Bayesian hierarchical model for combining misaligned two-resolution metrology data

Abstract

This article presents a Bayesian hierarchical model to combine misaligned two-resolution metrology data for inspecting the geometric quality of manufactured parts. High-resolution data points are scarce and scatter over the surface being measured, while low-resolution data are pervasive but less accurate and less precise. Combining the two datasets should produce better predictions than using a single dataset. One challenge in combining them is the misalignment existing between data from different resolutions. This article attempts to address this issue and make improved predictions. The proposed method improves on the methods of using a single dataset or a combined prediction that does not address the misalignment problem. Improvements of 24% to 74% are demonstrated both for simulated data of circles and datasets obtained for a milled sinewave surface measured by two coordinate measuring machines of different resolutions.

Review of the mathematical foundations of data fusion techniques in surface metrology

“…Thus, fusion of x, y and z data can be reduced down to fusion of z data only. Typical point cloud fusion algorithms include hierarchical Gaussian process fusion and its derivatives [59][60][61][62][63]. These Gaussian process-based fusion methods approximate the residuals between two reliability-differentiated datasets using Gaussian process models.…”

“…Denoising as a pre-process is optional because many registration [48] and fusion [62] processes are insensitive to noise. In some fusion methods, denoising is included in the fusion process, such as in Gaussian process fusion [63].…”

“…A typical RA-based fusion method is Gaussian process (GP) fusion, which links two datasets by approximating their residuals as a GP function [59,61,62]. GP approximation is a non-parametric fitting method [66].…”

“…For example, in references [60,62,63], Gaussian process-based surface fitting techniques are used to approximate the residuals between each pair of input datasets. Other fitting techniques, such as B-spline wavelets-based [89,90] surface approximation techniques, may also provide good fusion results.…”

Reduction of calibration effort in FEM-based optimization via numerical and experimental data fusion

“…A different class of hierarchical models can be defined, that take into account the potential variability or uncertainty of the response, as in (Xia et al, 2011), where a hierarchical Bayesian model is implemented. These models have been more recently and therefore less frequently applied and they are suited not just for merging the results of Hi-Fi and Lo-Fi simulations, but for the fusion of computer experiments and physical experiments.…”