Tristan A. Hearn

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...

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.

Application of denoising methods to regularizationof ill-posed problems

Linear systems of equations and linear least-squares problems with a matrix whose singular values “cluster” at the origin and with an error-contaminated data vector arise in many applications. Their numerical solution requires regularization, i.e., the replacement of the given problem by a nearby one, whose solution is less sensitive to the error in the data. The amount of regularization depends on a parameter. When an accurate estimate of the norm of the error in the data is known, this parameter can be determined by the discrepancy principle. This paper is concerned with the situation when the error is white Gaussian and no estimate of the norm of the error is available, and explores the possibility of applying a denoising method to both reduce this error and to estimate its norm. Applications to image deblurring are presented.

A Standard Platform for Testing and Comparison of MDAO Architectures

The Multidisciplinary Design Analysis and Optimization (MDAO) community has developed a multitude of algorithms and techniques, called architectures, for performing optimizations on complex engineering systems which involve coupling between multiple discipline analyses. These architectures seek to efficiently handle optimizations with computationally expensive analyses including multiple disciplines. We propose a new testing procedure 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: MDF, IDF, CO, BLISS, and BLISS-2000. We also demonstrate how using open source soft- ware development methods can allow the MDAO community to submit new problems and architectures to keep the test suite relevant.

Chemical-Equilibrium Analysis with Adjoint Derivatives for Propulsion Cycle Analysis

The design optimization of aircraft engines considering their integration with the airframe has been limited by challenges with existing propulsion modeling tools. Gradient-based optimization with derivatives computed using adjoint methods has been successful in solving aerodynamic and structural shape optimization problems but has not yet been applied to coupled propulsion–airframe optimization, partly because existing tools lack analytic derivative computation. As a step toward obtaining a full cycle analysis with efficient analytic derivative computation, a new chemical-equilibrium thermodynamics solver is developed for propulsion applications. This solver provides a continuous formulation that enables analytic derivative computation using a coupled adjoint approach. The results from this solver are verified against a well-established chemical-equilibrium code. The analytic derivatives are also verified by comparing them with finite-difference approximations. The performance of the analytic derivative ...

Extensions of the Justen---Ramlau blind deconvolution method

Blind deconvolution problems arise in many image restoration applications. Most available blind deconvolution methods are iterative. Recently, Justen and Ramlau proposed a novel non-iterative blind deconvolution method. The method was derived under the assumption of periodic boundary conditions. These boundary conditions may introduce oscillatory artifacts into the computed restoration. We describe extensions of the Justen–Ramlau method that allow the use of Neumann and antireflective boundary conditions.

Performance Calculations for a Boundary-Layer-Ingesting Fan Stage from Sparse Measurements

A test of the Boundary Layer Ingesting Inlet/Distortion Tolerant Fan was completed in NASA Glenn’s 8by 6-Foot Supersonic Wind Tunnel. Inlet and fan performance were measured by surveys using a set of rotating rake arrays upstream and downstream of the fan stage. Surveys were conducted along the 100% speed line as well as a constant exit corrected flow line passing through the aerodynamic design point. These surveys represented only a small fraction of the data collected during the test. For other operating points, data was recorded as “snapshots” without rotating the rakes which resulted in a sparser set of recorded data. This paper will discuss an approach to the analysis of these additional, lower-measurement-density data points to expand our coverage of the fan map. Several techniques will be used to enhance snapshot data and compare with survey data to assess​ ​the​ ​quality​ ​of​ ​the​ ​approach.