0
Research Papers: Materials Technology

Comparison of Various Surrogate Models to Predict Stress Intensity Factor of a Crack Propagating in Offshore Piping

[+] Author and Article Information
Arvind Keprate

Department of Mechanical and Structural
Engineering and Material Science,
University of Stavanger,
Stavanger 4036, Norway
e-mail: arvind.keprate@uis.no

R. M. Chandima Ratnayake

Department of Mechanical and Structural
Engineering and Material Science,
University of Stavanger,
Stavanger 4036, Norway
e-mail: chandima.ratnayake@uis.no

Shankar Sankararaman

NASA Ames Research Center,
SGT Inc.,
Moffett Field, CA 94035
e-mail: shankar.sankararaman@nasa.gov

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received April 10, 2017; final manuscript received July 13, 2017; published online August 16, 2017. Assoc. Editor: Hagbart S. Alsos.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Offshore Mech. Arct. Eng 139(6), 061401 (Aug 16, 2017) (10 pages) Paper No: OMAE-17-1055; doi: 10.1115/1.4037290 History: Received April 10, 2017; Revised July 13, 2017

This paper examines the applicability of the different surrogate-models (SMs) to predict the stress intensity factor (SIF) of a crack propagating in topside piping, as an inexpensive alternative to the finite element methods (FEM). Six different SMs, namely, multilinear regression (MLR), polynomial regression (PR) of order two, three, and four (with interaction), Gaussian process regression (GPR), neural networks (NN), relevance vector regression (RVR), and support vector regression (SVR) have been tested. Seventy data points (consisting of load (L), crack depth (a), half crack length (c) and SIF values obtained by FEM) are used to train the aforementioned SMs, while 30 data points are used for testing. In order to compare the accuracy of the SMs, four metrics, namely, root-mean-square error (RMSE), average absolute error (AAE), maximum absolute error (MAE), and coefficient of determination (R2) are used. A case study illustrating the comparison of the prediction capability of various SMs is presented. python and matlab are used to train and test the SMs. Although PR emerged as the best fit, GPR was selected as the best SM for SIF determination due to its capability of calculating the uncertainty related to the prediction values. The aforementioned uncertainty representation is quite valuable, as it is used to adaptively train the GPR model (GPRM), which further improves its prediction accuracy and makes it an accurate, faster, and alternative method to FEM for predicting SIF.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Keprate, A. , and Ratnayake, R. M. C. , 2017, “ Enhancing Offshore Process Safety by Selecting Fatigue Critical Piping Locations for Inspection Using Fuzzy-AHP Based Approach,” Process Saf. Environ. Prot., 102, pp. 71–84. [CrossRef]
EI, 2007, “ Guidelines for the Avoidance of Vibration Induced Fatigue Failure in Process Pipework,” The Energy Institute, London.
EI, 2013, “ Guidelines for the Design, Installation and Management of Small Bore Tubing Assemblies,” The Energy Institute, London.
Keprate, A. , and Ratnayake, R. M. C. , 2016, “ Handling Uncertainty in the Remnant Fatigue Life Assessment of Offshore Process Pipework,” ASME Paper No. IMECE2016-65504.
Keprate, A. , Ratnayake, R. M. C. , and Sankararaman, S. , 2017, “ Minimizing Hydrocarbon Release From Offshore Piping by Performing Probabilistic Fatigue Life Assessment,” Process Saf. Environ., 106, pp. 34–51. [CrossRef]
Naess, A. A. , 2009, Fatigue Handbook: Offshore Steel Structures, Tapir Publisher, Trondheim, Norway, Chap. 3.
DNV, 2015, “ Probabilistic Methods for Planning of Inspection for Fatigue Cracks in Offshore Structures,” Det Norske Veritas AS, Høvik, Norway, Standard No. DNV-RP-C210. https://global.ihs.com/doc_detail.cfm?&csf=TIA&input_doc_number=&input_doc_title=&document_name=DNVGL-RP-0001&item_s_key=00651479&item_key_date=850131&origin=DSSC
Antaki, G. A. , 2003, Piping and Pipeline Engineering: Design, Construction, Maintenance, Integrity, and Repair, CRC Press, Boca Raton, FL, Chap. 7. [CrossRef]
Lassen, T. , and Recho, N. , 2006, Fatigue Life Analyses of Welded Structures, ISTE, London, Chap. 6. [CrossRef]
Tada, H. P. , Paris, P. C. , and Irwin, G. R. , 1973, The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, PA.
Sih, G. C. , 1973, Handbook of Stress Intensity Factors: Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, PA.
Rooke, D. P. , and Cartwright, D. J. , 1976, Compendium of Stress Intensity Factors, HMSO, London.
Miedlar, P. C. , Berens, A. P. , Gunderson, A. , and Gallagher, J. P. , 2002, Handbook for Damage Tolerant Design, AFGROW, U.S. Air Force, Dayton, OH, pp. 11.2.1–11.2.5.
More, S. T. , and Bindu, R. S. , 2015, “ Effect of Mesh Size on Finite Element Analysis of Plate Structure,” Int. J. Eng. Sci. Innovative Technol., 4(3), pp. 181–185. http://www.ijesit.com/Volume%204/Issue%203/IJESIT201503_24.pdf
Chandresh, S. , 2002, “ Mesh Discretization Error and Criteria for Accuracy of Finite Element Solutions,” ANSYS Users Conference, Pittsburgh, PA, Apr. 22–24, pp. 45–56. http://www.ansys.com/-/media/Ansys/corporate/resourcelibrary/conference-paper/2002-Int-ANSYS-Conf-9.PDF
Deschrijver, D. , and Dhaene, T. , 2012, “ Surrogate Modelling Lab,” University of Ghent, Ghent, Belgium, accessed Mar. 3, 2017, http://www.sumo.intec.ugent.be/research
Hombal, V. K. , and Mahadevan, S. , 2013, “ Surrogate Modelling of 3D Crack Growth,” Int. J. Fatigue, 47, pp. 90–99. [CrossRef]
Forrester, A. I. J. , Sobester, A. , and Keane, A. J. , 2008, Engineering Design Via Surrogate Modelling, Wiley, Chichester, UK, Chap. 1. [CrossRef]
Sankararaman, S. , Ling, Y. , Shantz, C. , and Mahadevan, S. , 2011, “ Uncertainty Quantification and Model Validation of Fatigue Crack Growth Prediction,” Eng. Fract. Mech., 78(7), pp. 1487–1504. [CrossRef]
Leser, P. E. , Hochhalter, J. D. , Warner, J. E. , Newman, J. A. , Leser, W. P. , Wawrzynek, P. A. , and Yuan, F. G. , 2016, “ Probabilistic Fatigue Damage Prognosis Using Surrogate Models Trained Via Three-Dimensional Finite Element Analysis,” Struct. Health Monit., 16(3), pp. 291–308. [CrossRef]
Yuvraj, P. , Murthy, A. R. , Iyer, N. R. , Samui, P. , and Sekar, S. K. , 2014, “ Prediction of Critical Stress Intensity Factor for High Strength and Ultra High Strength Concrete Beams Using Support Vector Regression,” J. Struct. Eng., 40(3), pp. 224–233. https://www.academia.edu/5142486/Prediction_of_critical_stress_intensity_factor_for_high_strength_and_ultra_high_strength_concrete_beams_using_support_vector_regression
BS, 2013, “ Guide to Methods for Assessing Acceptability of Flaws in Metallic Structures,” British Standards Institute, London, Standard No. BS 7910.
API, 2007, “ Recommended Practice for Fitness-for-Service,” API Publishing Services, Washington, DC, API Recommended Practice 579.
Irwin, G. R. , 1957, “ Analysis of Stresses and Strains Near the End of a Crack Traversing in a Plate,” ASME J. Appl. Mech., 24(3), pp. 361–364.
Rooke, D. P. , Baratta, F. I. , and Cartwright, D. J. , 1981, “ Simple Methods of Determining Stress Intensity Factors,” Eng. Fract. Mech., 14(2), pp. 397–426. [CrossRef]
Ali, Z. , Meysam, K. E. S. , Iman, A. , Aydin, B. , and Yashar, B. , 2014, “ Finite Element Method Analysis of Stress Intensity Factor in Different Edge Crack Positions and Predicting Their Correlation Using Neural Network Method,” Res. J. Recent Sci., 3(2), pp. 69–73. http://www.isca.in/rjrs/archive/v3/i2/9.ISCA-RJRS-2013-411.pdf
Sankararaman, S. , 2012, “ Uncertainty Quantification and Integration in Engineering Systems,” Ph.D. dissertation, Vanderbilt University, Nashville, TN. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.468.3529&rep=rep1&type=pdf
Bishop, C. M. , 2006, Pattern Recognition and Machine Learning, Springer, New York, Chap. 12.
Jin, R. , Chen, W. , and Simpson, T. W. , 2001, “ Comparative Studies of Metamodelling Techniques Under Multiple Modelling Criteria,” Struct. Multidiscip., 23(1), pp. 1–13. [CrossRef]
McFarland, J. M. , 2008, “ Uncertainty Analysis for Computer Simulations Through Validation and Calibration,” Ph.D. dissertation, Vanderbilt University, Nashville, TN. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.332.7234&rep=rep1&type=pdf
Maureen, C. , 1987, “ Neural Network Primer—Part I,” AI Expert, 2(12), pp. 46–52. http://dl.acm.org/citation.cfm?id=38295&CFID=962199646&CFTOKEN=91644732
Siffman, D. , 2012, The Nature of Code, Self Published, Mountain View, CA, Chap. 1.
MathWorks, 1994, “ Deep Learning,” The MathWorks, Inc., Natick, MA, accessed Mar. 14, 2017, https://www.mathworks.com/products/neural-network/features.html#deep-learning
Forrester, A. I. J. , and Keane, A. J. , 2009, “ Recent Advances in Surrogate Based Optimization,” Prog. Aerosp. Sci., 45(1–3), pp. 50–79. [CrossRef]
Gunn, S. R. , 1998, “ Support Vector Machines for Classification and Regression,” University of Southampton, Southampton, UK, Technical Report No. ISIS-1-98. http://users.ecs.soton.ac.uk/srg/publications/pdf/SVM.pdf
Smola, A. J. , and Scholkopf, B. , 2004, “ A Tutorial on Support Vector Regression,” Stat. Comput., 14(3), pp. 199–222. [CrossRef]
Tipping, M. E. , 2001, “ Sparse Bayesian Learning and the Relevance Vector Machine,” J. Mach. Learn. Res., 1, pp. 211–244. http://www.jmlr.org/papers/volume1/tipping01a/tipping01a.pdf
Ren, Q. , Zou, T. , Li, D. , Tang, D. , and Peng, Y. , 2015, “ Numerical Study on the X80 UOE Pipe Forming Process,” J. Mater. Process. Technol., 215, pp. 264–277. [CrossRef]
Newman, J. C. , and Raju, I. S. , 1979, “ Stress Intensity Factors for a Wide Range of Semi-Elliptical Surface Cracks in Finite Thickness Plates,” Eng. Fract. Mech., 11(4), pp. 817–829. [CrossRef]
ANSYS, 2017, “ Product Data Sheet: ANSYS Student Data Sheet,” ANSYS, Inc., Canonsburg, PA, accessed Mar. 14, 2017, http://www.ansys.com/Products/Academic/ANSYS-Student
Keprate, A. , Ratnayake, R. M. C. , and Sankararaman, S. , 2017, “ Adaptive Gaussian Process Regression as an Alternative to FEM for Prediction of Stress Intensity Factor to Assess Fatigue Degradation in Offshore Piping,” Int. J. Pressure Vessels Piping, 153, pp. 45–58. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Methods for determining SIF (Adapted from Ref. [25])

Grahic Jump Location
Fig. 2

Schematic of crack geometry on offshore piping

Grahic Jump Location
Fig. 3

Schematic of a neural network. Adapted from Ref. [33].

Grahic Jump Location
Fig. 4

Schematic showing loss function and slack variable in SVR. Adapted from Ref. [36].

Grahic Jump Location
Fig. 5

Schematic of plate and crack geometry used in the case study

Grahic Jump Location
Fig. 6

FEM model of plate and crack geometry used in the case study

Grahic Jump Location
Fig. 7

Plots indicating relation between load, a, c, and SIF

Grahic Jump Location
Fig. 8

Flowchart to build SM for SIF prediction

Grahic Jump Location
Fig. 9

Comparison of SIF values obtained from ANSYS, BS7910, and different SMs

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In