Multidisciplinary design optimization (MDO) is concerned with solving design problems involving coupled numerical models of complex engineering systems. While various MDO software frameworks exist, none of them take full advantage of state-of-the-art algorithms to solve coupled models efficiently. Furthermore, there is a need to facilitate the computation of the derivatives of these coupled models for use with gradient-based optimization algorithms to enable design with respect to large numbers of variables. In this paper, we present the theory and architecture of OpenMDAO, an open-source MDO framework that uses Newton-type algorithms to solve coupled systems and exploits problem structure through new hierarchical strategies to achieve high computational efficiency. OpenMDAO also provides a framework for computing coupled derivatives efficiently and in a way that exploits problem sparsity. We demonstrate the framework's efficiency by benchmarking scalable test problems. We also summarize a number of OpenMDAO applications previously reported in the literature, which include trajectory optimization, wing design, and structural topology optimization, demonstrating that the framework is effective in both coupling existing models and developing new multidisciplinary models from the ground up. Given the potential of the OpenMDAO framework, we expect the number of users and developers to continue growing, enabling even more diverse applications in engineering analysis and design.

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.

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.

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Aircraft design optimization and airline allocation problems are two separate and wellresearched disciplines, but very little literature exists that solved the design and allocation problems simultaneously. Among the limited number of related efforts that combine them, most follow a sequential decomposition strategy. This sequential strategy has been successful in addressing the combined large-scale problem but the approach does not capture the coupling that exists between the aircraft design and airline allocation disciplines. Solving the aircraft design and airline allocation as a monolithic problem makes it a Mixed Integer Non-Linear Programming problem which is very difficult to solve for large numbers of integer variables. Because no existing generalized MINLP solver can address this problem, this work proposes a new algorithm combining branch and bound, Efficient Global Optimization, Kriging Partial Least Squares, and gradient-based optimization to solve MINLP problems with 100's of integer design variables, 1000's of continuous design variables. The algorithm was applied to an 8 route coupled aircraft design and allocation problem with the 19 allocation variables and solving a 6000 variable aircraft design optimization problem using an Euler CFD simulation. This test problem provides several key challenges for a MINLP problem: a moderate integer design space, a large continuous design space, and expensive analysis models.

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.

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. I

An introduction is given to a new rotating wheelspace test vehicle known as the GE Hot Gas Ingestion Rig (HGIR). This scaled 1.5 stage turbine rig is configured similar to a current generation heavy duty gas turbine. It has a broad spectrum of measurement capability, including radial and circumferential ports for CO2 measurements that are used to measure the sealing effectiveness from candidate rim seal geometries. Engine-matched conditions are presented in a non-dimensional form that demonstrate the value of this fully capable test facility, including static pressure signatures at stage 1 nozzle exit, exit Reynolds number, exit Mach number and rotational Reynolds number. This paper also provides details of the operating conditions and assessment of a thermal steady-state condition achieved consistently throughout each test. Part I of this two-part paper focuses on the geometric details of this new state-of-the-art wheelspace rig, the measurement capabilities currently available and planned, and the results from the baseline geometry. The test data from this test vehicle are used to validate reduced order models, including unsteady CFD models. Details of the CFD modeling and validation are presented in the Part II paper Ding et al. [1]. Measurement uncertainties for all key parameters as well as the repeatability of the test rig to reproduce test conditions are presented to demonstrate the rigor taken in the design and operation of this testing facility.