Tenavi Nakamura-Zimmerer

NASA NTRSDate not supplied

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗

NASA NTRSDate not supplied

Comparisons of Performance Metrics and Machine Learning Methods on an Entry Descent and Landing Database

This work focuses on evaluating machine learning methods and their applicability to the generation of an aerodynamic database, particularly for trajectory analysis of a capsule during entry, descent, and landing with a focus on uncertainty quantification. The source data to be used is the wind tunnel and computational data for the Integrated Design Assessment Team (IDAT) configuration of the Orion project, which has been publicly released. The methods used to generate the proposed databases are designed to naturally include a prediction interval, which will be evaluated both for their mean response as well as how well the prediction interval performs. These machine learning methods are compared to a traditionally generated database used by the Orion team as a baseline. It is found that while these machine learning methods perform well, the Orion database tends to still outperform them showing that engineering experience is still needed to make the best database possible. However, these methods still provide comparable results with significantly less effort.

Orion↗

NASA NTRSDate not supplied

Structured Covariance Gaussian Networks for Orion Crew Module Aerodynamic Uncertainty Quantification

In this paper we propose a new approach for nonlinear regression and uncertainty quantification. The method is based on a pair of neural networks which parameterize mean and dense covariance functions of a multivariate Gaussian process, trained together to maximize the log-likelihood of observing the given data. The covariance matrix is made positive definite at every input by construction. We also propose a sampling approach that produces viable surrogate function realizations from the Gaussian process. We call the proposed model a Structured Covariance Gaussian Network (SCGN). We illustrate the use of SCGNs for learning an aerodynamic response surface with built-in uncertainty for the Orion crew module. We find that SCGN provides an efficient and systematic way to learn nonlinear functional relationships and dense covariances. We compare results to a baseline Gaussian process regressor and observe that the SCGN provides comparable uncertainty descriptions with improved scalability to dataset size. The sample functions generated by SCGN are fast to evaluate online and are therefore convenient for use in trajectory simulations. These results suggest that SCGN may be a viable computational method for aerodynamic uncertainty quantification.

machine learning↗

NASA NTRSDate not supplied

Multihierarchy Gaussian Process Models for Probabilistic Aerodynamic Databases using Uncertain Nominal and Off-Nominal Configuration Data

Probabilistic aerodynamic databases are a crucial component of the development lifecycle for aerospace vehicles. A key challenge when building aerodynamic databases is that most data used to construct them represent various simplifications of the real flight vehicle. For example, wind tunnel models often simplify the vehicle geometry and surface roughness characteristics, while CFD computations often make simplifications to the physics being modeled, such as fully laminar or turbulent calculations. Multifidelity data fusion models rely on a user being able to define a hierarchy of fidelity levels anchored to some "truth" data. This approach is unsatisfactory when no data can be considered to accurately reflect real flight conditions. In this work, we provide an alternative approach by presenting a consistent mathematical framework for building probabilistic aerodynamic databases in the form of a conditional probability distribution described by an ensemble of multifidelity Gaussian Processes. Instead of relying on a single hierarchy of data fidelity levels, the presented framework identifies a "nominal" configuration and potential corrections to the nominal which represent specific physical phenomena not represented in the nominal data. The nominal and correction functions themselves are constructed as multifidelity Gaussian Processes and linearly combined to form an ensemble model which fuses the uncertainties associated nominal and correction models. Results obtained using the proposed framework on a simplified Orion Crew Module wind tunnel dataset demonstrate the predictive capability of the multihierarchy framework. We further demonstrate the benefits of such a probabilistic aerodynamic database approach through function sampling and computing the conditional distributions of derived quantities, such as the trim angle of attack and aerodynamic coefficients at trim.

Gaussian Processes↗

NASA NTRSDate not supplied

Multihierarchy Gaussian Process Models for Probabilistic Aerodynamic Databases using Uncertain Nominal and Off-Nominal Configuration Data

Explore the source record for details and available documents.

Gaussian Processes↗

NASA NTRSDate not supplied

AeroFusion: Data Fusion and Uncertainty Quantification for Entry Vehicles

AeroFusion is a NASA Langley initiative to incorporate advances in data science into the aerodynamic modeling process to improve efficiency. The effort can largely be categorized in three components: reduced-order modeling techniques, surrogate modeling techniques, and uncertainty quantification. By combining various methods from these categories, AeroFusion aims to reduce the development cost of aerodynamic models, both in terms of time and money.

Steven Snyder↗

NASA NTRSDate not supplied

AeroFusion: Data Fusion and Uncertainty Quantification for Entry Vehicles

AeroFusion is a NASA Langley initiative to incorporate advances in data science into the aerodynamic modeling process to improve efficiency. The effort can largely be categorized in three components: reduced-order modeling techniques, surrogate modeling techniques, and uncertainty quantification. By combining various methods from these categories, AeroFusion aims to reduce the development cost of aerodynamic models, both in terms of time and money.

Steven Snyder↗

NASA NTRSDate not supplied

Comparisons of Performance Metrics and Machine Learning Methods on an Entry, Descent, and Landing Database

This work focuses on evaluating machine learning methods and their applicability to the generation of an aerodynamic database, particularly for trajectory analysis of a capsule during entry, descent, and landing with a focus on uncertainty quantification. The source data to be used is the wind tunnel and computational data for the Integrated Design Assessment Team (IDAT) configuration of the Orion project, which has been publicly released. The methods used to generate the proposed databases are designed to naturally include a prediction interval, which will be evaluated both for their mean response as well as how well the prediction interval performs. These machine learning methods are compared to a traditionally generated database used by the Orion team as a baseline. It is found that while these machine learning methods perform well, the Orion database tends to still outperform them showing that engineering experience is still needed to make the best database possible. However, these methods still provide comparable results with significantly less effort.

Orion↗

NASA NTRSDate not supplied

Structured Covariance Gaussian Networks for Orion Crew Module Aerodynamic Uncertainty Quantification

In this paper we propose a new approach for nonlinear regression and uncertainty quantification. The method is based on a pair of neural networks which parameterize mean and dense covariance functions of a multivariate Gaussian process, trained together to maximize the log-likelihood of observing the given data. The covariance matrix is made positive definite at every input by construction. We also propose a sampling approach that produces viable surrogate function realizations from the Gaussian process. We call the proposed model a Structured Covariance Gaussian Network (SCGN). We illustrate the use of SCGNs for learning an aerodynamic response surface with built-in uncertainty for the Orion crew module. We find that SCGN provides an efficient and systematic way to learn nonlinear functional relationships and dense covariances. We compare results to a baseline Gaussian process regressor and observe that the SCGN provides comparable uncertainty descriptions with improved scalability to dataset size. The sample functions generated by SCGN are fast to evaluate online and are therefore convenient for use in trajectory simulations. These results suggest that SCGN may be a viable computational method for aerodynamic uncertainty quantification.

machine learning↗

NASA NTRSDate not supplied

Trajectory Planning and Online Performance Model Estimation for Advanced Air Mobility

We propose a framework for adaptive guidance based on optimal control and estimation using closed-loop performance models. In the proposed approach, parameters of a reduced-order performance model are estimated in real time so that trajectories and guidance commands are replanned with more accurate knowledge of the system's response and performance capabilities. To apply this methodology to flight control systems, we introduce a simple yet expressive performance model modified from a reference linear design model. The proposed framework is applied to guidance of a simulated Advanced Air Mobility class concept aircraft experiencing control effector failures. We demonstrate that, by optimizing performance model parameters in real time, guidance commands can be intelligently adjusted to recover system stability and the performance of a full-order vehicle model, even in the event of effector failures. Furthermore, the reduced-order performance model requires a fraction of the computational cost of the full-order model, facilitating real-time use of adaptive, optimal guidance.

Differential dynamic programming↗

NASA NTRSDate not supplied

Trajectory Planning and Online Performance Model Estimation for Advanced Air Mobility

We propose a framework for adaptive guidance based on optimal control and estimation using closed-loop performance models. In the proposed approach, parameters of a reduced-order performance model are estimated in real time so that trajectories and guidance commands are replanned with more accurate knowledge of the system's response and performance capabilities. To apply this methodology to flight control systems, we introduce a simple yet expressive performance model modified from a reference linear design model. The proposed framework is applied to guidance of a simulated Advanced Air Mobility class concept aircraft experiencing control effector failures. We demonstrate that, by optimizing performance model parameters in real time, guidance commands can be intelligently adjusted to recover system stability and the performance of a full-order vehicle model, even in the event of effector failures. Furthermore, the reduced-order performance model requires a fraction of the computational cost of the full-order model, facilitating real-time use of adaptive, optimal guidance.

Differential dynamic programming↗