Uncertainty Quantification in Fatigue Damage Prognosis
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Published
Mar 26, 2021
Shankar Sankararaman
You Ling
Chris Shantz
Sankaran Mahadevan
How to Cite
Sankararaman, S. ., Ling, Y. ., Shantz, C. ., & Mahadevan, S. (2021). Uncertainty Quantification in Fatigue Damage Prognosis. Annual Conference of the PHM Society, 1(1). Retrieved from https://papers.phmsociety.org/index.php/phmconf/article/view/1673
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Keywords
crack detection, damage detection, damage modeling, damage propagation model, fatigue crack growth, materials damage prognostics, structural health management, structural health monitoring
References
Joint service specification guide aircraft structures, JSSG- 2006. United States of America: Department of Defense; 1998.
J.P. Gallagher, A.P. Berens, and R.M. Engle Jr. (1984). USAF damage tolerant design handbook: guidelines for the analysis and design of damage tolerant aircraft structures. Final report. 1984.
A. Merati, and G. Eastaugh. (2007). Determination of fatigue related discontinuity state of 7000 series of aerospace aluminum alloys. Eng Failure Anal2007; 14(4):673–85.
J.N. Yang. (1980). Distribution of equivalent initial flaw size. In: Proceedings of the annual reliability and maintainability symposium. San Francisco (CA): 1980.
P. White, L. Molent, and S. Barter. (2005). Interpreting fatigue test results using a probabilistic fracture approach. Int J Fatigue 2005;27(7):752–67.
L. Molent, Q. Sun, and A. Green. (2006). Charcterisation of equivalent initial flaw sizes in 7050 aluminium alloy. J Fatigue Fract Eng Mater Struct 2006;29:916– 37.
PMGP. Moreira, PFP. de Matos, and PMST. de Castro. (2005). Fatigue striation spacing and equivalent initial flaw size in Al 2024-T3 riveted specimens. Theor Appl FractMech 2005;43(1):89–99.
S.A. Fawaz. (2000). Equivalent initial flaw size testing and analysis. 2000.
Y. Liu and S. Mahadevan. (2008). Probabilistic fatigue life prediction using an equivalent initial flaw size distribution, International Journal of Fatigue, Volume 31, Issue 3, March 2009, Pages 476-487, ISSN 0142- 1123, DOI: 10.1016/j.ijfatigue.2008.06.005.
H. Kitagawa, and S. Takahashi. (1976). Applicability of fracture mechanics to vary small cracks or cracks in early stage. In: Proceedings of the 2nd international conference on mechanical behavior of materials. USA (OH): ASM International; 1976.
M.H. El Haddad, T.H. Topper, and K.N. Smith. (1979) Prediction of non propagating cracks. Eng Fract Mech 1979;11:573–84.
S.W. Doebling, and F.M. Hemez. (2001) Overview of Uncertainty Assessment for Structural Health Monitoring. In the Proceedings of the 3rd International Workshop on Structural Health Monitoring, September 17-19, 2001, Stanford University, Stanford, California.
F.M. Hemez, A.N. Roberson, and A.C. Rutherford. (2003). Uncertainty Quantification and Model Validation for Damage Prognosis. In the Proceedings of the 4th International Workshop on Structural Health Monitoring, Stanford University, Stanford, California, September 15- 17, 2003
C.R. Farrar, G. Park, F.M. Hemez, T.B. Tippetts, H. Sohn, J. Wait, D.W. Allen, and B.R. Nadler. (2004). Damage Detection and Prediction for Composite Plates. J. of The Minerals, Metals and Materials Society, November 2004.
C.R. Farrar, and N.A.J. Lieven. (2006). Damage Prognosis : The Future of Structural Health Monitoring. Phil. Trans. R. Soc. A (2007) 365, 623–632 doi:10.1098/rsta.2006.1927. Published online 12 December 2006.
R. Patrick, M.E. Orchard, B. Zhang, M.D. Koelemay, G.J. Kacprzynski, A.A. Ferri, and G.J. V achtsevanos. (2007). An integrated approach to helicopter planetary gear fault diagnosis and failure prognosis. Autotestcon, 2007 IEEE , vol., no., pp.547-552, 17-20 Sept. 2007.
S. Gupta, and A. Ray. (2007). Real-time fatigue life estimation in mechanical structures. Meas. Sci. Technol. 18 (2007) 1947–1957. doi:10.1088/0957-0233/18/7/022.
S.G. Pierce, K. Worden, and A. Bezazi. (2007). Uncertainty analysis of a neural network used for fatigue lifetime prediction, Mechanical Systems and Signal Processing, Volume 22, Issue 6, Special Issue: Mechatronics, August 2008, Pages 1395-1411, ISSN 0888-3270, DOI: 10.1016/j.ymssp.2007.12.004.
J.M. Papazian, E.L. Anagnostou, S.J. Engel, D. Hoitsma, J. Madsen, R.P. Silberstein, G. Welsh, and J.B. Whiteside. (2008). A structural integrity prognosis system, Engineering Fracture Mechanics, V olume 76, Issue 5, Material Damage Prognosis and Life-Cycle Engineering, March 2009, Pages 620-632, ISSN 0013-7944, DOI: 10.1016/j.engfracmech.2008.09.007.
Y. Liu and S. Mahadevan. (2005). Multiaxial high- cycle fatigue criterion and life prediction for metals. International Journal of Fatigue, 2005. 27(7): p. 790-80
C. Rasmussen. (1996). Evaluation of Gaussian processes and other methods for non-linear regression. PhD thesis, University of Toronto, 1996
T.J. Santner, B.J. Williams, and W.I. Noltz. (2003). The Design and Analysis of Computer Experiments. Springer-Verlag, New York, 2003.
McFarland J. Uncertainty analysis for computer simulations through validation and calibration. Ph D. Dissertation, Vanderbilt University, 2008
S.A. Richards. (1997). Completed Richardson extrapolation in space and time. Comm Numer Methods Eng 1997;13:558–73.
R. Rebba. (2002) Computational model validation under uncertainty.Master’s thesis. Nashville, TN: Vanderbilt University; 2002.
S.A. Barter, P.K. Sharp, G. Holden, and G. Clark. (2002) Initiation and early growth of fatigue cracks in an aerospace aluminum alloy, Fatigue Fract. Eng. Mater. 25 (2002) (2), pp. 111–125.
A. Makeev, Y. Nikishkov, and E. Armanios. (2007). A concept for quantifying equivalent initial flaw size distribution in fracture mechanics based life prediction models, Int J Fatigue (2006), Vol. 29, No. 1, Jan. 2007.
R. Cross, A. Makeev, and E. Armanios. (2007). Simultaneous uncertainty quantification of fracture mechanics based life prediction model parameters, Int J Fatigue, Vol. 29, No. 8, Aug. 2007.
ANSYS. (2007). ANSYS theory reference, release 11.0. ANSYS Inc., 2007.
Y. Liu, L. Liu, and S. Mahadevan. (2007). Analysis of subsurface crack propagation under rolling contact loading in railroad wheels using FEM. Engineering Fracture Mechanics, Vol 74, pgs 2659-2674, 2007.
G.H. Besterfield, W.K. Liu, A.M. Lawrence, and T. Belytschko. (1991). Fatigue crack growth reliability by probabilistic finite elements, Computer Methods in Applied Mechanics and Engineering, Volume 86, Issue 3.
G.A.F. Seber, and C.J. Wild. 1989. Nonlinear Regression. New York: John Wiley and Sons, 1989.
M. Orchard, G. Kacprzynski, K. Goebel, B. Saha, and G. Vachtsevanos. Advances in Uncertainty Representation and Management for Particle Filtering Applied to Prognostics. In the Proceedings of the 1st Prognostics and Health Management (PHM) Conference, Denver, CO. Oct 6-9, 2008.
P.S. Song, B.C. Sheu, and L. Chang. A modified wheeler model to improve predictions of crack growth following a single overload. JSME Int J Series A 2001;44(1):117–22.
B.K.C. Yuen, and F. Taheri. Proposed modifications to the Wheeler retardation model for multiple overloading fatigue life prediction, International Journal of Fatigue, Volume 28, Issue 12, December 2006, Pages 1803-1819, ISSN 0142- 1123, DOI: 10.1016/j.ijfatigue.2005.12.007.
B.C. Sheu, P.S. Song, and S. Hwang. Shaping exponent in wheeler model under a single overload. Eng Fract Mech 1995;51(1): 135–43.
R. Rebba, S. Mahadevan, and S. Huang. (2004). Validation and error estimation of computational models, Reliability Engineering & System Safety, Volume 91, Issues 10-11, The Fourth International Conference on Sensitivity Analysis of Model Output (SAMO 2004) - SAMO 2004, October-November 2006, Pages 1390-1397, ISSN 0951-8320, DOI: 10.1016/j.ress.2005.11.035.
M. McDonald, K. Zaman, and S. Mahadevan. (2009). Representation and First-Order Approximations for Propagation of Aleatory and Distribution Parameter Uncertainty. In the Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 4 - 7 May 2009, Palm Springs, California.
A. Haldar, and S. Mahadevan. (2000). Probability, Reliability and Statistical Methods in Engineering Design, Wiley, New York, 2000.
J.P. Gallagher, A.P. Berens, and R.M. Engle Jr. (1984). USAF damage tolerant design handbook: guidelines for the analysis and design of damage tolerant aircraft structures. Final report. 1984.
A. Merati, and G. Eastaugh. (2007). Determination of fatigue related discontinuity state of 7000 series of aerospace aluminum alloys. Eng Failure Anal2007; 14(4):673–85.
J.N. Yang. (1980). Distribution of equivalent initial flaw size. In: Proceedings of the annual reliability and maintainability symposium. San Francisco (CA): 1980.
P. White, L. Molent, and S. Barter. (2005). Interpreting fatigue test results using a probabilistic fracture approach. Int J Fatigue 2005;27(7):752–67.
L. Molent, Q. Sun, and A. Green. (2006). Charcterisation of equivalent initial flaw sizes in 7050 aluminium alloy. J Fatigue Fract Eng Mater Struct 2006;29:916– 37.
PMGP. Moreira, PFP. de Matos, and PMST. de Castro. (2005). Fatigue striation spacing and equivalent initial flaw size in Al 2024-T3 riveted specimens. Theor Appl FractMech 2005;43(1):89–99.
S.A. Fawaz. (2000). Equivalent initial flaw size testing and analysis. 2000.
Y. Liu and S. Mahadevan. (2008). Probabilistic fatigue life prediction using an equivalent initial flaw size distribution, International Journal of Fatigue, Volume 31, Issue 3, March 2009, Pages 476-487, ISSN 0142- 1123, DOI: 10.1016/j.ijfatigue.2008.06.005.
H. Kitagawa, and S. Takahashi. (1976). Applicability of fracture mechanics to vary small cracks or cracks in early stage. In: Proceedings of the 2nd international conference on mechanical behavior of materials. USA (OH): ASM International; 1976.
M.H. El Haddad, T.H. Topper, and K.N. Smith. (1979) Prediction of non propagating cracks. Eng Fract Mech 1979;11:573–84.
S.W. Doebling, and F.M. Hemez. (2001) Overview of Uncertainty Assessment for Structural Health Monitoring. In the Proceedings of the 3rd International Workshop on Structural Health Monitoring, September 17-19, 2001, Stanford University, Stanford, California.
F.M. Hemez, A.N. Roberson, and A.C. Rutherford. (2003). Uncertainty Quantification and Model Validation for Damage Prognosis. In the Proceedings of the 4th International Workshop on Structural Health Monitoring, Stanford University, Stanford, California, September 15- 17, 2003
C.R. Farrar, G. Park, F.M. Hemez, T.B. Tippetts, H. Sohn, J. Wait, D.W. Allen, and B.R. Nadler. (2004). Damage Detection and Prediction for Composite Plates. J. of The Minerals, Metals and Materials Society, November 2004.
C.R. Farrar, and N.A.J. Lieven. (2006). Damage Prognosis : The Future of Structural Health Monitoring. Phil. Trans. R. Soc. A (2007) 365, 623–632 doi:10.1098/rsta.2006.1927. Published online 12 December 2006.
R. Patrick, M.E. Orchard, B. Zhang, M.D. Koelemay, G.J. Kacprzynski, A.A. Ferri, and G.J. V achtsevanos. (2007). An integrated approach to helicopter planetary gear fault diagnosis and failure prognosis. Autotestcon, 2007 IEEE , vol., no., pp.547-552, 17-20 Sept. 2007.
S. Gupta, and A. Ray. (2007). Real-time fatigue life estimation in mechanical structures. Meas. Sci. Technol. 18 (2007) 1947–1957. doi:10.1088/0957-0233/18/7/022.
S.G. Pierce, K. Worden, and A. Bezazi. (2007). Uncertainty analysis of a neural network used for fatigue lifetime prediction, Mechanical Systems and Signal Processing, Volume 22, Issue 6, Special Issue: Mechatronics, August 2008, Pages 1395-1411, ISSN 0888-3270, DOI: 10.1016/j.ymssp.2007.12.004.
J.M. Papazian, E.L. Anagnostou, S.J. Engel, D. Hoitsma, J. Madsen, R.P. Silberstein, G. Welsh, and J.B. Whiteside. (2008). A structural integrity prognosis system, Engineering Fracture Mechanics, V olume 76, Issue 5, Material Damage Prognosis and Life-Cycle Engineering, March 2009, Pages 620-632, ISSN 0013-7944, DOI: 10.1016/j.engfracmech.2008.09.007.
Y. Liu and S. Mahadevan. (2005). Multiaxial high- cycle fatigue criterion and life prediction for metals. International Journal of Fatigue, 2005. 27(7): p. 790-80
C. Rasmussen. (1996). Evaluation of Gaussian processes and other methods for non-linear regression. PhD thesis, University of Toronto, 1996
T.J. Santner, B.J. Williams, and W.I. Noltz. (2003). The Design and Analysis of Computer Experiments. Springer-Verlag, New York, 2003.
McFarland J. Uncertainty analysis for computer simulations through validation and calibration. Ph D. Dissertation, Vanderbilt University, 2008
S.A. Richards. (1997). Completed Richardson extrapolation in space and time. Comm Numer Methods Eng 1997;13:558–73.
R. Rebba. (2002) Computational model validation under uncertainty.Master’s thesis. Nashville, TN: Vanderbilt University; 2002.
S.A. Barter, P.K. Sharp, G. Holden, and G. Clark. (2002) Initiation and early growth of fatigue cracks in an aerospace aluminum alloy, Fatigue Fract. Eng. Mater. 25 (2002) (2), pp. 111–125.
A. Makeev, Y. Nikishkov, and E. Armanios. (2007). A concept for quantifying equivalent initial flaw size distribution in fracture mechanics based life prediction models, Int J Fatigue (2006), Vol. 29, No. 1, Jan. 2007.
R. Cross, A. Makeev, and E. Armanios. (2007). Simultaneous uncertainty quantification of fracture mechanics based life prediction model parameters, Int J Fatigue, Vol. 29, No. 8, Aug. 2007.
ANSYS. (2007). ANSYS theory reference, release 11.0. ANSYS Inc., 2007.
Y. Liu, L. Liu, and S. Mahadevan. (2007). Analysis of subsurface crack propagation under rolling contact loading in railroad wheels using FEM. Engineering Fracture Mechanics, Vol 74, pgs 2659-2674, 2007.
G.H. Besterfield, W.K. Liu, A.M. Lawrence, and T. Belytschko. (1991). Fatigue crack growth reliability by probabilistic finite elements, Computer Methods in Applied Mechanics and Engineering, Volume 86, Issue 3.
G.A.F. Seber, and C.J. Wild. 1989. Nonlinear Regression. New York: John Wiley and Sons, 1989.
M. Orchard, G. Kacprzynski, K. Goebel, B. Saha, and G. Vachtsevanos. Advances in Uncertainty Representation and Management for Particle Filtering Applied to Prognostics. In the Proceedings of the 1st Prognostics and Health Management (PHM) Conference, Denver, CO. Oct 6-9, 2008.
P.S. Song, B.C. Sheu, and L. Chang. A modified wheeler model to improve predictions of crack growth following a single overload. JSME Int J Series A 2001;44(1):117–22.
B.K.C. Yuen, and F. Taheri. Proposed modifications to the Wheeler retardation model for multiple overloading fatigue life prediction, International Journal of Fatigue, Volume 28, Issue 12, December 2006, Pages 1803-1819, ISSN 0142- 1123, DOI: 10.1016/j.ijfatigue.2005.12.007.
B.C. Sheu, P.S. Song, and S. Hwang. Shaping exponent in wheeler model under a single overload. Eng Fract Mech 1995;51(1): 135–43.
R. Rebba, S. Mahadevan, and S. Huang. (2004). Validation and error estimation of computational models, Reliability Engineering & System Safety, Volume 91, Issues 10-11, The Fourth International Conference on Sensitivity Analysis of Model Output (SAMO 2004) - SAMO 2004, October-November 2006, Pages 1390-1397, ISSN 0951-8320, DOI: 10.1016/j.ress.2005.11.035.
M. McDonald, K. Zaman, and S. Mahadevan. (2009). Representation and First-Order Approximations for Propagation of Aleatory and Distribution Parameter Uncertainty. In the Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 4 - 7 May 2009, Palm Springs, California.
A. Haldar, and S. Mahadevan. (2000). Probability, Reliability and Statistical Methods in Engineering Design, Wiley, New York, 2000.
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