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Description:
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This dissertation presents a Bayesian hierarchical model to combine two -resolution
metrology data for inspecting the geometric quality of manufactured parts . The high -
resolution data points are scarce , and thus scatter over the surface being measured ,
while the low -resolution data are pervasive , but less accurate or less precise . Combining the two datasets could supposedly make a better prediction of the geometric
surface of a manufactured part than using a single dataset . One challenge in combining the metrology datasets is the misalignment which exists between the low - and
high -resolution data points .
This dissertation attempts to provide a Bayesian hierarchical model that can
handle such misaligned datasets , and includes the following components : (a ) a Gaussian process for modeling metrology data at the low -resolution level ; (b ) a heuristic
matching and alignment method that produces a pool of candidate matches and
transformations between the two datasets ; (c ) a linkage model , conditioned on a
given match and its associated transformation , that connects a high -resolution data
point to a set of low -resolution data points in its neighborhood and makes a combined
prediction ; and finally (d ) Bayesian model averaging of the predictive models in (c )
over the pool of candidate matches found in (b ) . This Bayesian model averaging
procedure assigns weights to different matches according to how much they support
the observed data , and then produces the final combined prediction of the surface based on the data of both resolutions .
The proposed method improves upon the methods of using a single dataset as
well as a combined prediction without addressing the misalignment problem . This
dissertation demonstrates the improvements over alternative methods using both simulated data and the datasets from a milled sine -wave part , measured by two coordinate
measuring machines of different resolutions , respectively . |