Large-Scale Multidisciplinary Optimization of a Small Satellite’s Design and Operation

Abstract

The design of satellites and their operation is a complex task that involves a large number of variables and multiple engineering disciplines. Thus, it could benefit from the application of multidisciplinary design optimization, but previous efforts have been hindered by the complexity of the modeling and implementation, discontinuities in the design space, and the wide range of time scales. We address these issues by applying a new mathematical framework for gradient-based multidisciplinary optimization that automatically computes the coupled derivatives of the multidisciplinary system via a generalized form of the adjoint method. The modeled disciplines are orbit dynamics, attitude dynamics, cell illumination, temperature, solar power, energy storage, and communication. Many of these disciplines include functions with discontinuities and nonsmooth regions that are addressed to enable a numerically exact computation of the derivatives for all of the modeled variables. The wide-ranging time scales in the design problem, spanning 30 s to one year, are captured through a combination of multipoint optimization and the use of a small time step in the analyses. Optimizations involving over 25,000 design variables and 2.2 million state variables require 100 h to converge three and five orders of magnitude in optimality and feasibility, respectively. The results show that the geometric design variables yield a 40% improvement in the total data downloaded, which is the objective function, and the operational design variables yield another 40% improvement. This demonstrates not only the value in this approach for the design of satellites and their operation, but also promise for its application to the design of other large-scale engineering systems.

A modular adjoint approach to aircraft mission analysis and optimization

“…We then provide the numerical background of the prototype framework in the Numerical Framework subsection, and describe the implementation of the proposed nonlinear system of equations within the framework. Much of the core of the prototype framework developed by Hwang and Martins [20] has been implemented in the NASA OpenMDAO framework. The mission analysis tool has been incorporated into the OpenMDAO framework upon successful development and implementation within our prototype framework.…”

“…The second subsystem uses these inputs to generate B-spline interpolants, which allow us to reduce the number of input variables (which are design variables during optimization) while maintaining the accuracy of the collocation method. The B-spline implementation is similar to the approach taken by Hwang et al for a small satellite design optimization problem [20]. The third subsystem takes the parameterized input profiles, and computes the corresponding flight conditions at each collocation point explicitly.…”

Implementation of topology optimization using openMDAO

“…OpenMDAO is open-source and is written in Python, which is a language known for its ease of interfacing to compiled languages such as C++ and Fortran. OpenMDAO has been used to solve MDO problems in satellite design [15], wind turbine design [14], aircraft design [16], and aircraft trajectory optimization [17].…”

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

“…Hwang et al 15 developed an alternative, graph-free method for computing automatic system level sensitivities that used a global design variable vector. Their method addressed the scalability challenges with Moore's work by using a matrix-free approach with components providing partial derivatives via a linear operator.…”