Abstract
Background
Dynamic measurement and analysis of rotating components is an arduous and complex task that has always attracted great attention from the engineering community.
Objective
In order to propose a low-cost, efficient, high-precision, and high temporal and spatial resolution rotating vibration measurement scheme, three-dimensional Digital Image Correlation (3D DIC) combined with down-sampling technology is employed. Two defects of this scheme hinder its wide application: the additional initial shape function estimation in rotation correlation of DIC and the cumbersome experimental operation process of traditional down-sampling. Therefore, an extension of down-sampling technology and a comparative study on efficient initial value estimation algorithms were researched.
Methods
Comparative experiments of extended down-sampling proposed in this paper and high-frequency sampling were carried out on a rotating disc for its vibration Operational Deflection Shapes (ODSs) measurement. During the data processing procedure, an efficient initial value estimation algorithm is recommended by comparing the efficiency and accuracy of Fourier-Mellin Transform-based (FMT-based), Scale Invariant Feature Transform-based (SIFT-based), and Hough Transform-based (HT-based) algorithms.
Results
The experimental results indicate that the FMT-based algorithm is the most efficient, and its estimation accuracy guarantees accurate and efficient convergence of the sub-pixel iteration process, though slightly lower than that of the SIFT-based algorithm; The harmonic response and natural response ODSs of the disc were obtained in the high-frequency sampling experiment, and the corresponding harmonic response ODSs were obtained in the extended down-sampling experiment. The precision of the amplitude of obtained ODSs is on the order of submicron.
Conclusions
The proposed extended down-sampling technology has been verified to circumvent the limitation of the Nyquist-Shannon sampling theorem, and accurately restore different orders of harmonic response ODSs with sampling once at a low frequency. Combined with extended down-sampling technology, 3D DIC becomes an efficient, submicron precision, full-field rotating vibration measurement scheme with high temporal and spatial resolution using low-cost conventional cameras. Simultaneously, the FMT-based rotation parameters estimation algorithm can efficiently provide accurate initial value estimation for 3D DIC.
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Data Availability
The data that supports the findings of this study is available from the corresponding author upon reasonable request.
References
Matsushita O, Tanaka M, Kanki H, Kobayashi M, Keogh P (2017) Vibrations of rotating machinery. Springer. https://doi.org/10.1007/978-4-431-55456-1
Niezrecki C, Baqersad J, Di Maio D (2019) Rotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019: Springer. https://doi.org/10.1007/978-3-030-47721-9
Yang L, Mao Z, Chen X, Yan R, Xie J, Hu H (2022) Dynamic coupling vibration of rotating shaft–disc–blade system—Modeling, mechanism analysis and numerical study. Mech Mach Theory 167:104542. https://doi.org/10.1016/j.mechmachtheory.2021.104542
Tamrakar R, Mittal N (2016) Campbell diagram analysis of open cracked rotor. Eng Solid Mech 4(3):159–166. https://doi.org/10.5267/j.esm.2016.1.001
Zielinski M, Ziller G (2000) Noncontact vibration measurements on compressor rotor blades. Meas Sci Technol 11(7):847. https://doi.org/10.1088/0957-0233/11/7/301
Šároši P, Harčarík T, Huňady R (2015) Vibrational study of the spinning disc using LDV techniqueApplied Mechanics and Materials. Trans Tech Publ, p 469–473. https://doi.org/10.4028/www.scientific.net/AMM.816.469
Peters WH, Ranson WF (1982) Digital imaging techniques in experimental stress analysis. Opt Eng 21(3):427–431. https://doi.org/10.1117/12.7972925
Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR (1983) Determination of displacements using an improved digital correlation method. Image Vision Comput 1(3):133–139. https://doi.org/10.1016/0262-8856(83)90064-1
Chu TC, Ranson WF, Sutton MA (1985) Applications of digital-image-correlation techniques to experimental mechanics. Exp Mech 25(3):232–244. https://doi.org/10.1007/BF02325092
Schreier H, Orteu J, Sutton MA (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, vol. 1. https://doi.org/10.1007/978-0-387-78747-3
Huang J, Zhu T, Pan X, Qin L, Peng X, Xiong C, Fang J (2010) A high-efficiency digital image correlation method based on a fast recursive scheme. Meas Sci Technol 21(3):35101. https://doi.org/10.1088/0957-0233/21/3/035101
Pan B, Li K, Tong W (2013) Fast, robust and accurate digital image correlation calculation without redundant computations. Exp Mech 53(7):1277–1289. https://doi.org/10.1007/s11340-013-9717-6
Wang L, Bi S, Lu X, Gu Y, Zhai C (2019) Deformation measurement of high-speed rotating drone blades based on digital image correlation combined with ring projection transform and orientation codes. Measurement 148:106899. https://doi.org/10.1016/j.measurement.2019.106899
Fang Z, Gao Y, Gao Z, Liu Y, Wang Y, Su Y, Zhang Q (2020) Efficient and automated initial value estimation in digital image correlation for large displacement, rotation, and scaling. Appl Optics 59(33):10523–10531. https://doi.org/10.1364/AO.405551
Wang L, Bi S, Li H, Gu Y, Zhai C (2020) Fast initial value estimation in digital image correlation for large rotation measurement. Opt Laser Eng 127:105838. https://doi.org/10.1016/j.optlaseng.2019.105838
Hild F, Raka B, Baudequin M, Roux S, Cantelaube F (2002) Multiscale displacement field measurements of compressed mineral-wool samples by digital image correlation. Appl Optics 41(32):6815–6828. https://doi.org/10.1364/AO.41.006815
Pan B, Wang Y, Tian L (2017) Automated initial guess in digital image correlation aided by Fourier-Mellin transform. Opt Eng 56(1):14103. https://doi.org/10.1117/1.OE.56.1.014103
Zhou Y, Pan B, Chen YQ (2012) Large deformation measurement using digital image correlation: a fully automated approach. Appl Optics 51(31):7674–7683. https://doi.org/10.1364/AO.51.007674
Wu R, Qian H, Zhang D (2016) Robust full-field measurement considering rotation using digital image correlation. Meas Sci Technol 27(10):105002. https://doi.org/10.1088/0957-0233/27/10/105002
Zhang Z, Kang Y, Wang H, Qin Q, Qiu Y, Li X (2006) A novel coarse-fine search scheme for digital image correlation method. Measurement 39(8):710–718. https://doi.org/10.1016/j.measurement.2006.03.008
Reddy BS, Chatterji BN (1996) An FFT-based technique for translation, rotation, and scale-invariant image registration. IEEE T Image Process 5(8):1266–1271. https://doi.org/10.1109/83.506761
Lowe DG (1999) Object recognition from local scale-invariant featuresProceedings of the seventh IEEE international conference on computer vision. IEEE, p 1150–1157. https://doi.org/10.1109/ICCV.1999.790410
Lowe DG (2004) Distinctive image features from scale-invariant keypoints. Int J Comput Vision 60(2):91–110. https://doi.org/10.1023/B:VISI.0000029664.99615.94
Zhou Y, Chen YQ (2013) Feature matching for automated and reliable initialization in three-dimensional digital image correlation. Opt Laser Eng 51(3):213–223. https://doi.org/10.1016/j.optlaseng.2012.10.011
Wang Z, Vo M, Kieu H, Pan T (2014) Automated fast initial guess in digital image correlation. Strain 50(1):28–36. https://doi.org/10.1111/str.12063
Yang J, Huang J, Jiang Z, Dong S, Tang L, Liu Y, Liu Z, Zhou L (2020) SIFT-aided path-independent digital image correlation accelerated by parallel computing. Opt Laser Eng 127:105964. https://doi.org/10.1016/j.optlaseng.2019.105964
Rizo-Patron S, Sirohi J (2017) Operational modal analysis of a helicopter rotor blade using digital image correlation. Exp Mech 57(3):367–375. https://doi.org/10.1007/s11340-016-0230-6
Huňady R, Pavelka P, Lengvarský P (2019) Vibration and modal analysis of a rotating disc using high-speed 3D digital image correlation. Mech Syst Signal Pr 121:201–214. https://doi.org/10.1016/j.ymssp.2018.11.024
Rader C (1977) Recovery of undersampled periodic waveforms. IEEE Trans Acoust Speech Signal Process 25(3):242–249. https://doi.org/10.1109/TASSP.1977.1162937
Choi H, Gomes AV, Chatterjee A (2010) Signal acquisition of high-speed periodic signals using incoherent sub-sampling and back-end signal reconstruction algorithms. IEEE T VLSI Syst 19(7):1125–1135. https://doi.org/10.1109/TVLSI.2010.2048135
Endo MT, Montagnoli AN, Nicoletti R (2015) Measurement of shaft orbits with photographic images and sub-sampling technique. Exp Mech 55(2):471–481. https://doi.org/10.1007/s11340-014-9951-6
Warburton JR, Lu G, Buss TM, Docx H, Matveev MY, Jones IA (2016) Digital image correlation vibrometry with low speed equipment. Exp Mech 56(7):1219–1230. https://doi.org/10.1007/s11340-016-0162-1
Chen W, Jin M, Huang J, Chen Y, Song H (2021) A method to distinguish harmonic frequencies and remove the harmonic effect in operational modal analysis of rotating structures. Mech Syst Signal Pr 161:107928. https://doi.org/10.1016/j.ymssp.2021.107928
Chen DJ, Chiang F, Tan YS, Don HS (1993) Digital speckle-displacement measurement using a complex spectrum method. Appl Optics 32(11):1839–1849. https://doi.org/10.1364/AO.32.001839
Jiang Z, Kemao Q, Miao H, Yang J, Tang L (2015) Path-independent digital image correlation with high accuracy, speed and robustness. Opt Laser Eng 65:93–102. https://doi.org/10.1016/j.optlaseng.2014.06.011
Hung P, Voloshin AS (2003) In-plane strain measurement by digital image correlation. J Braz Soc Mech Sci 25(3):215–221. https://doi.org/10.1590/S1678-58782003000300001
Muja M, Lowe DG (2009) Fast approximate nearest neighbors with automatic algorithm configuration. VISAPP (1) 2(331–340):2. https://doi.org/10.5220/0001787803310340
Fischler MA, Bolles RC (1981) Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun ACM 24(6):381–395. https://doi.org/10.1145/358669.358692
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11627803, 11872354), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB22040502).
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Wang, Y., Gao, Z., Fang, Z. et al. Rotating Vibration Measurement Using 3D Digital Image Correlation. Exp Mech 63, 565–579 (2023). https://doi.org/10.1007/s11340-022-00934-7
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DOI: https://doi.org/10.1007/s11340-022-00934-7