Research Papers

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

[+] Author and Article Information
Yongxiang Hu

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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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. 7

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

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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. 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. 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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