A multi-fidelity analysis selection method using a constrained discrete optimization formulation.

摘要

The purpose of this research is to develop a method for selecting the fidelity of contributing analyses in computer simulations. Model uncertainty is a significant component of result validity, yet it is neglected in most conceptual design studies. When it is considered, it is done so in only a limited fashion, and therefore brings the validity of selections made based on these results into question. Neglecting model uncertainty can potentially cause costly redesigns of concepts later in the design process or can even cause program cancellation. Rather than neglecting it, if one were to instead not only realize the model uncertainty in tools being used but also use this information to select the tools for a contributing analysis, studies could be conducted more efficiently and trust in results could be quantified. Methods for performing this are generally not rigorous or traceable, and in many cases the improvement and additional time spent performing enhanced calculations are washed out by less accurate calculations performed downstream. The intent of this research is to resolve this issue by providing a method which will minimize the amount of time spent conducting computer simulations while meeting accuracy and concept resolution requirements for results.;In many conceptual design programs, only limited data is available for quantifying model uncertainty. Because of this data sparsity, traditional probabilistic means for quantifying uncertainty should be reconsidered. This research proposes to instead quantify model uncertainty using an evidence theory formulation (also referred to as Dempster-Shafer theory) in lieu of the traditional probabilistic approach. Specific weaknesses in using evidence theory for quantifying model uncertainty are identified and addressed for the purposes of the Fidelity Selection Problem. A series of experiments was conducted to address these weaknesses using n-dimensional optimization test functions. These experiments found that model uncertainty present in analyses with 4 or fewer input variables could be effectively quantified using a strategic distribution creation method; if more than 4 input variables exist, a Frontier Finding Particle Swarm Optimization should instead be used.;Once model uncertainty in contributing analysis code choices has been quantified, a selection method is required to determine which of these choices should be used in simulations. Because much of the selection done for engineering problems is driven by the physics of the problem, these are poor candidate problems for testing the true fitness of a candidate selection method. Specifically moderate and high dimensional problems' variability can often be reduced to only a few dimensions and scalability often cannot be easily addressed. For these reasons a simple academic function was created for the uncertainty quantification, and a canonical form of the Fidelity Selection Problem (FSP) was created. Fifteen best- and worst-case scenarios were identified in an effort to challenge the candidate selection methods both with respect to the characteristics of the tradeoff between time cost and model uncertainty and with respect to the stringency of the constraints and problem dimensionality. The results from this experiment show that a Genetic Algorithm (GA) was able to consistently find the correct answer, but under certain circumstances, a discrete form of Particle Swarm Optimization (PSO) was able to find the correct answer more quickly. To better illustrate how the uncertainty quantification and discrete optimization might be conducted for a "real world" problem, an illustrative example was conducted using gas turbine engines.