Gaussian Processes with Input Location Error and Applications to the Composite Parts Assembly Process
Gaussian Processes with Input Location Error and Applications to the Composite Parts Assembly Process
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DOI：
10.1137/20m1312447
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Wenjia Wang;Xiaowei Yue;Ben Haaland;C. F. Wu
中科院分区：
文献类型：
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作者：
Wenjia Wang;Xiaowei Yue;Ben Haaland;C. F. Wu
本文研究了具有输入位置误差的高斯过程回归问题，其中输入被噪声污染。在这里，我们考虑两种情况下的最佳线性无偏预测，根据是否有噪声在目标未尝试的位置或没有。我们表明，均方预测误差不收敛到零，在任何情况下。我们调查使用随机克里格在高斯过程的输入位置误差的预测，并表明，随机克里格是一个很好的近似时，样本量很大。给出了几个数值例子来说明结果，并提出了一个案例研究的复合材料零件的装配。技术证明见附录。
In this paper, we investigate Gaussian process regression with input location error, where the inputs are corrupted by noise. Here, we consider the best linear unbiased predictor for two cases, according to whether there is noise at the target untried location or not. We show that the mean squared prediction error does not converge to zero in either case. We investigate the use of stochastic Kriging in the prediction of Gaussian processes with input location error, and show that stochastic Kriging is a good approximation when the sample size is large. Several numeric examples are given to illustrate the results, and a case study on the assembly of composite parts is presented. Technical proofs are provided in the Appendix.