A general framework for probabilistic prognosis and uncertainty management under fatigue cyclic loading is proposed in this article. First, the general idea using the Bayesian updating in prognosis is introduced. Several sources of uncertainties are discussed and included in the Bayesian updating framework. An equivalent stress level model is discussed for the mechanism-based fatigue crack growth analysis, which serves as the deterministic model for the lap joint fatigue life prognosis. Next, an in situ lap joint fatigue test with pre-installed piezoelectric sensors is designed and performed to collect experimental data. Signal processing techniques are used to extract damage features for crack length estimation. Following this, the proposed methodology is demonstrated using the experimental data under both constant and variable amplitude loadings. Finally, detailed discussion on validation metrics of the proposed prognosis algorithm is given. Several conclusions and future work are drawn based on the proposed study.
AdamMT (2002) G104-A2LA Guide for Estimation of Measurement Uncertainty in Testing (Manual). Frederick, MD: American Association of Laboratory Accreditation, pp. 10–18.
2.
BellS (2001) A beginner’s guide to uncertainty of measurement. The National Physical Laboratory2: 9–16.
3.
BoxGTiaoG (1992) Bayesian Inference in Statistical Analysis. New York: Wiley.
4.
CatichaAGiffinA (2006) Updating probabilities. In: GoyalPGiffinAKnuthKH. (eds) Bayesian Inference and Maximum Entropy Methods in Science and Engineering: 31st International Workshop on Bayesian Inference and Maximum Entropy ... and Engineering (AIP Conference Proceedings). College Park, MD: American Institute of Physics, p. 872.
5.
ChongKP (1999) Health monitoring of civil structures. Journal of Intelligent Material Systems and Structures9: 892–898.
6.
CowlesMKCarlinBP (1996) Markov chain Monte Carlo convergence diagnostics: a comparative review. Journal of the American Statistical Association91: 883–904.
7.
DempsterA (2008) A generalization of Bayesian inference. In: YagerRRLiuL (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Berlin: Springer-Verlag, pp. 73–104.
8.
DietrichFListC (2013) Reasons for (prior) belief in Bayesian epistemology. Synthese190: 787–808.
9.
EbdenM (2008) Gaussian Processes for Regression: A Quick Introduction. Oxford: Robotics Research Group, Department on Engineering Science, University of Oxford.
FormanR (1967) Numerical analysis of crack propagation in cyclic-loaded structures. Journal of Basic Engineering89: 459–464.
12.
FortGMoulinesEPriouretP (2012) Convergence of adaptive and interacting Markov chain Monte Carlo algorithms. Annals of Statistics39: 3262–3289.
13.
GilboaISchmeidlerD (1992) Updating Ambiguous Beliefs. San Francisco, CA: Morgan Kaufmann Publishers Inc., pp. 143–162.
14.
GiurgiutiuV (2003) Lamb wave generation with piezoelectric wafer active sensors for structural health monitoring. In: Proceedings of SPIE, smart structures and materials 2003: smart structures and integrated systems, 5 August, vol. 5056, pp. 111–122. Bellingham, Wash., USA.
15.
GiurgiutiuV (2005) Tuned Lamb wave excitation and detection with piezoelectric wafer active sensors for structural health monitoring. Journal of Intelligent Material Systems and Structures16: 291–305.
16.
GiurgiutiuVZagraiABaoJJ (2002) Piezoelectric wafer embedded active sensors for aging aircraft structural health monitoring. Structural Health Monitoring1: 41–61.
17.
GuanXLiuYJhaR. (2011) Comparison of two probabilistic fatigue damage assessment approaches using prognostic performance metrics. International Journal of Prognostics and Health Management2: 11.
18.
HastingWK (1970) Monte Carlo sampling methods using Markov chain and their applications. Biometrika57: 97–109.
19.
HijaziALSmithBLLacyTE (2004) Linkup strength of 2024-T3 bolted lap joint panels with multiple-site damage. Journal of Aircraft41: 359–364.
20.
IhnJBChangFK (2004) Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: I. Diagnostics. Smart Materials and Structures13: 609–620.
21.
KazysRSvilainisL (1997) Ultrasonic detection and characterization of delaminations in thin composite plates using signal processing technique. Ultrasonics35: 367–383.
22.
KeilersCHJRChangF-K (1993) Identifying delamination in composite beams using built-in piezoelectrics. Journal of Intelligent Material Systems and Structures6: 649–672.
23.
KimSBLeeCGHongJ-W. (2010) Applications of an instantaneous damage detection technique to plates with additional complexities. Journal of Nondestructive Evaluation29: 189–205.
24.
KitagawaHTakahashiS (1976) Applicability of fracture mechanics to very small cracks or cracks in the early stage. In: Proceedings of the 2nd international conference on mechanical behavior of materials, Boston, MA, 16–20 August. Metals Park, OH: American Society for Metals, pp. 627–631.
25.
KorukçuMÖKilicM (2009) The usage of IR thermography for the temperature measurements inside an automobile cabin. International Communications in Heat and Mass Transfer36: 872–877.
26.
LairdC (1979) Mechanisms and theories of fatigue, in fatigue and microstructure. Papers presented at the 1978 ASM Materials Science Seminar, St. Louis, MI, 14–15 October. Metals Park, OH: American Society for Metals, pp. 149–203.
27.
LemistreMBalageasD (2001) Structural health monitoring system based on diffracted Lamb wave analysis by multiresolution processing. Smart Materials and Structures10: 504.
28.
LiuYMahadevanS (2009) Probabilistic fatigue life prediction using an equivalent initial flaw size distribution. International Journal of Fatigue31: 476–687.
29.
LuZLiuY (2010) Small time scale fatigue crack growth analysis. International Journal of Fatigue32: 1306–1321.
30.
MasriSFShengL-HCaffreyJP. (2004) Application of a web-enabled real-time structural health monitoring system for civil infrastructure systems. Smart Materials and Structures13: 1269–1283.
31.
MofakhamiMRBollerC (2009) Scattering of lamb waves from edge cracks in circular holes for understanding damage detection in more complex structures. Materials Forum33: 396–403.
32.
MonkhouseRWilcoxPCawleyP (1997) Flexible interdigital PVDF transducers for the generation of Lamb waves in structures. Ultrasonics35: 489–498.
33.
NicolletoAAnzelottiaGKonečnábR (2010) X-ray computed tomography vs. metallography for pore sizing and fatigue of cast Al-alloys. Procedia Engineering2: 547–554.
34.
ParisPErdoganF (1963) A critical analysis of crack propagation laws. Journal of Basic Engineering85: 528–534.
35.
PengTSaxenaAGoebelK. (2013) A novel Bayesian imaging method for probabilistic delamination detection of composite materials. Smart Materials and Structures22: 125019.
36.
PeskunPH (1973) Optimum Monte-Carlo sampling using Markov chains. Biometrika57: 97–109.
37.
PressS (2003) Subjective and Objective Bayesian Statistics: Principles, Models, and Applications. Hoboken, NJ: Wiley-Interscience.
38.
RasmussenCEWilliamsCKI (2006) Gaussian Process for Machine Learning. Cambridge, MA: The MIT Press.
39.
RitchieRLankJ (1996) Small fatigue cracks: a statement of the problem and potential solutions. Materials Science and Engineering84: 11–16.
40.
SantoniGBYuLXuB (2007) Lamb wave-mode tuning of piezoelectric wafer active sensors for structural health monitoring. Journal of Vibration and Acoustics: Transactions of the ASME129: 752–762.
41.
SaxenaACelayaJSahaB. (2010) Metrics for offline evaluation of prognostic performance. International Journal of Prognostics and Health Management1: 20.
42.
SaxenaACelayaJSahaB. (2011) Uncertainty quantification in fatigue crack growth prognosis. International Journal of Prognostics and Health Management2: 15.
43.
SuZYeL (2009) Identification of Damage Using Lamb Waves: From Fundamentals to Applications (Lecture Notes in Applied and Computational Mechanics, series no. 48). Berlin: Springer, pp. 195–254.
44.
WangQYuanS (2009) Baseline-free imaging method based on new PZT sensor arrangements. Journal of Intelligent Material Systems and Structures20: 1663–1673.
45.
WardMDButtryDA (1990) In situ interfacial mass detection with piezoelectric transducers. Science249: 1000–1007.
46.
XiangYLiuY (2011) An equivalent stress level model for efficient fatigue crack growth prediction. In: Proceeding of the 52nd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Denver, CO, 4–7 April. Reston, VA: American Institute of Aeronautics and Astronautics.
47.
ZhaoXGaoHZhangG. (2007) Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. Defect detection, localization and growth monitoring. Smart Materials and Structures16: 1208.
