Structure Fatigue Crack Length Estimation and Prediction Using Ultrasonic Wave Data Based on Ensemble Linear Regression and Paris’s Law
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Abstract
This paper presents methods for the 2019 PHM Conference Data Challenge developed by the team named "Angler". This Challenge aims to estimate the fatigue crack length of a type of aluminum structure using ultrasonic signals at the current load cycle and to predict the crack length at multiple future load cycles (multiple-step-ahead prediction) as accurately as possible. For estimating crack length, four crack-sensitive features are extracted from ultrasonic signals, namely, the first peak value, root mean square value, logarithm of kurtosis, and correlation coefficient. An ensemble linear regression model is presented to map these features and their second-order interactions with the crack length. The Best Subset Selection method is employed to select the optimal features. For predicting crack length, variations of the Paris’ law are derived to describe the relationships between the crack length and the number of load cycles. The material parameters and stress range of Paris’ law are learned using the Genetic Algorithm. These parameters will be updated based on the previous-step predicted crack length. After that, the crack length corresponding to a future load cycle number for either the constant amplitude load case or variable amplitude load case is predicted. The presented methods achieved a score of 16.14 based on the score-calculation rule provided by the Data Challenge committees, and was ranked third best among all participating teams.
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Crack propagation, crack prediction, ultrasonic guided waves, Linear Regression, Ensemble, Paris law
Campbell, F. C. (2018). Elements of Metallurgy and Engineering Alloys. Materials Park, Ohio, America: ASM International.
Chen, Y., Liang, X., and Zuo, M. J. (2019). ‘Sparse time series modeling of the baseline vibration from a gearbox under time-varying speed condition’, Mechanical Systems and Signal Processing, 134, 106342. https://doi.org/10.1016/j.ymssp.2019.106342
Courtney, C. R., Drinkwater, B. W., Neild, S. A., & Wilcox, P. D. (2008). Factors affecting the ultrasonic intermodulation crack detection technique using bispectral analysis. NDT & E International, 41(3), 22-234. https://doi.org/10.1016/j.ndteint.2007.09.004
Cui, W. (2002). A state-of-the-art review on fatigue life prediction methods for metal structures. Journal of Marine Science and Technology, 7(1), 43–56. https://doi.org/10.1007/s007730200012
Esslinger, V., Kieselbach, R., Koller, R., & Weisse, B. (2004). The railway accident of Eschede–technical background. Engineering Failure Analysis, 11(4), 515-535. https://doi.org/10.1016/j.engfailanal.2003.11.001
Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning. Cambridge, Massachusetts, America: MIT Press.
He, J., Guan, X., Peng, T., Liu, Y., Saxena, A., Celaya, J., & Goebel, K. (2013). A multi-feature integration method for fatigue crack detection and crack length estimation in riveted lap joints using Lamb waves. Smart Materials and Structures, 22(10), 1–11. doi:10.1088/0964-1726/22/10/105007
He, J., Huo, H., Guan, X., & Yang, J. (2020). A Lamb wave quantification model for inclined cracks with experimental validation. Chinese Journal of Aeronautics. https://doi.org/10.1016/j.cja.2020.02.010
Huang, X., Torgeir, M., & Cui, W. (2008). An engineering model of fatigue crack growth under variable amplitude load. International Journal of Fatigue, 30(1), 2–10. https://doi.org/10.1016/j.ijfatigue.2007.03.004
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning. New York: Springer.
Lee, C. K. H. (2018). A review of applications of genetic algorithms in operations management. Engineering Applications of Artificial Intelligence, 76, 1–12. https://doi.org/10.1016/j.engappai.2018.08.011
Li, Y., Wang, H., & Gong, D. (2012). The interrelation of the parameters in the Paris equation of fatigue crack growth. Engineering Fracture Mechanics, 96, 500– 509.https://doi.org/10.1016/j.engfracmech.2012.08.016
Lim, H. J., Sohn, H., Kim, Y. (2018). Data-driven fatigue crack quantification and prognosis using nonlinear ultrasonic modulation. Mechanical Systems and Signal Processing, 109, 185–195. https://doi.org/10.1016/j.ymssp.2018.03.003
Lim, H. J., Sohn, H., DeSimio, M. P., Brown, K. (2014). Reference-free fatigue crack detection using nonlinear ultrasonic modulation under various temperature and load conditions. Mechanical Systems and Signal Processing, 45(2), 468–478. https://doi.org/10.1016/j.ymssp.2013.12.001
Liu, S., Du, C., Mou, J., Martua, L., Zhang, J., & Lewis, F. L. (2013). Diagnosis of structural cracks using wavelet transform and neural networks. NDT & E International, 54, 9–18. https://doi.org/10.1016/j.ndteint.2012.11.004
Paris, P. C. (1961). A rational analytic theory of fatigue. The Trend in Engineering, 13(9).
Paris, P., & Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Basic Engineering, 85(4), 528–33. https://doi.org/10.1115/1.3656900
PHM Society. (2019). PHM Conference Data Challenge. Retrieved from https://www.phmdata.org/2019datachallenge/
Pook, L. P., & Frost, N. E. (1973). A fatigue crack growth theory. International Journal of Fracture, 9(1), 53–61. https://doi.org/10.1007/BF00035955
Pugno, N., Ciavarella, M., Cornetti, P., & Carpinteri, A. (2006). A generalized Paris’ law for fatigue crack growth. Journal of the Mechanics and Physics of Solids, 54(7), 1333–1349. https://doi.org/10.1016/j.jmps.2006.01.007
Qing, X., Li, W., Wang, Y., & Sun, H. (2019). Piezoelectric transducer-based structural health monitoring for aircraft applications. Sensors, 19(545), 1-27. doi:10.3390/s19030545
Rajabipour, A., & Melchers R. E. (2015). Application of Paris’ law for estimation of hydrogen-assisted fatigue crack growth. International Journal of Fatigue, 80, 357–363. https://doi.org/10.1016/j.ijfatigue.2015.06.027
Wang, D., He, J., Guan, X., Yang, J., & Zhang, W. (2018). A model assessment method for predicting structural fatigue life using Lamb waves. Ultrasonics, 84, 319–328. https://doi.org/10.1016/j.ultras.2017.11.017