bands after single-level decomposition using DMWT Fig. 6 Scaling and wavelet functions of (a), (b) LV, (c), (d) CL and (e), (f) DGHM multiwavelets

6 456 INDIAN J. ENG. MATER. SCI., AUGUST 2015 identification problems for the case G were presented in Fig. 8. As it can be noticed the resulted D-coefficients show only the central point of the impact damage, whereas in the results obtained using DGHM multiwavelet (see Fig.7c) the delamination region around the crack was also detectable. Moreover, the lower noise level was observed for results obtained using the mentioned multiwavelet with respect to the results presented in Fig. 8. DMWT-based algorithm Based on the comparative studies it was shown that the DGHM multiwavelet is the most effective with respect to the other analyzed multiwavelets and wavelets used in literature. The proposed algorithm was applied Fig. 7 Results of impact damage identification for case G using (a) LV, (b) CL and (c) DGHM multiwavelets Fig. 8 Results of impact damage identification for case G using (a) reversed biorthogonal 5.5, (b) symlet 4 and (c) symlet 6 wavelets

7 KATUNIN: IMPACT DAMAGE ASSESSMENT IN COMPOSITE STRUCTURES 457 Fig. 9 Results of impact damage identification for cases A-F based on the DMWT algorithm for remained cases considered in this study. Resulted sets of D-coefficients were presented in Fig. 9. The resulted D-coefficients clearly depict the.8impact damage in all cases. The increase of magnitudes of D-coefficients in the location of a damage with respect to other coefficients is observable, which is in agreement with mechanical nature of damaging, i.e., for the cases A-D only the surface cracks and/or delaminations are detectable, while for the cases E-G, among others, the penetration through the matrix occurs. It can also be observed that the shapes of damage sites were accurately identified, what was not possible using the DWT-based algorithm (cf. Fig). In order to verify the obtained results the additional ultrasound tests were carried out. The tests were performed using the air-coupled ultrasonic transducers system HFUS 2400 AirTech manufactured by the Ingenieurbüro Dr. Hiliger. The scanning region was assumed as a square with a geometrical center same as for the tested plates and a side length of 120 mm. The focusing distance between 250 khz emitter AirTech 4412 and receiver AirTech 4422 probes was set to 50 mm and the attenuation range was assumed as 31 0 db with a step of 2 levels. The obtained C-scans for the investigated plates were presented in Fig.10. One can observe that the shapes of impact damage sites in the resulted D-coefficients sets (Fig. 9) match the shapes of internal damage (delamination) obtained using ultrasonic scanning with the accuracy adequate to the resolution of measurement points defined

8 458 INDIAN J. ENG. MATER. SCI., AUGUST 2015 Fig. 10 C-scans of the investigated plates with impact damages

9 KATUNIN: IMPACT DAMAGE ASSESSMENT IN COMPOSITE STRUCTURES 459 for the vibrometer. This confirms the effectiveness of the presented approach for the structural damage detection and identification in composite elements. Conclusions This study presents the new approach for impact damage detection and identification in composite structures using the analysis of modal shapes via multiwavelet transform. The tested specimens were damaged with various impactors. The experimental studies were performed using the laser Doppler vibrometer in order to achieve high-precise values of velocity of vibrations. Obtained modal shapes were analyzed using the proposed multiwavelet-based technique. The resulted coefficients obtained after transform allow for detection and localization of impact damage as well as evaluation of its shape, including internal damage (delaminations). The effectiveness of a proposed approach was proven based on the comparative studies for various multiwavelets and wavelets (using the discrete wavelet transform). The results show that the multiwavelet approach with use of DGHM multiwavelet is characterized by the best sensitivity to various types of damage, including cracks and delaminations. This was also proven by comparing the resulted sets after the analysis with the C-scans obtained using ultrasonic measurements for the tested specimens. It was shown that the shapes of damage sites are similar considering the results of both techniques. Due to the high effectivenes of the presented approach it can be successfully applied in engineering problems of non-destructive testing. Acknowledgements The research project was financed by the National Science Centre (Poland) granted according the decision no. DEC-2011/03/N/ST8/ References 1 Wang Q & Deng X, J Eng Mech, 36 (1999) Chang C C & Chen L W, Appl Acoust, 65 (2004) Douka E, Loutridis S & Trochidis A, J Solids Struct, 40 (2003) Rucka M & Wilde K, J Sound Vib, 297 (2006) Katunin A, Mech Syst Signal Process, 25 (2011) Katunin A & Holewik F, Arch Civ Mech Eng, 13 (2013) Lin G & Liu Z M, IEEE Trans Image Process, 9 (2000) Sun H, He Z, Zi Y, Yuan J, Wang X, Chen J & He S, Mech Syst Signal Proc, 43 (2014) Katunin A, J Appl Math Comput Mech, 12 (2013) Zanandrea A, Neto C R, Rosa R R & Ramos F F, Physica A, 283 (2000) Yuan J, He Z & Zi Y, Mech Syst Signal Proc, 24 (2010) Li M & Zhu J, Eng Anal Bound Elem, 35 (2011) Katunin A & Sznura M, Aparatura Badawcza i Dydaktyczna, 18 (2013) Strela V, Multiwavelet theory and applications, Ph D Thesis, Massachusetts Institute of Technology, Cambridge, MA Douka E, Loutridis S & Trochidis A, J Sound Vib, 270 (2004) Loutridis S, Douka E, Hadjileontiadis L J & Trochidis A Eng, Struct, 27 (2005)