An Optimization-Based Approach to Determine Requirements and Aircraft Design under Multi-domain Uncertainties

Parithi Govindaraju, Purdue University


Determining the optimal requirements for and design variable values of new systems, which operate along with existing systems to provide a set of overarching capabilities, as a single task is challenging due to the highly interconnected effects that setting requirements on a new system's design can have on how an operator uses this newly designed system. This task of determining the requirements and the design variable values becomes even more difficult because of the presence of uncertainties in the new system design and in the operational environment. This research proposed and investigated aspects of a framework that generates optimum design requirements of new, yet-to-be-designed systems that, when operating alongside other systems, will optimize fleet-level objectives while considering the effects of various uncertainties. Specifically, this research effort addresses the issues of uncertainty in the design of the new system through reliability-based design optimization methods, and uncertainty in the operations of the fleet through descriptive sampling methods and robust optimization formulations. In this context, fleet-level performance metrics result from using the new system alongside other systems to accomplish an overarching objective or mission. This approach treats the design requirements of a new system as decision variables in an optimization problem formulation that a user in the position of making an acquisition decision could solve. This solution would indicate the best new system requirements–and an associated description of the best possible design variable variables for that new system–to optimize the fleet level performance metric(s). Using a problem motivated by recorded operations of the United States Air Force Air Mobility Command for illustration, the approach is demonstrated first for a simplified problem that only considers demand uncertainties in the service network and the proposed methodology is used to identify the optimal design requirements and optimal aircraft sizing variables of new, yet-to-be-introduced aircraft. With this new aircraft serving alongside other existing aircraft, the fleet of aircraft satisfy the desired demand for cargo transportation, while maximizing fleet productivity and minimizing fuel consumption via a multi-objective problem formulation. The approach is then extended to handle uncertainties in both the design of the new system and in the operations of the fleet. The propagation of uncertainties associated with the conceptual design of the new aircraft to the uncertainties associated with the subsequent operations of the new and existing aircraft in the fleet presents some unique challenges. A computationally tractable hybrid robust counterpart formulation efficiently handles the confluence of the two types of domain-specific uncertainties. This hybrid formulation is tested on a larger route network problem to demonstrate the scalability of the approach. Following the presentation of the results obtained, a summary discussion indicates how decision-makers might use these results to set requirements for new aircraft that meet operational needs while balancing the environmental impact of the fleet with fleet-level performance. Comparing the solutions from the uncertainty-based and deterministic formulations via a posteriori analysis demonstrates the efficacy of the robust and reliability-based optimization formulations in addressing the different domain-specific uncertainties. Results suggest that the aircraft design requirements and design description determined through the hybrid robust counterpart formulation approach differ from solutions obtained from the simplistic deterministic approach, and leads to greater fleet-level fuel savings, when subjected to real-world uncertain scenarios (more robust to uncertainty). The research, though applied to a specific air cargo application, is technically agnostic in nature and can be applied to other facets of policy and acquisition management, to explore capability trade spaces for different vehicle systems, mitigate risks, define policy and potentially generate better returns on investment. Other domains relevant to policy and acquisition decisions could utilize the problem formulation and solution approach proposed in this dissertation provided that the problem can be split into a non-linear programming problem to describe the new system sizing and the fleet operations problem can be posed as a linear/integer programming problem.




CROSSLEY, Purdue University.

Subject Area

Aerospace engineering|Operations research

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