Gaussian Processes with Input Location Error and Applications to the Composite Parts Assembly Process

TL;DR

This paper studies Gaussian process prediction when input locations are noisy, analyzing the effects on prediction error and evaluating stochastic Kriging's effectiveness, with applications to composite parts assembly.

Contribution

It introduces analysis of Gaussian process prediction with input location error and assesses stochastic Kriging as an approximation method.

Findings

Prediction error converges to a non-zero constant with input noise.

Stochastic Kriging approximates Gaussian process prediction well with large samples.

Case study demonstrates practical application in composite parts assembly.

Abstract

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.