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Research Papers

Predictive Modeling and Uncertainty Quantification of Laser Shock Processing by Bayesian Gaussian Processes With Multiple Outputs

[+] Author and Article Information
Yongxiang Hu

Mem. ASME
State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: huyx@sjtu.edu.cn

Zhi Li

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: reborn@sjtu.edu.cn

Kangmei Li

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: lkm718@sjtu.edu.cn

Zhenqiang Yao

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zqyao@sjtu.edu.cn

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received October 3, 2013; final manuscript received April 18, 2014; published online May 21, 2014. Assoc. Editor: Y. B. Guo.

J. Manuf. Sci. Eng 136(4), 041014 (May 21, 2014) (10 pages) Paper No: MANU-13-1360; doi: 10.1115/1.4027539 History: Received October 03, 2013; Revised April 18, 2014

Accurate numerical modeling of laser shock processing, a typical complex physical process, is very difficult because several input parameters in the model are uncertain in a range. And numerical simulation of this high dynamic process is very computational expensive. The Bayesian Gaussian process method dealing with multivariate output is introduced to overcome these difficulties by constructing a predictive model. Experiments are performed to collect the physical data of shock indentation profiles by varying laser power densities and spot sizes. A two-dimensional finite element model combined with an analytical shock pressure model is constructed to obtain the data from numerical simulation. By combining observations from experiments and numerical simulation of laser shock process, Bayesian inference for the Gaussian model is completed by sampling from the posterior distribution using Morkov chain Monte Carlo. Sensitivities of input parameters are analyzed by the hyperparameters of Gaussian process model to understand their relative importance. The calibration of uncertain parameters is provided with posterior distributions to obtain concentration of values. The constructed predictive model can be computed efficiently to provide an accurate prediction with uncertainty quantification for indentation profile by comparing with experimental data.

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References

Ye, C., Liao, Y., and Cheng, G. J., 2010, “Warm Laser Shock Peening Driven Nanostructures and Their Effects on Fatigue Performance in Aluminum Alloy 6160,” Adv. Eng. Mater., 12(4), pp. 291–297. [CrossRef]
Hu, Y. X., Xu, X. X., Yao, Z. Q., and Hu, J., 2010, “Laser Peen Forming Induced Two Way Bending of Thin Sheet Metals and Its Mechanisms,” J. Appl. Phys., 108(7), p. 073117. [CrossRef]
Huang, S., Zhou, J. Z., Sheng, J., Lu, J. Z., Sun, G. F., Meng, X. K., Zuo, L. D., Ruan, H. Y., and Chen, H. S., 2013, “Effects of Laser Energy on Fatigue Crack Growth Properties of 6061-T6 Aluminum Alloy Subjected to Multiple Laser Peening,” Eng. Fract. Mech., 99, pp. 87–100. [CrossRef]
Hu, Y. X., Han, Y. F., Yao, Z. Q., and Hu, J., 2010, “Three-Dimensional Numerical Simulation and Experimental Study of Sheet Metal Bending by Laser Peen Forming,” ASME J. Manuf. Sci. Eng., 132(6), p. 061001. [CrossRef]
Bhamare, S., Ramakrishnan, G., Mannava, S. R., Langer, K., Vasudevan, V. K., and Qian, D., 2013, “Simulation-Based Optimization of Laser Shock Peening Process for Improved Bending Fatigue Life of Ti–6al–2sn–4zr–2mo Alloy,” Surf. Coat. Technol., 232, pp. 464–474. [CrossRef]
Hu, Y. X., and Yao, Z. Q., 2008, “Numerical Simulation and Experimentation of Overlapping Laser Shock Processing With Symmetry Cell,” Int. J. Mach. Tools Manuf., 48(2), pp. 152–162. [CrossRef]
Cao, Y., Zhao, X., and Shin, Y. C., 2013, “Analysis of Nanosecond Laser Ablation of Aluminum With and Without Phase Explosion in Air and Water,” J. Laser Appl., 25(3), p. 032002. [CrossRef]
Hu, Y. X., Gong, C. M., Yao, Z. Q., and Hu, J., 2009, “Investigation on the Non-Homogeneity of Residual Stress Field Induced by Laser Shock Peening,” Surf. Coat. Technol., 203(23), pp. 3503–3508. [CrossRef]
Sealy, M. P., and Guo, Y. B., 2010, “Surface Integrity and Process Mechanics of Laser Shock Peening of Novel Biodegradable Magnesium–Calcium (Mg–Ca) Alloy,” J. Mech. Behav. Biomed. Mater., 3(7), pp. 488–496. [CrossRef]
Park, I., Amarchinta, H. K., and Grandhi, R. V., 2010, “A Bayesian Approach for Quantification of Model Uncertainty,” Reliab. Eng. Syst. Saf., 95(7), pp. 777–785. [CrossRef]
Amarchinta, H., Tarpey, T., and Grandhi, R. V., 2010, “Regression Uncertainty Quantification Using Bootstrap Method for Residual Stress Field Predictions,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, S. Mahadevan, ed., Orlando, FL, Apr. 12–15.
Kennedy, M. C., and O'Hagan, A., 2001, “Bayesian Calibration of Computer Models,” J. R. Stat. Soc.: Ser. B, 63(3), pp. 425–464. [CrossRef]
Bayarri, M. J., Berger, J. O., Paulo, R., Sacks, J., Cafeo, J. A., Cavendish, J., Lin, C.-H., and Tu, J., 2007, “A Framework for Validation of Computer Models,” Technometrics, 49(2), pp. 138–154. [CrossRef]
Higdon, D., Gattiker, J., Williams, B., and Rightley, M., 2008, “Computer Model Calibration Using High-Dimensional Output,” J. Am. Stat. Assoc., 103(482), pp. 570–583. [CrossRef]
Sollier, A., Berthe, L., and Fabbro, R., 2001, “Numerical Modeling of the Transmission of Breakdown Plasma Generated in Water During Laser Shock Processing,” Eur. Phys. J.: Appl. Phys., 16(2), pp. 131–139. [CrossRef]
Fabbro, R., Fournier, J., Ballard, P., Devaux, D., and Virmont, J., 1990, “Physical Study of Laser-Produced Plasma in Confined Geometry,” J. Appl. Phys., 68(2), pp. 775–784. [CrossRef]
Berthe, L., Fabbro, R., Peyre, P., Tollier, L., and Bartnicki, E., 1997, “Shock Waves From a Water-Confined Laser-Generated Plasma,” J. Appl. Phys., 82(6), pp. 2826–2832. [CrossRef]
Zhang, W., Yao, Y. L., and Noyan, I. C., 2004, “Microscale Laser Shock Peening of Thin Films, Part 1: Experiment, Modeling and Simulation,” ASME J. Manuf. Sci. Eng., 126(1), pp. 10–17. [CrossRef]
Johnson, G., and Cook, W., 1983, “A Constitutive Model and Data for Metals Subjected to Large Strains, High Srain Rates and High Temperatures,” Proceedings of the 7th International Symposium on Ballistics, M. J. M ed., The Netherlands, Apr. 19–21.
Holloway, J. P., Bingham, D., Chou, C.-C., Doss, F., Paul Drake, R., Fryxell, B., Grosskopf, M., Van Der Holst, B., Mallick, B. K., Mcclarren, R., Mukherjee, A., Nair, V., Powell, K. G., Ryu, D., Sokolov, I., Toth, G., and Zhang, Z., 2011, “Predictive Modeling of a Radiative Shock System,” Reliab. Eng. Syst. Saf., 96(9), pp. 1184–1193. [CrossRef]
Rasmussen, C. E., and Williams, C., 2006, Gaussian Processes for Machine Learning, MIT Press, Boston, MA.
Higdon, D., Kennedy, M., Cavendish, J., Cafeo, J., and Ryne, R., 2004, “Combining Field Data and Computer Simulations for Calibration and Prediction,” SIAM J. Sci. Comput., 26(2), pp. 448–466. [CrossRef]
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E., 1953, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys., 21(6), pp. 1087–1092. [CrossRef]
Robert, C., and Casella, G., 2004, Monte Carlo Statistical Methods, Springer-Verlag, New York.
Bates, R. A., Buck, R. J., Riccomagno, E., and Wynn, H. P., 1996, “Experimental Design and Observation for Large Systems,” J. R. Stat. Soc. Ser. B, 58(1), pp. 77–94. [CrossRef]
Johnson, M., Moore, L., and Ylvisaker, D., 1990, “Minimax and Maximin Distance Designs,” J. Stat. Plann. Inference26(2), pp. 131–148. [CrossRef]

Figures

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Fig. 1

Schematic of laser shock processing

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Fig. 2

Schematic of experimental setup for laser shock processing: 1-Nd:YAG laser, 2-beam splitter, 3-reflecting mirrors, 4-lens, 5-water, 6-nozzle, 7-container, 8-X/Y stage, 9-water outlet, and10-computer

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Fig. 3

Laser shock induced surface indentation and its profile measurement

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Fig. 4

Experimental observed laser shock induced indentations under different conditions of laser spot size and power density (90% confidence): (a) Indentation depth; (b) Indention cross-sectional area

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Fig. 5

Axisymmetric finite element mesh for one shock with round spot

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Fig. 6

Modeling procedure of LSP with inputs and outputs

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Fig. 10

Calibrated predictions of laser shock indentation with 90% posterior credible intervals as a function of laser power density compared with experimental observations: (a) Spot diameter DL = 1.0 mm, (b) Spot diameter DL = 1.6 mm

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Fig. 9

Posterior distributions of the five calibration parameters: five figures on the left side provide stationary Markov chains for five unknown parameters via MCMC, respectively, where the value for each parameter is standardized in the interval [0, 1]; five figures at the right side provide the posterior distribution for each parameter by sampling from stationary Markov chain outputs on the left side

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Fig. 8

Boxplots of the posterior distribution for each ρωik.: (a) ρω1k for the first output of indentation depth and (b) ρω2k for the second output of cross-sectional area. The box plots show the median (central red line), and 1st and 3rd quartiles (edges of box). The whiskers on each box show the location of the most extreme data in each direction that is within 1.5 times the interquartile range beyond the edge of the box. Outliers are then shown by red crosses.

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Fig. 7

Scatter plots of the 100 points of the input design over seven parameters (x, u) by Latin hypercube design

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