带输入位置误差的高斯过程及其在复合材料零件装配过程中的应用
Gaussian Processes with Input Location Error and Applications to the Composite Parts Assembly Process
摘要：
在本文中，我们研究了输入位置误差的高斯过程建模，其中输入被噪声破坏。在这里，最好的线性无偏预测器的两种情况下，根据是否有噪声的目标未观察到的位置。我们表明，均方预测误差收敛到一个非零常数，如果有噪声的目标未观察到的位置，并提供了一个上界的均方预测误差，如果没有噪声的目标未观察到的位置。我们研究了随机克里格法在具有输入位置误差的高斯过程预测中的应用，并表明当样本量较大时，随机克里格法是一个很好的近似。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。
英文摘要：
In this paper, we investigate Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, the best linear unbiased predictor for two cases is considered, according to whether there is noise at the target unobserved location or not. We show that the mean squared prediction error converges to a non-zero constant if there is noise at the target unobserved location, and provide an upper bound of the mean squared prediction error if there is no noise at the target unobserved location. 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.
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