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Research Papers: Structures and Safety Reliability

# Experimental Validation of the Adaptive Gaussian Process Regression Model Used for Prediction of Stress Intensity Factor as an Alternative to Finite Element Method

[+] 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

SGT, Inc.,
NASA Ames Research Center,
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 July 21, 2017; final manuscript received August 23, 2018; published online October 18, 2018. Assoc. Editor: Myung Hyun Kim.

J. Offshore Mech. Arct. Eng 141(2), 021606 (Oct 18, 2018) (11 pages) Paper No: OMAE-17-1120; doi: 10.1115/1.4041457 History: Received July 21, 2017; Revised August 23, 2018

## Abstract

Currently, in the oil and gas industry, finite element method (FEM)-based commercial software (such as ANSYS and abaqus) is commonly employed for determining the stress intensity factor (SIF). In their earlier work, the authors proposed an adaptive Gaussian process regression model (AGPRM) for the SIF prediction of a crack propagating in topside piping, as an inexpensive alternative to FEM. This paper is the continuation of the earlier work, as it focuses on the experimental validation of the proposed AGPRM. For validation purposes, the values of SIF obtained from experiments available in the literature are used. The experimental validation of AGPRM also consists of the comparison of the prediction accuracy of AGPRM and FEM relative to the experimentally derived SIF values. Five metrics, namely, root-mean-square error (RMSE), average absolute error (AAE), mean absolute percentage error (MAPE), maximum absolute error (MAE), and coefficient of determination ($R2$), are used to compare the accuracy. A case study illustrating the development and experimental validation of the AGPRM is presented. Results indicate that the prediction accuracy of AGPRM is comparable with and even higher than FEM, provided the training points of AGPRM are chosen aptly. Good prediction accuracy coupled with less time consumption favors AGPRM as an alternative to FEM for SIF prediction.

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## References

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.
Det Norske Veritas (DNV), 2010, “ Risk Based Inspection of Offshore Topsides Static Mechanical Equipment,” DNV aS, Høvik, Norway, Standard No. DNV-RP-G101.
Energy Institute (EI), 2007, Guidelines for the Avoidance of Vibration Induced Fatigue Failure in Process Pipework, The Energy Institute, London.
Keprate, A. , and Ratnayake, R. M. C. , 2017, “ Generic Approach for Risk Assessment of Offshore Piping Subjected to Vibration Induced Fatigue,” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B, 4(2), p. 021006.
Naess, A. A. , 2009, Fatigue Handbook: Offshore Steel Structures, Tapir Publisher, Trondheim, Norway, Chap. 3.
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.
Keprate, A. , Ratnayake, R. M. C. , and Sankararaman, S. , 2017, “ Comparison of Various Surrogate Models to Predict Stress Intensity Factor of a Crack Propagating in Offshore Piping,” ASME J. Offshore Mech. Arct., 139(6).
McFarland, J. M. , 2008, “ Uncertainty Analysis for Computer Simulations Through Validation and Calibration,” Ph.D. dissertation, Vanderbilt University, Nashville, TN.
Sankararaman, S. , 2012, “ Uncertainty Quantification and Integration in Engineering Systems,” Ph.D. dissertation, Vanderbilt University, Nashville, TN.
Tamimi, A. A. , 2014, “ Improved Probabilistic Life Estimation in Engineering Structures. Modelling Multi-Site Fatigue Cracking,” Ph.D. dissertation, University of Maryland, College Park, MD.
Newman, J. C. , and Raju, I. S. , 1981, “ An Empirical Stress Intensity Factory Equation for the Surface Crack,” Eng. Fract. Mech., 15(1–2), pp. 185–192.
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.

## Figures

Fig. 2

Schematic of the sample used in the experiment (dimensions in mm). Adapted from Ref. [10].

Fig. 3

Crack geometry induced in the samples. Adapted from Ref. [10].

Fig. 1

Flowchart used for development and validation of AGPRM

Fig. 5

SIF prediction using experiment, ANSYS, and GPRM for validation Set 1

Fig. 6

SIF prediction using experiment, ANSYS, and GPRM for validation Set 2

Fig. 7

SIF prediction using experiment, ANSYS, and GPRM for validation Set 3

Fig. 8

SIF prediction using experiment, ANSYS, and GPRM for validation Set 4

Fig. 4

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

Fig. 9

Graph showing relationship between the maximum variance (of validation data set 4) and the AGPRM version

Fig. 10

Graph showing relationship between the RMSE (of validation data set 4) and the AGPRM version

Fig. 11

SIF prediction using experiment, ANSYS, GPRM, and AGPRM for validation Set 4

## Errata

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