Identifying nonlinear variaiton patterns in multivariate manufacturing processes
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This dissertation develops a set of nonlinear variation pattern identification methods that are intended to aid in diagnosing the root causes of product variability in complex manufacturing processes, in which large amounts of high dimensional in-process measurement data are collected for quality control purposes. First, a nonlinear variation pattern model is presented to generically represent a single nonlinear variation pattern that results from a single underlying root cause, the nature of which is unknown a priori. We propose a modified version of a principal curve estimation algorithm for identifying the variation pattern. Principal curve analysis is a nonlinear generalization of principal components analysis (PCA) that lends itself well to interpretation and also has theoretically rich underpinnings. The principal curve modification involves a dimensionality reduction step that is intended to improve estimation accuracy by reducing noise and improving the robustness of the algorithm with the high-dimensional data typically encountered in manufacturing. An effective visualization technique is also developed to help interpret the identified nonlinear variation pattern and aid in root cause identification and elimination. To further improve estimation robustness and accuracy and reduce computational expense, we propose a local PCA based polygonal line algorithm to identify the nonlinear patterns. We also develop an approach for separating and identifying the effects of multiple nonlinear variation patterns that are present simultaneously in the measurement data. This approach utilizes higher order cumulants and pairwise distance based clustering to separate the patterns and borrows from techniques that are used in linear blind source separation. With the groundwork laid for a versatile flexible and powerful nonlinear variation pattern modeling and identification framework, applications in autobody assembly and stamping processes are investigated. The pattern identification algorithms, together with the proposed visualization approach, provides an effective tool to aid in understanding the nature of the root causes of variation that affect a manufacturing process.
Zhang, Feng (2004). Identifying nonlinear variaiton patterns in multivariate manufacturing processes. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from