Statistical and engineering methods for model enhancement
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Models which describe the performance of physical process are essential for quality prediction, experimental planning, process control and optimization. Engineering models developed based on the underlying physics/mechanics of the process such as analytic models or finite element models are widely used to capture the deterministic trend of the process. However, there usually exists stochastic randomness in the system which may introduce the discrepancy between physics-based model predictions and observations in reality. Alternatively, statistical models can be used to develop models to obtain predictions purely based on the data generated from the process. However, such models tend to perform poorly when predictions are made away from the observed data points. This dissertation contributes to model enhancement research by integrating physics-based model and statistical model to mitigate the individual drawbacks and provide models with better accuracy by combining the strengths of both models. The proposed model enhancement methodologies including the following two streams: (1) data-driven enhancement approach and (2) engineering-driven enhancement approach. Through these efforts, more adequate models are obtained, which leads to better performance in system forecasting, process monitoring and decision optimization. Among different data-driven enhancement approaches, Gaussian Process (GP) model provides a powerful methodology for calibrating a physical model in the presence of model uncertainties. However, if the data contain systematic experimental errors, the GP model can lead to an unnecessarily complex adjustment of the physical model. In Chapter 2, we proposed a novel enhancement procedure, named as "Minimal Adjustment", which brings the physical model closer to the data by making minimal changes to it. This is achieved by approximating the GP model by a linear regression model and then applying a simultaneous variable selection of the model and experimental bias terms. Two real examples and simulations are presented to demonstrate the advantages of the proposed approach. Different from enhancing the model based on data-driven perspective, an alternative approach is to focus on adjusting the model by incorporating the additional domain or engineering knowledge when available. This often leads to models that are very simple and easy to interpret. The concepts of engineering-driven enhancement are carried out through two applications to demonstrate the proposed methodologies. In the first application where polymer composite quality is focused, nanoparticle dispersion has been identified as a crucial factor affecting the mechanical properties. Transmission Electron Microscopy (TEM) images are commonly used to represent nanoparticle dispersion without further quantifications on its characteristics. In Chapter 3, we developed the engineering-driven nonhomogeneous Poisson random field modeling strategy to characterize nanoparticle dispersion status of nanocomposite polymer, which quantitatively represents the nanomaterial quality presented through image data. The model parameters are estimated through the Bayesian MCMC technique to overcome the challenge of limited amount of accessible data due to the time consuming sampling schemes. The second application is to calibrate the engineering-driven force models of laser-assisted micro milling (LAMM) process statistically, which facilitates a systematic understanding and optimization of targeted processes. In Chapter 4, the force prediction interval has been derived by incorporating the variability in the runout parameters as well as the variability in the measured cutting forces. The experimental results indicate that the model predicts the cutting force profile with good accuracy using a 95% confidence interval. To conclude, this dissertation is the research drawing attention to model enhancement, which has considerable impacts on modeling, design, and optimization of various processes and systems. The fundamental methodologies of model enhancement are developed and further applied to various applications. These research activities developed engineering compliant models for adequate system predictions based on observational data with complex variable relationships and uncertainty, which facilitate process planning, monitoring, and real-time control.