Confidence-based design optimization under aleatory and epistemic uncertainty

Abstract

A computational model having high credibility has been an indispensable tool to predict the behavior of engineering systems under various input conditions. Thus, the high necessity was the driving force for improving the methodologies for development, calibration, and validation of the simulation model. However, the system inherently may be surrounded by various sources of uncertainty, and the quantification and management of uncertainty and propagation to system response of interest using the computational model have been a challenge in uncertainty analysis and design optimization. Therefore, this dissertation presents a comprehensive and integrated framework to characterize and quantify two sources of uncertainty, aleatory and epistemic uncertainty, in design optimization given three types of data: input, simulation, and experimental data. Aleatory uncertainty is an objective and irreducible uncertainty arising from inherent randomness such as natural variability of the random variable, and epistemic uncertainty is a subjective and reducible uncertainty that stems from a lack of knowledge about actual values such as inaccurate probability density function (PDF) and simulation model. In this dissertation, three epistemic uncertainties that occurred in quantifying aleatory uncertainty of model parameters are individually characterized and propagated to the uncertainty of reliability. The first is the input model uncertainty associated with the unknown PDFs of observable model parameters of the system, which can be explicitly measured, such as operating conditions. The second is the surrogate model uncertainty. Since uncertainty analysis and design optimization are often unaffordable for a complex computational model, the surrogate model is frequently exploited due to its convenience. However, it cannot perfectly emulate the simulation model and causes the discrepancy called surrogate model uncertainty. The third is simulation model uncertainty, represented as uncertainty on estimations of implicit model parameters and model bias between simulation and experiment caused by insufficient experimental data. In other words, given the input, simulation, and experimental data, the proposed framework provides procedures for modeling, analysis, and design optimization encompassing aleatory and epistemic uncertainty. Mainly, since both uncertainties are fully characterized in design space, confidence-based design optimization (CBDO) can be performed to find the reliable and conservative optimum in terms of aleatory and epistemic uncertainty, respectively. Then, the model validation under aleatory and epistemic uncertainty is performed using validation data obtained from CBDO optimum. Moreover, the separation of aleatory and epistemic uncertainty in reliability analysis can clarify which uncertainty influences total uncertainty, and resource allocations to provide the guidelines on cost-effectively reducing the predictive uncertainty is available. Finally, the uncertainty in the thermoelectric generator (TEG) system is characterized and quantified to analyze the power generation from the TEG system. The uncertainty on power generation caused by two sources of uncertainty is quantified, and the design optimization accounting for each source of uncertainty is conducted through the proposed framework. Therefore, the effectiveness and necessity of the integrated framework for CBDO are successfully verified in engineering applications.