Hybrid Machine Learning Method for Remaining Fatigue Life Prediction of the Metallic Materials under Two-step Loading

doi:10.3901/JME.2025.12.073

Abstract

Abstract: Remaining fatigue life prediction is crucial for the safety and reliability of engineering structures. When the structure is subjected to multi-step loading, it becomes challenging to predict the remaining fatigue life due to the complexity of fatigue damage accumulation and inherent noise and uncertainty in the data. To address this problem, a hybrid machine learning method, the GA-BP-GPR method, is established, which uses the GA-BP method (genetic algorithm-backpropagation neural network) to map the complex relationship between input features and remaining fatigue life and combines with GPR (Gaussian process regression) to obtain the corresponding uncertainty, for estimating the remaining fatigue life of metal materials under two-step loading. The GA-BP-GPR method is comprehensively evaluated on a dataset of 328 samples from 12 metal materials. The predicted results of the test set using the proposed method fall within the ±3 scatter band. In comparison with the five machine learning methods and two traditional methods, the results indicate that the proposed method can achieve higher accuracy and reliability in predicting remaining fatigue life under two-step loading. In addition, the predicted results of the proposed method for Al-2024-T42 fall within the ±2 scatter band, indicating the proposed method has generalization ability for remaining fatigue life prediction under two-step loading for new materials.

Key words: remaining fatigue life, fatigue life prediction, genetic algorithm, Gaussian process regression, machine learning

CLC Number:

O346

XU Zili, GAO Jingjing, QIN Manqing, HE Mengfu. Hybrid Machine Learning Method for Remaining Fatigue Life Prediction of the Metallic Materials under Two-step Loading[J]. Journal of Mechanical Engineering, 2025, 61(12): 73-82.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://www.cjmenet.com.cn/EN/10.3901/JME.2025.12.073

http://www.cjmenet.com.cn/EN/Y2025/V61/I12/73

References

[1] JORDAN M I，MITCHELL T M. Machine learning：Trends，perspectives，and prospects[J]. Science，2015，349(6245)：255-260.
[2] FARID M. Data-driven method for real-time prediction and uncertainty quantification of fatigue failure under stochastic loading using artificial neural networks and Gaussian process regression[J]. International Journal of Fatigue，2021，155：106415.
[3] AFSHARI S S，ENAYATOLLAHI F，XU X，et al. Machine learning-based methods in structural reliability analysis：A review[J]. Reliability Engineering & System Safety，2022，219：108223.
[4] CHEN J，LIU Y. Fatigue modeling using neural networks：A comprehensive review[J]. Fatigue & Fracture of Engineering Materials & Structures，2022，45(4)：945-979.
[5] BOCK F E，AYDIN R C，CYRON C J，et al. A review of the application of machine learning and data mining approaches in continuum materials mechanics[J]. Frontiers in Materials，2019，6(110)：1-23.
[6] JOHNSON N S，VULIMIRI P S，TO A C，et al. Invited review：Machine learning for materials developments in metals additive manufacturing[J]. Additive Manufacturing，2020，36：101641.
[7] NASIRI S，KHOSRAVANI M R，WEINBERG K. Fracture mechanics and mechanical fault detection by artificial intelligence methods：A review[J]. Engineering Failure Analysis，2017，81：270-293.
[8] WANG C，TAN X P，TOR S B，et al. Machine learning in additive manufacturing：State-of-the-art and perspectives[J]. Additive Manufacturing，2020，36：101538.
[9] GAO J，WANG C，XU Z，et al. Gaussian process regression based remaining fatigue life prediction for metallic materials under two-step loading[J]. International Journal of Fatigue，2022，158：106730.
[10] GALANOPOULOS G，MILANOSKI D，ELEFTHEROGLOU N，et al. Acoustic emission-based remaining useful life prognosis of aeronautical structures subjected to compressive fatigue loading[J]. Engineering Structures，2023，290：116391.
[11] LEI G，ZHAO X，WU H，et al. Estimation of remaining fatigue life under two-step loading based on kernel-extreme learning machine[J]. International Journal of Fatigue，2021，148：106190.
[12] LI J，CAO X，CHEN R，et al. Prediction of remaining fatigue life of metal specimens using data-driven method based on acoustic emission signal[J]. Applied Acoustics，2023，211：109571.
[13] GAN L，WU H，ZHONG Z. Integration of symbolic regression and domain knowledge for interpretable modeling of remaining fatigue life under multistep loading[J]. International Journal of Fatigue，2022，161：106889.
[14] FENG S Z，HAN X，LI Z，et al. Ensemble learning for remaining fatigue life prediction of structures with stochastic parameters：A data-driven approach[J]. Applied Mathematical Modelling，2022，101：420-431.
[15] GU H，WANG R，ZHU S，et al. Machine learning assisted probabilistic creep-fatigue damage assessment[J]. International Journal of Fatigue，2022，156：106677.
[16] HENG J，ZHENG K，FENG X，et al. Machine learning-assisted probabilistic fatigue evaluation of Rib-to-Deck joints in orthotropic steel decks[J]. Engineering Structures，2022，265：114496.
[17] CHEN J，LIU Y. Probabilistic physics-guided machine learning for fatigue data analysis[J]. Expert Systems with Applications，2021，168：114316.
[18] HU D，SU X，LIU X，et al. Bayesian-based probabilistic fatigue crack growth evaluation combined with machine-learning-assisted GPR[J]. Engineering Fracture Mechanics，2020，229：106933.
[19] GAO J，WANG J，XU Z，et al. Multiaxial fatigue prediction and uncertainty quantification based on back propagation neural network and Gaussian process regression[J]. International Journal of Fatigue，2023，168：107361.
[20] CYBENKO G V. Approximation by superpositions of a sigmoidal function[J]. Mathematics of Control，Signals，and Systems，1989，2(4)：303-314.
[21] KATOCH S，CHAUHAN S S，V K. A review on genetic algorithm：Past，present，and future[J]. Multimedia Tools and Applications，2021，80：8091-8126.
[22] SHENG H，LIU X，BAI L，et al. Small sample state of health estimation based on weighted Gaussian process regression[J]. Journal of Energy Storage，2021，41：102816.
[23] HAN G S，LEE J. Prediction of pricing and hedging errors for equity linked warrants with Gaussian process models[J]. Expert Systems with Applications，2008，35(1-2)：515-523.
[24] PAVLOU D G. A phenomenological fatigue damage accumulation rule based on hardness increasing，for the 2024-T42 aluminum[J]. Engineering Structures，2002，24(11)：1363-1368.
[25] MESMACQUE G，GARCIA S，AMROUCHE A，et al. Sequential law in multiaxial fatigue，a new damage indicator[J]. International Journal of Fatigue，2005，27(4)：461-467.
[26] MANSON S S，FRECHE J C，ENSIGN C R. Application of a double linear damage rule to cumulative fatigue[R]. National Aeronautics and Space Administration，1967.
[27] KAMAYA M，KAWAKUBO M. Loading sequence effect on fatigue life of type 316 stainless steel[J]. International Journal of Fatigue，2015，81：10-20.
[28] 谢里阳，吕文阁，师照峰. 两级载荷作用下疲劳损伤状态的试验研究[J]. 机械强度，1994，16(3)：52-54. XIE Liyang，LÜ Wenge，SHI Zhaofeng. Experimental study on fatigue damage under two level loading. Journal of Mechinical Strength，1994，16(3)：52-54.
[29] ZHU S，LIAO D，LIU Q，et al. Nonlinear fatigue damage accumulation：Isodamage curve-based model and life prediction aspects[J]. International Journal of Fatigue，2019，128：105185.
[30] SUBRAMANYAN S. A cumulative damage rule based on the knee point of the S-N curve[J]. Journal of Engineering Materials & Technology，1976，98(4)：316.
[31] XIA F，ZHU S，LIAO D，et al. Isodamage curve-based fatigue damage accumulation model considering the exhaustion of static toughness[J]. Engineering Failure Analysis，2020，115：104575.
[32] DATTOMA V，GIANCANE S，NOBILE R，et al. Fatigue life prediction under variable loading based on a new non-linear continuum damage mechanics model[J]. International Journal of Fatigue，2006，28(2)：89-95.
[33] 方义庆，胡明敏，罗艳利. 基于全域损伤测试建立的连续疲劳损伤模型[J]. 机械强度，2006，28(4)：582-586. FANG Yiqing，HU Mingmin，LUO Yanli. New continuous fatigue damage model based on whole damage field measurement[J]. Journal of Mechanical Strength，2006，28(4)：582-586.
[34] AID A，AMROUCHE A，BOUIADJRA B B，et al. Fatigue life prediction under variable loading based on a new damage model[J]. Materials & Design，2011，32(1)：183-191.
[35] SHANG D，YAO W. A nonlinear damage cumulative model for uniaxial fatigue[J]. International Journal of Fatigue，1999，21(2)：187-194.
[36] PEREIRA H F S G，DE JESUS A M P，RIBEIRO A S，et al. Fatigue damage behavior of a structural component made of P355NL1 steel under block loading[J]. Journal of Pressure Vessel Technology，2009，131(2)：021407.
[37] FANG Y，HU M，LUO Y. New continuous fatigue damage model based on whole damage field measurement[J]. Journal of Mechanical Strength，2006，28(4)：582-586.
[38] HECHT NIELSEN R. Kolmogorov’s mapping neural network existence theorem[C]//Proceedings of the International Conference on Neural Networks，New York, NY, USA：IEEE Press, 1987：11-14.
[39] RIPLEY B D. Pattern recognition and neural networks[M]. New York：Cambridge University Press，2007.
[40] WANG C. A theory of generalization in learning machines with neural network applications[M]. Philadelphia：University of Pennsylvania，1994.
[41] KAASTRA I，BOYD M. Designing a neural network for forecasting financial and economic time series[J]. Neurocomputing，1996，10(3)：215-236.
[42] SHIBATA K，IKEDA Y. Effect of number of hidden neurons on learning in large-scale layered neural networks[C]//ICROS-SICE International Joint Conference，August 18-21，2009，Fukuoka International Congress Center，Japan，ICCAS-SIC，New York：IEEE，2009：5008-5013.
[43] YE D，WANG Z. A new approach to low-cycle fatigue damage based on exhaustion of static toughness and dissipation of cyclic plastic strain energy during fatigue[J]. International Journal of Fatigue，2001，23(8)：679-687.
[44] MINER M A. Cumulative damage in fatigue[J]. Journal of Applied Mechanics，1945，12(3)：A159-A164
[45] WANG S，XIA P，CHEN K. Prediction and optimization model of sustainable concrete properties using machine learning，deep learning and swarm intelligence：A review[J]. Journal of Building Engineering，2023：108065.
[46] SUN Q，ZHANG H C，SUN Z. Ridge regression and artificial neural network to predict the thermodynamic properties of alkali metal Rankine cycles for space nuclear power[J]. Energy Conversion and Management，2022，273：116385.