Justin S. Gray

OpenMDAO: An Open Source Framework for Multidisciplinary Analysis and Optimization

This paper describes the progress made in the development of OpenMDAO, an open source framework for performing Multidisciplinary Analysis and Optimization (MDAO). NASA intends to use OpenMDAO to aid in the design of unconventional aircraft, but the general structure and methods may be applied to solve any number of engineering-related design problems. The framework currently supports data passing capabilities, and several example problems have been executed with it. Recent work has focused on enabling the creation of more complex MDAO strategies, such as collaborative optimization and surrogate modeling techniques. An example is presented that demonstrates an implementation of the surrogate model generation using Kriging surrogate models augmented with the expected improvement method.

Automatic Evaluation of Multidisciplinary Derivatives Using a Graph-Based Problem Formulation in OpenMDAO

The optimization of multidisciplinary systems with respect to large numbers of design variables is best pursued using a gradient-based optimization together with a method that efficiently evaluates coupled derivatives, such as the coupled adjoint method. However, implementing such a method in a problem with more than a few disciplines is time consuming and error prone. To address this issue, we develop an automated procedure for assembling and solving the coupled derivative equations that takes into account the disciplinary couplings using the interdisciplinary dependency graph of the problem. The coupled derivatives can be computed completely analytically, if analytic derivatives are available for all disciplines; otherwise, the coupled derivatives are computed semi-analytically. The procedure determines the disciplinary analyses execution order, detects iterative cycles, and uses this information to converge the coupled analysis, and evaluate the coupled derivatives as efficiently as possible by exploiting sparsity. Sparsity can occur at two levels within a multidisciplinary problem: between disciplines, when certain analyses do not affect all outputs, and within a discipline when, the Jacobian of that discipline is sparse. The numerical procedures are implemented in NASA’s OpenMDAO framework, providing a flexible API for declaring discipline-level derivatives that can handle sparsity within a discipline. The tool is demonstrated in two MDO problems: the design of a small satellite and its operation with the objective of maximizing downloaded data to a ground station, and the design of a horizontal-axis wind turbine with the objective of minimizing the cost of energy. In both cases, the method demonstrated improved efficiency by taking advantage of analytic gradients considering sparsity. This new capability in OpenMDAO greatly facilitates the implementation of system-level direct and adjoint coupled derivative evaluations, and is applicable for general problems.

Standard Platform for Benchmarking Multidisciplinary Design Analysis and Optimization Architectures

The multidisciplinary design analysis and optimization community has developed a multitude of algorithms and techniques, called architectures, for performing optimizations on complex engineering systems that involve coupling between multiple discipline analyses. These architectures seek to efficiently handle optimizations with computationally expensive analyses including multiple disciplines. A new testing procedure is proposed that can provide a quantitative and qualitative means of comparison among architectures. The proposed test procedure is implemented within the open-source framework, OpenMDAO, and comparative results are presented for five well-known architectures: multiple design feasible, individual design feasible, collaborative optimization, bilevel integrated systems synthesis, and bilevel integrated systems synthesis 2000. How using open-source software development methods can allow the multidisciplinary design analysis and optimization community to submit new problems and architectures to ke...

The Development of an Open Source Framework for Multidisciplinary Analysis and Optimization

This paper presents the motivation for the development of an open source framework for performing Multidisciplinary Analysis and Optimization (MDAO) to aid in the design of unconventional aircraft. While a number of frameworks already exist, critical and desirable requirements are still not satisfactorily met. For developing a new framework, an open source development is the most logical choice, in particular because it provides the means to rapidly develop a community of users who can also contribute enhancements, components, and knowledge to the framework. Presently, the framework development project has finished the requirements gathering stage and has begun prototyping some of the capability in the cross-platform scripting language Python, which already provides many of the basic building blocks needed to create an MDAO framework.

A modular adjoint approach to aircraft mission analysis and optimization

Aircraft design and trajectory optimization are typically performed sequentially, which can lead to suboptimal results. To address this, we develop a new mission analysis and trajectory optimization tool that is efficient, robust, and modular. This enables large-scale optimization in problems involving trajectory and other disciplines. The most important feature that sets this tool apart from existing mission analysis software is the use of a computational framework to provide benefits in efficiency and modularity. Through different test cases, we are able to demonstrate the efficiency and the robustness of the developed approach. The generated mission analysis results match well with data from other tools. Runge oscillations are evident in trajectory optimization cases with insufficient number of altitude design variables. Therefore, we provide a relation between the minimum number of altitude design variables needed and the range of the mission for avoiding these oscillations efficiently.

Open-Source Conceptual Sizing Models for the Hyperloop Passenger Pod

Hyperloop is a new mode of transportation proposed as an alternative to Californias high speed rail project, with the intended benefits of higher performance at lower overall costs. It consists of a passenger pod traveling through a tube under a light vacuum and suspended on air bearings. The pod travels up to transonic speeds resulting in a 35 minute travel time between the intended route from Los Angeles and San Francisco. Of the two variants outlined, the smaller system includes a 1.1 meter tall passenger capsule traveling through a 2.2 meter tube at 700 miles per hour. The passenger pod features water-based heat exchangers as well as an on-board compression system that reduces the aerodynamic drag as it moves through the tube. Although the original proposal looks very promising, it assumes that tube and pod dimensions are independently sizable without fully acknowledging the constraints of the compressor system on the pod geometry. This work focuses on the aerodynamic and thermodynamic interactions between the two largest systems; the tube and the pod. Using open-source toolsets, a new sizing method is developed based on one-dimensional thermodynamic relationships that accounts for the strong interactions between these sub-systems. These additional considerations require a tube nearly twice the size originally considered and limit the maximum pod travel speed to about 620 miles per hour. Although the results indicate that Hyperloop will need to be larger and slightly slower than originally intended, the estimated travel time only increases by approximately five minutes, so the overall performance is not dramatically affected. In addition, the proposed on-board heat exchanger is not an ideal solution to achieve reasonable equilibrium air temperatures within the tube. Removal of this subsystem represents a potential reduction in weight, energy requirements and complexity of the pod. In light of these finding, the core concept still remains a compelling possibility, although additional engineering and economic analyses are markedly necessary before a more complete design can be developed.

Design Optimization of a Variable-Speed Power Turbine

NASAs Rotary Wing Project is investigating technologies that will enable the development of revolutionary civil tilt rotor aircraft. Previous studies have shown that for large tilt rotor aircraft to be viable, the rotor speeds need to be slowed significantly during the cruise portion of the flight. This requirement to slow the rotors during cruise presents an interesting challenge to the propulsion system designer as efficient engine performance must be achieved at two drastically different operating conditions. One potential solution to this challenge is to use a transmission with multiple gear ratios and shift to the appropriate ratio during flight. This solution will require a large transmission that is likely to be maintenance intensive and will require a complex shifting procedure to maintain power to the rotors at all times. An alternative solution is to use a fixed gear ratio transmission and require the power turbine to operate efficiently over the entire speed range. This concept is referred to as a variable-speed power-turbine (VSPT) and is the focus of the current study. This paper explores the design of a variable speed power turbine for civil tilt rotor applications using design optimization techniques applied to NASAs new meanline tool, the Object-Oriented Turbomachinery Analysis Code (OTAC).

Trajectory Optimization of Electric Aircraft Subject to Subsystem Thermal Constraints

Electric aircraft pose a unique design challenge in that they lack a simple way to reject waste heat from the power train. While conventional aircraft reject most of their excess heat in the exhaust stream, for electric aircraft this is not an option. To examine the implications of this challenge on electric aircraft design and performance, we developed a model of the electric subsystems for the NASA X-57 electric testbed aircraft. We then coupled this model with a model of simple 2D aircraft dynamics and used a Legendre-GaussLobatto collocation optimal control approach to find optimal trajectories for the aircraft with and without thermal constraints. The results show that the X-57 heat rejection systems are well designed for maximum-range and maximum-efficiency flight, without the need to deviate from an optimal trajectory. Stressing the thermal constraints by reducing the cooling capacity or requiring faster flight has a minimal impact on performance, as the trajectory optimization technique is able to find flight paths which honor the thermal constraints with relatively minor deviations from the nominal optimal trajectory.

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.