Recent advances in computing power have facilitated the use of computational simulations as design guidelines in a range of fields including the semiconductor industry, biosensors, microfluidic devices, and even nano-sized devices. Although simulation can capture the physics behind the experiment, deterministic simulations with parameters derived from least-square fitting are significantly limited for understanding output distributions from experiments. This deviation between computational simulation and experiment may arise for a number of reasons: the stochastic nature of design parameters, external environmental fluctuations, measurement noise, and so forth. These are called uncertainties. Understanding the effect of these uncertainties is important in manufacturing processes, because manufacturing processes incorporate multi-scale and multi-physics sub-steps, with uncertainties in inputs accumulated and propagated through the sub-steps, resulting in significant deviations in the performance of final products.A systematic approach to understanding the variations in the output from various uncertainty sources is called uncertainty quantification (UQ). To integrate uncertainty quantification fully into the design process, the sources of uncertainty must be identified and quantified; then, the uncertainty needs to be characterized and parameterized to create a statistical model. The parameterized statistical model is fed into a physics-based deterministic model (e.g., a finite element model) to quantify the deviations in the final products arising from the uncertainty parameters. By understanding the effect of stochastic parameters in inputs as well as manufacturing processes, computational simulations can provide more reliable design guidelines across a range of manufacturing fields. This dissertation consists of two parts. The first part describes how simulation can assist in understanding experimental results. The specific physical systems considered in this dissertation are a MEMS-based resonator (Chapter 2) and a microfluidic device (Chapter 3). The results show that simulation is a powerful tool for describing details of experimental results that cannot be explained easily due to the complexity of the systems. However, distinctive discrepancies between the results from current computational predictions and experiments still exist, especially when various uncertainties are present. Therefore, the second part of this dissertation is devoted to developing a systematic approach to modeling stochastic input variables through experimental data, and describing how this can be incorporated into a modeling framework.This dissertation suggests a systematic approach to developing a finite element model that can estimate the mechanical properties of final products with spatial uncertainties in the 3D printing process (Chapter 4), and those arising from variations in microstructure in the die-casting process (Chapter 5). Those input uncertainties are extracted from the images of final products. The data-driven modeling approach with Gaussian process is proposed to consider the probabilistic behavior of uncertainties. The realizations sampled from the calibrated Gaussian process model are incorporated into the deterministic model, generating more realistic simulation model. The systematic approach developed in this study can assist in understanding the effect of input uncertainties on the variance of the mechanical performance of final products from 3D printing and die-casting. This approach will be beneficial to other manufacturing processes where input uncertainties are important.
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