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Completed TRL 4 (started at 2, targeting 4)
Project Objective
To address continuous and discrete variables in the concept of operations (CONOPS) and logistics problem spaces present in the model, optimization, and synthesis of space exploration campaign (SEC) architectures.
Project Description
Space exploration campaigns (SECs) are a multi-element system-of-systems (SoS). The individual elements within the campaign need to be orchestrated to meet all needs, goals, and objectives in a technically feasible and programmatically viable manner. Given the intractable number of possible alternatives, exploring a meaningful subset of the tradespace for downselection to a handful of recommended alternatives remains a difficult challenge for the Agency. To advance the Agency’s SEC architecting efficiency and enable data-driven decision making, a digitally integrated testbed that leverages mature digital technologies is necessary to synthesize technically feasible SECs. The purpose of a Digitally Integrated Exploration Campaign Architecture Synthesis Testbed (DIECAST) is to rigorously evaluate SEC alternatives for Pre-Phase A activities.
The synthesis of technically feasible SECs uses an optimization process to first establish feasibility by satisfying requirements and constraints and then use the remaining degrees of freedom to improve the solutions’ desirability with respect to needs, goals, and objectives. These solutions are then assessed for programmatic viability. Generating solutions constitutes a large-scale optimization of an SoS problem, where the degrees of freedom increase exponentially with SECs that require more elements. This class of problem is very challenging, as it involves both continuous variables traditionally addressed by gradient-based optimizers as well as discrete variables in a CONOPS and logistics problem space that is known to be NP-hard. As such, modeling and optimizing this class of problem necessitates introducing mathematical methods that are not typically employed within the conceptual design of SEC architectures. These methods are then combined with the digital testbed for synthesizing SECs to improve architecture desirability. The goal of this project is to demonstrate this combined evaluation method on the nuclear thermal propulsion (NTP) architecture from the set of Mars Transit Vehicle (MTV) alternatives.
Project Results and Conclusions
Mixed Integer Programming (MIP) and Mixed Integer Nonlinear Programming (MINLP) techniques are typically used in bespoke formulations for SEC-related problems, such as space logistics. The inclusion of discrete variables and MIP/MINLP in-the-loop of sizing and synthesizing an architecture concept, especially in a generalized manner, has not been done before. Depending on the scope and level of analysis of an SEC and its elements, multiple subproblems with different sets of discrete variables can be identified. This project focused on the drop tank CONOPS of the NTP architecture, showing proof-of-concept in combining the discrete distribution, usage, and disposal of the propellant drop tanks with the nonlinear sizing and performance of the NTP element throughout its mission.
A global optimization approach was developed to model and solve this problem, which cannot solely rely on current state-of-the-art solver libraries and methods. The physics-based nonlinear problem space is highly nonlinear and not provably convex, which eliminates many of the current methods. The use case for the integer portion of the problem space does not have a common analogy in other fields that use MIP/MINLP, and there is a need to have the CONOPS modeling formulated in such a way that it can integrate with the current digital testbed for architecture sizing and synthesis. This approach splits the overarching NTP architecture synthesis problem into multiple subproblems that focus on the nonlinear sizing, the mission profile, and the drop tank operations as either continuous, MIP, or MINLP problems; a larger master problem acts to converge all three subproblems using the Augmented Lagrangian Coordination (ALC) method. Additional MIP-related techniques, such as Column Generation, were used to improve convergence for the relevant subproblems.
The stated project milestones were presentation charts on the approach, documented work, and code implementation of the developed algorithms and models for the demonstration problem. Conference and journal articles have been submitted and accepted for this work. The resulting algorithms have been used extensively in the past year to exercise the NTP architecture concept in the digital testbed for multiple purposes, including cryogenic fluid management (CFM) technology assessments and creation of data products for the Mars Architecture Team.
This effort advances the Agency’s ability to rigorously evaluate SEC alternatives for Pre-Phase A activities. SECs are highly complex SoS problems, in which the downselection of feasible alternatives for programmatic assessment is difficult mainly due to the factionalized paradigm of modeling alternatives across the Agency. DIECAST is meant to address this issue, and a key enabler of modeling SECs is capturing the discrete problem spaces that are typically excluded from the conceptual design of SEC architectures. MIP/MINLP methods were demonstrated by modeling the NTP architecture among the set of MTV alternatives, showcasing the effects of including discrete variables in the sizing and synthesis process. The effort resulted in a new formulation to model the architecture and its CONOPS, as well as a novel approach and algorithms to solve the formulated mathematical optimization problem. Continuations in this research area will extend this approach and its techniques to cover other discrete portions of the SEC problem space.
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