Ph.D. Thesis Defense

By

Turab Zaidi

(Advisor: Prof. Dimitri N. Mavris)

9:00 AM, Tuesday, June 21, 2016

Weber Space Science and Technology Building (SST-II)

Collaborative Visualization Environment (CoVE)

A Methodology for Probabilistic Aircraft Technology Assessment and Selection
Under Uncertainty

ABSTRACT:

The high degree of complexity and uncertainty associated with aerospace engineering applications has driven designers and engineers towards the use of probabilistic and statistical analysis tools in order to understand and design for that uncertainty. As a result, probabilistic and statistical methods have permeated the aerospace field to the extent that single point deterministic designs are no longer credible, particularly in systems analysis, performance assessment, technology impact quantification, etc. However as probability and statistics theory are not the primary focus of most aerospace practitioners, incorrect assumptions and flawed methods are often unknowingly used in design.

A common assumption of many probabilistic assessments in the field of aerospace is the independence of random variables. The justification for the assumed independence is usually not discussed in the literature even though this can have a substantial effect on probabilistic assessment and uncertainty quantification results. Probabilistic assessments yield large amounts of data which is not effectively used due to the sheer volume of data and poor traceability of the drivers of uncertainty. The literature shows optimization techniques are resorted to in order to select from competing alternatives in multi-objective spaces, however, these techniques generally do not handle uncertainty well. The motivating question is How can improvements be made to the probabilistic assessment process for aircraft technology assessments that capture technology impact tradeoffs and dependencies, and ultimately enable decision makers to make an axiomatic and rational selection under uncertainty?

Copula theory is suggested to address the problem of assumed independence on the input side of probabilistic assessments in aerospace applications. Copulas are functions that can be used to define probabilistic relationships between random variables. They are well documented in the literature and have been used in many fields such as the statistics, finance, and insurance industries. Utility theory is proposed as a solution to the challenge of effectively using output data from probabilistic assessments to make decisions under uncertainty. Utility theory is a powerful tool used in economics, marketing, psychiatry, etc., to express preferences among competing alternatives. The key contributions of this research are (1) an Archimedean copula selection tree enabling practitioners to rapidly translate their qualitative  understanding of dependence into copula families that match it (2) estimation of the quantified effect of using copulas to capture probabilistic dependence in three representative aerospace applications (3) an expected utility formulation for axiomatically ranking and selecting aircraft technology packages under uncertainty and (4) a strategic elicitation procedure for multi-attribute utility functions that does not need assumptions of independence conditions on preferences between the attributes.

Committee Members: Dr. Dimitri Mavris, Dr. Hernando Jimenez, Dr. Daniel Schrage, Dr. Graeme Kennedy, and Dr. Roger Cooke (TU Delft, Dept of Mathematics)