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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Shape Optimization by Bayesian-Validated Computer-Simulation Surrogates

A nonparametric-validated, surrogate approach to optimization has been applied to the computational optimization of eddy-promoter heat exchangers and to the experimental optimization of a multielement airfoil. In addition to the baseline surrogate framework, a surrogate-Pareto framework has been applied to the two-criteria, eddy-promoter design problem. The Pareto analysis improves the predictability of the surrogate results, preserves generality, and provides a means to rapidly determine design trade-offs. Significant contributions have been made in the geometric description used for the eddy-promoter inclusions as well as to the surrogate framework itself. A level-set based, geometric description has been developed to define the shape of the eddy-promoter inclusions. The level-set technique allows for topology changes (from single-body,eddy-promoter configurations to two-body configurations) without requiring any additional logic. The continuity of the output responses for input variations that cross the boundary between topologies has been demonstrated. Input-output continuity is required for the straightforward application of surrogate techniques in which simplified, interpolative models are fitted through a construction set of data. The surrogate framework developed previously has been extended in a number of ways. First, the formulation for a general, two-output, two-performance metric problem is presented. Surrogates are constructed and validated for the outputs. The performance metrics can be functions of both outputs, as well as explicitly of the inputs, and serve to characterize the design preferences. By segregating the outputs and the performance metrics, an additional level of flexibility is provided to the designer. The validated outputs can be used in future design studies and the error estimates provided by the output validation step still apply, and require no additional appeals to the expensive analysis. Second, a candidate-based a posteriori error analysis capability has been developed which provides probabilistic error estimates on the true performance for a design randomly selected near the surrogate-predicted optimal design.

Patera, Anthony T.↗
NASA NTRS2016

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases.1 Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission.2 Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an Advanced Design Methods (ADM) based approach. This approach applies the concepts of Design of Experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development e ort. In order to t a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of Ground Rules and Assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated \what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are t to the outputs of each environment and are integrated via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any \what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will have the potential to lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.↗
NASA NTRS2016

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases. Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission. Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an advanced design methods (ADM) based approach. This approach applies the concepts of design of experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development effort. In order to fit a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of ground rules and assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated "what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are fit to the outputs of each environment and are "integrated" via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any ''what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will help ensure lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.↗
NASA NTRS2008

Gaseous Surrogate Hydrocarbons for a Hifire Scramjet that Mimic Opposed Jet Extinction Limits for Cracked JP Fuels

This paper describes, first, the top-down methodology used to define simple gaseous surrogate hydrocarbon (HC) fuel mixtures for a hypersonic scramjet combustion subtask of the HiFIRE program. It then presents new and updated Opposed Jet Burner (OJB) extinction-limit Flame Strength (FS) data obtained from laminar non-premixed HC vs. air counterflow diffusion flames at 1-atm, which follow from earlier investigations. FS represents a strain-induced extinction limit based on cross-section-average air jet velocity, U(sub air), that sustains combustion of a counter jet of gaseous fuel just before extinction. FS uniquely characterizes a kinetically limited fuel combustion rate. More generally, Applied Stress Rates (ASRs) at extinction (U(sub air) normalized by nozzle or tube diameter, D(sub n or t) can directly be compared with extinction limits determined numerically using either a 1-D or (preferably) a 2-D Navier Stokes simulation with detailed transport and finite rate chemistry. The FS results help to characterize and define three candidate surrogate HC fuel mixtures that exhibit a common FS 70% greater than for vaporized JP-7 fuel. These include a binary fuel mixture of 64% ethylene + 36% methane, which is our primary recommendation. It is intended to mimic the critical flameholding limit of a thermally- or catalytically-cracked JP-7 like fuel in HiFIRE scramjet combustion tests. Our supporting experimental results include: (1) An idealized kinetically-limited ASR reactivity scale, which represents maximum strength non-premixed flames for several gaseous and vaporized liquid HCs; (2) FS characterizations of Colket and Spadaccini s suggested ternary surrogate, of 60% ethylene + 30% methane + 10% n-heptane, which matches the ignition delay of a typical cracked JP fuel; (3) Data showing how our recommended binary surrogate, of 64% ethylene + 36% methane, has an identical FS; (4) Data that characterize an alternate surrogate of 44% ethylene + 56% ethane with identical FS and nearly equal molecular weights; this could be useful when systematically varying the fuel composition. However, the mixture liquefies at much lower pressure, which limits on-board storage of gaseous fuel; (5) Dynamic Flame Weakening results that show how oscillations in OJB input flow (and composition) can weaken (extinguish) surrogate flames up to 200 Hz, but the weakening is 2.5x smaller compared to pure methane; and finally, (6) FS limits at 1-atm that compare with three published 1-D numerical OJB extinction results using four chemical kinetic models. The methane kinetics generally agree closely at 1-atm, whereas, the various ethylene models predict extinction limits that average ~ 45% high, which represents a significant problem for numerical simulation of surrogate-based flameholding in a scramjet cavity. Finally, we continue advocating the FS approach as more direct and fundamental for assessing idealized scramjet flameholding potentials than measurements of "unstrained" premixed laminar burning velocity or blowout in a Perfectly Stirred Reactor.

Pellett, Gerald L.↗
NASA NTRS2011

The Proposed Use of Unmanned Aerial System Surrogate Research Aircraft for National Airspace System Integration Research

Research is needed to determine what procedures, aircraft sensors and other systems will be required to allow Unmanned Aerial Systems (UAS) to safely operate with manned aircraft in the National Airspace System (NAS). This paper explores the use of Unmanned Aerial System (UAS) Surrogate research aircraft to serve as platforms for UAS systems research, development, and flight testing. These aircraft would be manned with safety pilots and researchers that would allow for flight operations almost anywhere in the NAS without the need for a Federal Aviation Administration (FAA) Certificate of Authorization (COA). With pilot override capability, these UAS Surrogate aircraft would be controlled from ground stations like true UAS s. It would be possible to file and fly these UAS Surrogate aircraft in the NAS with normal traffic and they would be better platforms for real world UAS research and development over existing vehicles flying in restricted ranges or other sterilized airspace. These UAS surrogate aircraft could be outfitted with research systems as required such as computers, state sensors, video recording, data acquisition, data link, telemetry, instrumentation, and Automatic Dependent Surveillance-Broadcast (ADS-B). These surrogate aircraft could also be linked to onboard or ground based simulation facilities to further extend UAS research capabilities. Potential areas for UAS Surrogate research include the development, flight test and evaluation of sensors to aide in the process of air traffic "see-and-avoid". These and other sensors could be evaluated in real-time and compared with onboard human evaluation pilots. This paper examines the feasibility of using UAS Surrogate research aircraft as test platforms for a variety of UAS related research.

Howell, Charles T., III↗
NASA NTRS2017

Program to Optimize Simulated Trajectories II (POST2) Surrogate Models for Mars Ascent Vehicle (MAV) Performance Assessment

The primary purpose of the multiPOST tool is to enable the execution of much larger sets of vehicle cases to allow for broader trade space exploration. However, this exploration is not achieved solely with the increased case throughput. The multiPOST tool is applied to carry out a Design of Experiments (DOE), which is a set of cases that have been structured to capture a maximum amount of information about the design space with minimal computational effort. The results of the DOE are then used to fit a surrogate model, ultimately enabling parametric design space exploration. The approach used for the MAV study includes both DOE and surrogate modeling. First, the primary design considerations for the vehicle were used to develop the variables and ranges for the multiPOST DOE. The final set of DOE variables were carefully selected in order to capture the desired vehicle trades and take into account any special considerations for surrogate modeling. Next, the DOE sets were executed through multiPOST. Following successful completion of the DOE cases, a manual verification trial was performed. The trial involved randomly selecting cases from the DOE set and running them by hand. The results from the human analyst's run and multiPOST were then compared to ensure that the automated runs were being executed properly. Completion of the verification trials was then followed by surrogate model fitting. After fits to the multiPOST data were successfully created, the surrogate models were used as a stand-in for POST2 to carry out the desired MAV trades. Using the surrogate models in lieu of POST2 allowed for visualization of vehicle sensitivities to the input variables as well as rapid evaluation of vehicle performance. Although the models introduce some error into the output of the trade study, they were very effective at identifying areas of interest within the trade space for further refinement by human analysts. The next section will cover all of the ground rules and assumptions associated with DOE setup and multiPOST execution. Section 3.1 gives the final DOE variables and ranges, while section 3.2 addresses the POST2 specific assumptions. The results of the verification trials are given in section 4. Section 5 gives the surrogate model fitting results, including the goodness-of-fit metrics for each fit. Finally, the MAV specific results are discussed in section 6.

Zwack, M. R.↗
NASA NTRS1996

A Surrogate Approach to the Experimental Optimization of Multielement Airfoils

The incorporation of experimental test data into the optimization process is accomplished through the use of Bayesian-validated surrogates. In the surrogate approach, a surrogate for the experiment (e.g., a response surface) serves in the optimization process. The validation step of the framework provides a qualitative assessment of the surrogate quality, and bounds the surrogate-for-experiment error on designs "near" surrogate-predicted optimal designs. The utility of the framework is demonstrated through its application to the experimental selection of the trailing edge ap position to achieve a design lift coefficient for a three-element airfoil.

Otto, John C.↗
NASA NTRS2010

The NASA Langley Research Center's Unmanned Aerial System Surrogate Research Aircraft

Research is needed to determine what procedures, aircraft sensors and other systems will be required to allow Unmanned Aerial Systems (UAS) to safely operate with manned aircraft in the National Airspace System (NAS). The NASA Langley Research Center has transformed a Cirrus Design SR22 general aviation (GA) aircraft into a UAS Surrogate research aircraft to serve as a platform for UAS systems research, development, flight testing and evaluation. The aircraft is manned with a Safety Pilot and systems operator that allows for flight operations almost anywhere in the NAS without the need for a Federal Aviation Administration (FAA) Certificate of Authorization (COA). The UAS Surrogate can be controlled from a modular, transportable ground station like a true UAS. The UAS Surrogate is able to file and fly in the NAS with normal traffic and is a better platform for real world UAS research and development than existing vehicles flying in restricted ranges or other sterilized airspace. The Cirrus Design SR22 aircraft is a small, singleengine, four-place, composite-construction aircraft that NASA Langley acquired to support NASA flight-research programs like the Small Aircraft Transportation System (SATS) Project. Systems were installed to support flight test research and data gathering. These systems include: separate research power; multi-function flat-panel displays; research computers; research air data and inertial state sensors; video recording; data acquisition; data-link; S-band video and data telemetry; Common Airborne Instrumentation System (CAIS); Automatic Dependent Surveillance-Broadcast (ADS-B); instrumented surfaces and controls; and a systems operator work station. The transformation of the SR22 to a UAS Surrogate was accomplished in phases. The first phase was to modify the existing autopilot to accept external commands from a research computer that was connected by redundant data-link radios to a ground control station. An electro-mechanical auto-throttle was added in the next phase to provide ground station control of airspeed. Additional phases are in progress to add waypoint navigation and long range satellite voice and data communications. Potential areas for UAS Surrogate research include the development, flight test and evaluation of sensors to aid in the process of air traffic detect-sense-and-avoid. These sensors could be evaluated in real-time and compared with onboard human evaluation pilots. This paper describes the systems and design considerations that were incorporated in the development of the UAS Surrogate along with details of development problems encountered and the corresponding solutions.

Howell, Charles T., III↗
NASA NTRS1995

Computer-Simulation Surrogates for Optimization: Application to Trapezoidal Ducts and Axisymmetric Bodies

Engineering design and optimization efforts using computational systems rapidly become resource intensive. The goal of the surrogate-based approach is to perform a complete optimization with limited resources. In this paper we present a Bayesian-validated approach that informs the designer as to how well the surrogate performs; in particular, our surrogate framework provides precise (albeit probabilistic) bounds on the errors incurred in the surrogate-for-simulation substitution. The theory and algorithms of our computer{simulation surrogate framework are first described. The utility of the framework is then demonstrated through two illustrative examples: maximization of the flowrate of fully developed ow in trapezoidal ducts; and design of an axisymmetric body that achieves a target Stokes drag.

Otto, John C.↗
NASA NTRS2005

Surrogate-based Analysis and Optimization

A major challenge to the successful full-scale development of modem aerospace systems is to address competing objectives such as improved performance, reduced costs, and enhanced safety. Accurate, high-fidelity models are typically time consuming and computationally expensive. Furthermore, informed decisions should be made with an understanding of the impact (global sensitivity) of the design variables on the different objectives. In this context, the so-called surrogate-based approach for analysis and optimization can play a very valuable role. The surrogates are constructed using data drawn from high-fidelity models, and provide fast approximations of the objectives and constraints at new design points, thereby making sensitivity and optimization studies feasible. This paper provides a comprehensive discussion of the fundamental issues that arise in surrogate-based analysis and optimization (SBAO), highlighting concepts, methods, techniques, as well as practical implications. The issues addressed include the selection of the loss function and regularization criteria for constructing the surrogates, design of experiments, surrogate selection and construction, sensitivity analysis, convergence, and optimization. The multi-objective optimal design of a liquid rocket injector is presented to highlight the state of the art and to help guide future efforts.

Queipo, Nestor V.↗
NASA NTRS2017

The Use of a Satellite Communications System for Command and Control of the National Aeronautics and Space Administration Surrogate Unmanned Aerial System Research Aircraft

The NASA Langley Research Center has transformed a Cirrus Design SR22 general aviation (GA) aircraft into an Unmanned Aerial Systems (UAS) Surrogate research aircraft which has served for several years as a platform for unmanned systems research and development. The aircraft is manned with a Safety Pilot and a Research Systems Operator (RSO) that allows for flight operations almost any-where in the national airspace system (NAS) without the need for a Federal Aviation Administration (FAA) Certificate of Authorization (COA). The UAS Surrogate can be remotely controlled from a modular, transportable ground control station (GCS) like a true UAS. Ground control of the aircraft is accomplished by the use of data links that allow the two-way passage of the required data to control the aircraft and provide the GCS with situational awareness. The original UAS Surrogate data-link system was composed of redundant very high frequency (VHF) data radio modems with a maximum range of approximately 40 nautical miles. A new requirement was developed to extend this range beyond visual range (BVR). This new requirement led to the development of a satellite communications system that provided the means to command and control the UAS Surrogate at ranges beyond the limits of the VHF data links. The system makes use of the Globalstar low earth orbit (LEO) satellite communications system. This paper will provide details of the development, implementation, and flight testing of the satellite data communications system on the UAS Surrogate research aircraft.

Howell, Charles T.↗
NASA NTRS2018

Probabilistic Sensitivity Analyses Incorporating Surrogate Models for the Structural Response of a Representative Inflatable Space Structure

This study concentrates on results from probabilistic analysis and numerical simulation tools to identify parameter sensitivities and assess surrogate model suitability for a novel inflatable airlock concept, specifically the Non-Axisymmetric Inflatable Pressure Structure (NAIPS) under NASA's Minimalistic Advanced Softgoods Hatch (MASH) Program. The current studies extended the demonstration of probabilistic analysis tools to identify parameter sensitivities by: incorporating nonlinear material load-strain property curves and orthotropic representation of the fabric; and exploring the use of surrogate models to facilitate rapid evaluations as new information becomes available, as well as enable optimizations. The airlock model has been simplified to focus on the end dome section. Brief overviews of the finite element model and associated surrogate models are provided along with the probabilistic sensitivity analysis approaches. Responses of interest include the sensitivities of various loads in the structural elements of the NAIPS to material properties, cord lengths, inflation pressure and friction between softgoods components. The use of surrogate models was explored to facilitate rapid sensitivity evaluations as parameter ranges change. The completion of the sensitivity studies improved understanding of the dependence of load responses to several uncertain parameters and confidence in the ability to use surrogate models to represent the finite element simulations.

Lyle, Karen H.↗
NASA NTRSDate not supplied

Enabling in-time Prognostics with Surrogate Modeling through Physics-enhanced Dynamic Mode Decomposition Method

Computational models provide essential quantitative tools for assessing and predicting the health and performance of physical systems. However, high-fidelity models are rarely used in real-time operations or large optimization loops, due to their time-intensive nature. A common approach to improving computational efficiency of prognosis is to employ surrogate models. Such models can significantly decrease computation time for some accuracy loss. In this context, use of Dynamic Mode Decomposition (DMD) is proposed to generate surrogate models for lithium-ion (Li-ion) battery discharge. DMD has been suggested and used successfully in the area of fluid dynamics for over a decade, but it has not been applied to the PHM domain, where far-ahead prediction of nonlinear behavior is crucial to propagate faults or predict Remaining Useful Life (RUL). For Li-ion battery health management, the standard application of DMD using only the observable quantities of interest was unable to capture the nonlinear discharge of batteries exhibited in lab testing. The Koopman theory, however, provides a mechanism to tradeoff low dimensional nonlinear models with high-dimensional linear ones in a DMD framework, by augmenting nonlinear state variables into the system representation. In this way, DMD allows for configurable simulation accuracy dependent on the dimensionality of the Koopman operator. For battery health management, we augmented the observable variables with the hidden states of a higher-fidelity physics model to build the DMD surrogate. In comparison to a high-fidelity model, the surrogate improved computational efficiency with only a minimal loss of accuracy, and enabled long-term prognostics horizons. A generalized method for this was implemented in the prog models python package.

prognostics and health management↗
NASA NTRS1993

Surrogates for numerical simulations; optimization of eddy-promoter heat exchangers

Although the advent of fast and inexpensive parallel computers has rendered numerous previously intractable calculations feasible, many numerical simulations remain too resource-intensive to be directly inserted in engineering optimization efforts. An attractive alternative to direct insertion considers models for computational systems: the expensive simulation is evoked only to construct and validate a simplified, input-output model; this simplified input-output model then serves as a simulation surrogate in subsequent engineering optimization studies. A simple 'Bayesian-validated' statistical framework for the construction, validation, and purposive application of static computer simulation surrogates is presented. As an example, dissipation-transport optimization of laminar-flow eddy-promoter heat exchangers are considered: parallel spectral element Navier-Stokes calculations serve to construct and validate surrogates for the flowrate and Nusselt number; these surrogates then represent the originating Navier-Stokes equations in the ensuing design process.

Patera, Anthony T.↗
NASA NTRS2018

Greedy Sampling and Incremental Surrogate Model-Based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

This paper presents a data analysis and modeling framework to tailor and develop linear parameter-varying (LPV) aeroservoelastic (ASE) model database for flexible aircrafts in broad 2D flight parameter space. The Kriging surrogate model is constructed using ASE models at a fraction of grid points within the original model database, and then the ASE model at any flight condition can be obtained simply through surrogate model interpolation. The greedy sampling algorithm is developed to select the next sample point that carries the worst relative error between the surrogate model prediction and the benchmark model in the frequency domain among all input-output channels. The process is iterated to incrementally improve surrogate model accuracy till a pre-determined tolerance or iteration budget is met. The methodology is applied to the ASE model database of a flexible aircraft currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that the proposed method can reduce the number of models in the original database by 67%. Even so the ASE models obtained through Kriging interpolation match the model in the original database constructed directly from the physics-based tool with the worst relative error far below 1%. The interpolated ASE model exhibits continuously-varying gains along a set of prescribed flight conditions. More importantly, the selected grid points are distributed non-uniformly in the parameter space, a) capturing the distinctly different dynamic behavior and its dependence on flight parameters, and b) reiterating the need and utility for adaptive space sampling techniques for ASE model database compaction. The present framework is directly extendible to high-dimensional flight parameter space, and can be used to guide the ASE model development, model order reduction, robust control synthesis and novel vehicle design of flexible aircraft.

numerical analysi↗
NASA NTRS2019

Surrogate Modeling and Optimization of a Combustor with an Interdigitated Flushwall Injector

Design and Analysis of Computer Experiments (DACE) methods are applied and used to perform surrogate modeling and optimization of a simplified combustor flowpath with an interdigitated flushwall injector. The objectives of the optimization are the thrust potential and combustion efficiency, which are evaluated across a range of flight Mach numbers, duct heights, spanwise spacings, and injection angles. The focus of this work is to highlight the application of a sequential learning approach, in order to learn about the responses of the objective functions over the design space and to identify local regions of interest for further analysis. This approach is contrasted to a previous effort where only a single sampling set was used to fit surrogate models and perform optimization. The optimal solutions resulting from the previous and present approaches are different, due to surrogate model-guided local refinement of the design space allowed by the sequential learning method. The values of the global error estimates between the previous and present approaches are comparable, but the sequential method proved more computationally cost-effective. Further refinement in the optimal regions might be needed to improve predictive capability of surrogate models and to obtain the optimal solutions sets.

Rajiv R Shenoy↗
NASA NTRS2021

Optimal Experimental Design With Fast Neural Network Surrogate Models

Designing optimal experiments minimizes the uncertainty of results and maximizes the efficient use of resources. Herein, machine learning surrogate models and the approximate coordinate exchange (ACE) algorithm are used to determine optimum experimental designs over large or arbitrarily restrictive design spaces. Optimal experimental design is particularly salient in materials science where experiments are expensive and material properties must often be inferred indirectly. The proposed framework is demonstrated by finding optimal experiments with which the hidden constituent properties of composite materials can be most efficiently inferred from observable experimental outcomes. The optimum experimental design is given by an information-theoretic criteria, which maximizes the conditional mutual information between the hidden properties and the expected experimental outcomes. To perform tractable optimization a neural network is trained as a surrogate model to mimic a physics based simulation, which can calculate the expected experimental outcome based on a candidate experimental design and sampled constituent properties. The ACE algorithm is used to optimize over large design spaces with many tests and controlled parameters where an exhaustive search would be intractable even with the surrogate model. Using this approach, optimal experimental designs that are consistent with those produced by heuristic knowledge and established best practices are found; then optimal designs in larger design spaces where heuristic knowledge is unavailable are examined.

machine learning↗
NASA NTRSDate not supplied

Probabilistic Calibration of Expensive Models using Efficiently Trained Surrogates

Calibration of computational models in the presence of uncertainty is often cast as a Bayesian inference problem and solved via sampling methods, e.g., Markov chain Monte Carlo. When the computational model is expensive, this task becomes intractable due to the large number of samples required to accurately estimate the posterior distribution of the calibration parameters. A popular solution to this problem is to use machine learning to develop a faster-to-evaluate, lower-fidelity substitute for the original model to serve as a surrogate while solving the inference problem. Although considered an offline cost, generating training data to construct this surrogate model can still be an expensive task in practice. An active learning algorithm is presented that focuses training on improving surrogate accuracy specifically in and around the bulk of the posterior distribution, as this is where the model is exercised during calibration. Candidate samples are drawn from families of distributions related to an approximation of the posterior. The sample maximizing predictive variance is then selected for evaluation by the original computational model, yielding a label for the training point. Iterating this approach increases efficiency relative to space filling designs (e.g., Latin hypercube sampling) by avoiding low probability points. Practical considerations are discussed, including the benefits of using a sequential Monte Carlo sampling approach, convergence heuristics, and the importance of both exploration and exploitation given that the true posterior is unknown a priori.

uncertainty quantification↗