Accurate characterization and prediction of loading, while properly accounting for uncertainty, are essential for probabilistic fatigue damage prognosis. Three different techniques, including rainflow counting, the Markov chain method, and autoregressive moving average (ARMA) method, are reviewed for stochastic characterization and reconstruction of the fatigue load spectrum for prognosis. The ARMA method is extended by introducing random coefficients and probabilistic weights, to account for the uncertainty in the selection of models, inherent variability of loading, and uncertainty due to sparse data. A continuous model updating framework based on usage monitoring data is developed and applied to all the three techniques mentioned above. The relation between prediction accuracy and updating period is evaluated quantitatively. A quantitative model validation metric is proposed for assessing the accuracy of load prediction
How to Cite
fatigue loading, rainflow counting, Markov chain, ARMA, uncertainty quantification, Bayesian updating, model validation, prognosis
Amzallag, C., Gerey, J., Robert, J., & Bahuaud, J. (1994). Standardization of the rainflow counting method for fatigue analysis. International journal of fatigue, 16(4), 287–293.
Benasciutti, D., & Tovo, R. (2005). Cycle distribution and fatigue damage assessment in broad-band non- Gaussian random processes. Probabilistic Engineering Mechanics, 20(2), 115-127.
Benasciutti, D., & Tovo, R. (2007). On fatigue damage assessment in bimodal random processes. International Journal of Fatigue, 29(2), 232-244.
Box, G., Jenkins, G., & Reinsel, G. (1994). Time Series Analysis: Forecasting and Control (3 ed.). Englewood Cliffs, NJ: Prentice-Hall, Inc.
Doebling, S., & Hemez, F. (2001). Overview of Uncertainty Assessment for Structural Health Monitoring. In Proceedings of the 3rd Intl Workshop on Structural Health Monitoring (Vol. 6950). Stanford University, Stanford, California.
Dowling, N. (1972). Fatigue failure predictions for complicated stress-strain histories. J Mater JMLSA, 7(1), 71–87. ILLINOIS UNIV URBANA DEPT OF THEORETICAL AND APPLIED MECHANICS.
Dressler, K., Hack, M., & Krüger, W. (1997). Stochastic Reconstruction of Loading Histories from a Rainflow Matrix. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 77(3), 217-226.
Farrar, C., & Lieven, N. (2007). Damage prognosis: the future of structural health monitoring. Philosophical Transactions of the Royal Society A, 365, 623-32. doi: 10.1098/rsta.2006.1927.
Gupta, S., & Ray, A. (2007). Real-time fatigue life estimation in mechanical structures. Measurement Science and Technology, 18(7), 1947-1957. doi: 10.1088/0957-0233/18/7/022.
Haldar, A., & Mahadevan, S. (2000). Probability, reliability, and statistical methods in engineering design. New York: Wiley.
Hanke, J., & Wichern, D. (2005). Business Forecasting (8 ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.
Heuler, P., & Klatschke, H. (2005). Generation and use of standardised load spectra and load–time histories. International Journal of Fatigue, 27(8), 974-990.
Jeffreys, H. (1961). Theory of probability (3 ed.). London: Oxford University Press.
Karlin, S. (1966). A First Course in Stochastic Processes (1 ed.). New York, NY: Academic Press.
Khosrovaneh, A. K., Dowling, N. E., Berens, A. P., & Gallagher, J. P. (1989). Fatigue life estimates for helicopter loading spectra. Contractor (pp. B40- 41). NASA contractor report 181941.
Khosrovaneh, A., & Dowling, N. (1990). Fatigue loading history reconstruction based on the rainflow technique. International Journal of Fatigue, 12(2), 99-106.
Krenk, S., & Gluver, H. (1989). A Markov matrix for fatigue load simulation and rainflow range evaluation. Structural Safety, 6(2-4), 247–258.
Leser, C., Juneja, L., Thangjitham, S., & Dowling, N. (1998). On Multi-axial Random Fatigue Load Modeling. SAE transactions, 107, 481–494. AMERICAN TECHNICAL PUBLISHERS LTD.
Leser, C., Thangjitham, S., & Dowling, N. (1994). Modeling of random vehicle loading histories for fatigue analysis. International Journal of Vehicle design, 15, 467-483.
Ljung, G. M., & Box, G. E. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297-303. doi: 10.1093/biomet/65.2.297.
Miner, M. A. (1945). Cumulative damage in fatigue. Journal of Applied Mechanics, 12, A159-A164.
Moreno, B., Zapatero, J., & Dominguez, J. (2003). An experimental analysis of fatigue crack growth under random loading. International Journal of Fatigue, 25(7), 597-608.
Pierce, S., Worden, K., & Bezazi, a. (2008). Uncertainty analysis of a neural network used for fatigue lifetime prediction. Mechanical Systems and Signal Processing, 22(6), 1395-1411.
Rebba, R., Mahadevan, S., & Huang, S. (2006). Validation and error estimation of computational models. Reliability Engineering & System Safety, 91(10-11), 1390-1397.
Rychlik, I. (1996). Simulation of load sequences from rainflow matrices: Markov method. International Journal of Fatigue, 18(7), 429-438.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2009). Uncertainty Quantification in Fatigue Damage Prognosis. In Annual Conference of the Prognostics and Health Management Society. San Diego, CA.
Soares, C. (1997). Quantification of model uncertainty in structural reliability. In C. Soares, Probabilistic methods for structural design (p. 17–38). Netherlands: Kluwer Academic Publishers.
Tovo, R. (2002). Cycle distribution and fatigue damage under broad-band random loading. International Journal of Fatigue, 24(11), 1137–1147.
Wei, L., Delosrios, E., & James, M. (2002). Experimental study and modelling of short fatigue crack growth in aluminium alloy Al7010-T7451 under random loading. International Journal of Fatigue, 24(9), 963-975.
Xiong, J., & Shenoi, R. (2008). A load history generation approach for full-scale accelerated fatigue tests. Engineering Fracture Mechanics, 75(10), 3226-3243.
Zapatero, J., Moreno, B., Gonzalezherrera, a., & Dominguez, J. (2005). Numerical and experimental analysis of fatigue crack growth under random loading. International Journal of Fatigue, 27(8), 878-890.
Zhang, R., & Mahadevan, S. (2000). Model uncertainty and Bayesian updating in reliability-based inspection. Structural Safety, 22(2), 145–160.
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