Search NASA⌕ Search

SEARCH · Search NASA

Results for “estimation steps”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

Overcoming time-integration errors in SINDA's FWDBCK solution routine

The FWDBCK time step, which is usually chosen intuitively to achieve adequate accuracy at reasonable computational costs, can in fact lead to large errors. NASA observed such errors in solving cryogenic problems on the COBE spacecraft, but a similar error is also demonstrated for a single node radiating to space. An algorithm has been developed for selecting the time step during the course of the simulation. The error incurred when the time derivative is replaced by the FWDBCK time difference can be estimated from the Taylor-Series expression for the temperature. The algorithm selects the time step to keep this error small. The efficacy of the method is demonstrated on the COBE and single-node problems.

Skladany, J. T.↗

Discretization Error Estimation and Control for Farfield Acoustic Signatures

We investigate the utility of adjoint-based error estimates for sonic boom farfield simulations governed by solutions of the augmented Burgers’ equation. Solution of this nonlinear system uses operator splitting with a second-order finite volume discretization in space and second-order Runge-Kutta time marching, while the absorption and molecular relaxation are solved using second-order central differencing. The discretization error in selected ground sonic boom cost functionals is estimated using the method of adjoint-weighted residuals. Key elements of the implementation process are emphasized with details provided on the practical aspects as appliedto the sonic boom farfield propagation. We establish the accuracy of the adjoint solutions usingcomplex step and finite difference approaches, and examine the accuracy of the error estimates using analytical N-wave solutions. We then apply it to a pressure waveform corresponding to the X-59 research aircraft. The investigations demonstrate that the method of adjoint-weighted residuals accurately predicts the level of discretization error present in sonic boom farfield simulations while offering insight into which features of the near field signal are the primary drivers of ground noise metrics. The numerical results indicate that at sampling frequencies as low as50kHz, discretization error in the propagation is under 0.01 dB[A] for realistically complex examples.

CST↗

Market Analysis of the Subsonic Single Aft Engine (SUSAN) Transport Aircraft Concept

This paper presents a detailed market analysis of the U.S. domestic aviation market in support of the NASA subsonic single aft engine (SUSAN) regional aircraft concept. The current scoping of the SUSAN concept is intended to compete in the medium to large (160-180 seats) narrow body market, with range capabilities of up to 2,500 nautical miles, and expected fuel burn reduction up to 40% relative to conventional 2 engine aircraft. Recent historical trends suggest growth in aviation passenger demand will continue to be met by the narrow body fleet of aircraft; however, a comprehensive review is required to understand how these current fleet trends could evolve in the future. Moreover, estimating and forecasting the potential market size is the critical first step when developing a new aircraft concept to determine commercial viability. To assist in the trade space exploration of the SUSAN concept, a generalized traffic and fleet forecast of the U.S. aviation market is conducted. Using publicly available aviation data from the U.S. Bureau of Transportation Statistics and passenger demand forecasts from FAA, a multinomial logit model is estimated to predict the composition of the future fleet by aircraft size. These fleet forecasts are then used as inputs for a fleet evolution model to provide required operational forecasts at the aircraft specific level. Forecast scenarios with and without the SUSAN concept are compared, and a breakeven analysis is performed to evaluate the commercial viability of the SUSAN aircraft from an operating cost perspective. Results from the multinomial logit fleet forecast indicate the narrow body size category of 150+ seats dominating the market, comprising 87% of the future revenue passenger miles market share in 2050 (up from 60% in 2019). Forecast scenarios with the SUSAN concept see a maximum cumulative decline in fuel cost of 20% by 2050, while a breakeven analysis shows competitive advantage of the SUSAN aircraft, due to expected fuel burn reduction, at moderate levels of increased maintenance and capital costs.

Jacob M. Wishart↗

An Ensemble Recentering Kalman Filter with an Application to Argo Temperature Data Assimilation into the NASA GEOS-5 Coupled Model

A two-step ensemble recentering Kalman filter (ERKF) analysis scheme is introduced. The algorithm consists of a recentering step followed by an ensemble Kalman filter (EnKF) analysis step. The recentering step is formulated such as to adjust the prior distribution of an ensemble of model states so that the deviations of individual samples from the sample mean are unchanged but the original sample mean is shifted to the prior position of the most likely particle, where the likelihood of each particle is measured in terms of closeness to a chosen subset of the observations. The computational cost of the ERKF is essentially the same as that of a same size EnKF. The ERKF is applied to the assimilation of Argo temperature profiles into the OGCM component of an ensemble of NASA GEOS-5 coupled models. Unassimilated Argo salt data are used for validation. A surprisingly small number (16) of model trajectories is sufficient to significantly improve model estimates of salinity over estimates from an ensemble run without assimilation. The two-step algorithm also performs better than the EnKF although its performance is degraded in poorly observed regions.

Particle Filter↗

On-Orbit Multi-Field Wavefront Control with a Kalman Filter

A document describes a multi-field wavefront control (WFC) procedure for the James Webb Space Telescope (JWST) on-orbit optical telescope element (OTE) fine-phasing using wavefront measurements at the NIRCam pupil. The control is applied to JWST primary mirror (PM) segments and secondary mirror (SM) simultaneously with a carefully selected ordering. Through computer simulations, the multi-field WFC procedure shows that it can reduce the initial system wavefront error (WFE), as caused by random initial system misalignments within the JWST fine-phasing error budget, from a few dozen micrometers to below 50 nm across the entire NIRCam Field of View, and the WFC procedure is also computationally stable as the Monte-Carlo simulations indicate. With the incorporation of a Kalman Filter (KF) as an optical state estimator into the WFC process, the robustness of the JWST OTE alignment process can be further improved. In the presence of some large optical misalignments, the Kalman state estimator can provide a reasonable estimate of the optical state, especially for those degrees of freedom that have a significant impact on the system WFE. The state estimate allows for a few corrections to the optical state to push the system towards its nominal state, and the result is that a large part of the WFE can be eliminated in this step. When the multi-field WFC procedure is applied after Kalman state estimate and correction, the stability of fine-phasing control is much more certain. Kalman Filter has been successfully applied to diverse applications as a robust and optimal state estimator. In the context of space-based optical system alignment based on wavefront measurements, a KF state estimator can combine all available wavefront measurements, past and present, as well as measurement and actuation error statistics to generate a Maximum-Likelihood optimal state estimator. The strength and flexibility of the KF algorithm make it attractive for use in real-time optical system alignment when WFC alone cannot effectively align the system.

Lou, John↗

Analytic methods for design of wave cycles for wave rotor core engines

A procedure to design a preliminary wave rotor cycle for any application is presented. To complete a cycle with heat addition there are two separate but related design steps that must be followed. The 'wave' boundary conditions determine the allowable amount of heat added in any case and the ensuing wave pattern requires certain pressure discharge conditions to allow the process to be made cyclic. This procedure, when applied, gives a first estimate of the cycle performance and the necessary information for the next step in the design process, namely the application of a characteristic based or other appropriate detailed one dimensional wave calculation that locates the proper porting around the periphery of the wave rotor. Four examples of the design procedure are given to demonstrate its utility and generality. These examples also illustrate the large gains in performance that could be realized with the use of wave rotor enhanced propulsion cycles.

Resler, Edwin L., Jr.↗

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗

Global Burned Area and Biomass Burning Emissions from Small Fires

In several biomes, including croplands, wooded savannas, and tropical forests, many small fires occur each year that are well below the detection limit of the current generation of global burned area products derived from moderate resolution surface reflectance imagery. Although these fires often generate thermal anomalies that can be detected by satellites, their contributions to burned area and carbon fluxes have not been systematically quantified across different regions and continents. Here we developed a preliminary method for combining 1-km thermal anomalies (active fires) and 500 m burned area observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate the influence of these fires. In our approach, we calculated the number of active fires inside and outside of 500 m burn scars derived from reflectance data. We estimated small fire burned area by computing the difference normalized burn ratio (dNBR) for these two sets of active fires and then combining these observations with other information. In a final step, we used the Global Fire Emissions Database version 3 (GFED3) biogeochemical model to estimate the impact of these fires on biomass burning emissions. We found that the spatial distribution of active fires and 500 m burned areas were in close agreement in ecosystems that experience large fires, including savannas across southern Africa and Australia and boreal forests in North America and Eurasia. In other areas, however, we observed many active fires outside of burned area perimeters. Fire radiative power was lower for this class of active fires. Small fires substantially increased burned area in several continental-scale regions, including Equatorial Asia (157%), Central America (143%), and Southeast Asia (90%) during 2001-2010. Globally, accounting for small fires increased total burned area by approximately by 35%, from 345 Mha/yr to 464 Mha/yr. A formal quantification of uncertainties was not possible, but sensitivity analyses of key model parameters caused estimates of global burned area increases from small fires to vary between 24% and 54%. Biomass burning carbon emissions increased by 35% at a global scale when small fires were included in GFED3, from 1.9 Pg C/yr to 2.5 Pg C/yr. The contribution of tropical forest fires to year-to-year variability in carbon fluxes increased because small fires amplified emissions from Central America, South America and Southeast Asia-regions where drought stress and burned area varied considerably from year to year in response to El Nino-Southern Oscillation and other climate modes.

Randerson, J. T.↗

Resolving the Issues with Flywheel Position Sensors

For the past few years, the Advanced Electrical Systems Branch here at NASA Glenn has been pursuing research in the area of flywheels. The purpose of these pursuits has been t o explore the potential for flywheels to replace current battery-powered systems in space. So far it has been learned that flywheels offer large momentum storage capacity, comparatively small volume, high durability, and near- complete discharge capabilities, all of which are advancements over the existing nickel hydrogen and nickel cadmium batteries. Another significant advantage of flywheels is the potential they offer for combining the function of attitude control with energy storage. During the summer of 2004, I worked with Dr. Barbara Kenny in the Advanced Electrical Systems Branch, supporting the work she is doing by analyzing and testing some new components for the new Generation-2 flywheel. To monitor the speed and angular position of the flywheel rotor, a once-around (OAR) signal along with a sensorless algorithm is used. The OAR signal is used for the magnetic bearings that keep the flywheel suspended for frictionless operation. The sensorless algorithm is used for the flywheel motor/generator control. The OAR is generated from position sensors that monitor a circular plate. The plate has a cut down the middle such that one half of the circle is on a slightly lower level than the other. Every half-turn, or 180, the sensors detect the "cut" on the plate, and trigger the OAR, telling the computer that the rotor has made half a revolution. This, however, doesn't provide needed detailed information about the angular position of the rotor, since it only provides a signal alert every half- revolution. This is enough information for the magnetic bearing control but is insufficient for the motor/generator control. A new resolver was designed such that it would give continuous angle information rather than the 180 degree information of the OAR. The new resolver has two separate observable pieces: a flat middle section to monitor vertical motion, and an angled section around the circumference, which, when observed from above, produces a sine-wave displacement through the entire 360" revolution. My first job when I arrived this summer was to calibrate the sensors that would be mounted on the inside of the flywheel casing to monitor the position (angular and vertical) of the shaft. After calibration, I used the sensors to evaluate voltage outputs created by position differences between two pairs of sensors on the angled portion of the resolver for eight different angular positions, moving the resolver vertically and laterally through its entire potential range of motion. The results of these tests will be used to determine the rotor angular (and axial) position from the sensor readings once the new flywheel unit is assembled. The sensorless algorighm mentioned above consists of two operations: the signal injection method and the back electro-motive force (EMF). The signal injection is meant to work at low speeds, while the back EMF algorithm is meant to work at higher speeds. Both work together to determine the correct estimate of rotor position and speed based on the measured motor/generator current. It was determined that we wanted to know exactly how accurate our estimation methods were, and so a resolver (a commercially available mechanical sensor mounted to the motor/generator shaft to measure rotor position and speed) and a "Resolver to Digital" (R2D) circuit board was purchased to make the comparison to the existing estimation. My work related to the R2D board has included the following: creating two connector cables (one to power the circuit and one to get readable output off the board), writing Simulink code to process the board's output, and building a dSpace panel to control and monitor the circuit. The next step in the process will be to perform tests to compare the estimated rotor position and speed from the sensorless algorithm to the actual rotor and speed from the resolver signal.

Fehrmann, Elizabeth A.↗

Protocol to detect dilution cycles in chemostat experiments and estimate growth rate slopes with linear modeling with R software chemostat_regression

Chemostat growth chambers measure optical density over time and require manual calculation of growth rates. Here, we present chemostat_regression, R software that enables users to automatically identify chemostat cycles and estimate growth rate using a linear regression approach. We describe steps for creating requisite software environment(s), formatting input data, executing the software via command line/RStudio/R-Shiny, interpreting results, assessing the validity of results, and modifying input parameters.

59 BASIC BIOLOGICAL SCIENCES↗

The digital step edge

The facet model was used to accomplish step edge detection. The essence of the facet model is that any analysis made on the basis of the pixel values in some neighborhood has its final authoritative interpretation relative to the underlying grey tone intensity surface of which the neighborhood pixel values are observed noisy samples. Pixels which are part of regions have simple grey tone intensity surfaces over their areas. Pixels which have an edge in them have complex grey tone intensity surfaces over their areas. Specially, an edge moves through a pixel only if there is some point in the pixel's area having a zero crossing of the second directional derivative taken in the direction of a non-zero gradient at the pixel's center. To determine whether or not a pixel should be marked as a step edge pixel, its underlying grey tone intensity surface was estimated on the basis of the pixels in its neighborhood.

Haralick, R. M.↗

Spread-spectrum code acquisition in the presence of Doppler shift and data modulation

A spread-spectrum code acquisition technique for a direct-sequence (DS) system in the presence of Doppler effect and data modulation is investigated. Both the carrier-frequency offset and code-frequency offset due to severe Doppler effect are considered. The code-chip slipping during the correlation process caused by code-frequency offset can degrade the acquisition performance significantly. However, this issue can be alleviated by compensating code-frequency offset in an appropriate manner. Results are presented for the cases with and without data modulation. Coherent detection is considered when there is no data modulation. If data modulation is present, the authors partition the correlation time into subintervals and the integration results in these subintervals are square-law noncoherently combined for detection. The implementation of this code acquisition technique using the fast Fourier transform (FFT) algorithm is described. The use of theoretical results to estimate the hardware complexity of an actual system is illustrated step by step, showing that implementation is feasible with existing technology. The tradeoff between hardware complexity and acquisition performance is discussed.

Cheng, Unjeng↗

Motor Control of Two Flywheels Enabling Combined Attitude Control and Bus Regulation

This presentation discussed the flywheel technology development work that is ongoing at NASA GRC with a particular emphasis on the flywheel system control. The "field orientation" motor/generator control algorithm was discussed and explained. The position-sensorless angle and speed estimation algorithm was presented. The motor current response to a step change in command at low (10 kRPM) and high (60 kRPM) was discussed. The flywheel DC bus regulation control was explained and experimental results presented. Finally, the combined attitude control and energy storage algorithm that controls two flywheels simultaneously was presented. Experimental results were shown that verified the operational capability of the algorithm. shows high speed flywheel energy storage (60,000 RPM) and the successful implementation of an algorithm to simultaneously control both energy storage and a single axis of attitude with two flywheels. Overall, the presentation demonstrated that GRC has an operational facility that

Kenny, Barbara H.↗

Partitioning Evapotranspiration in Semiarid Grassland and Shrubland Ecosystems Using Diurnal Surface Temperature Variation

The encroachment of woody plants in grasslands across the Western U.S. will affect soil water availability by altering the contributions of evaporation (E) and transpiration (T) to total evapotranspiration (ET). To study this phenomenon, a network of flux stations is in place to measure ET in grass- and shrub-dominated ecosystems throughout the Western U.S. A method is described and tested here to partition the daily measurements of ET into E and T based on diurnal surface temperature variations of the soil and standard energy balance theory. The difference between the mid-afternoon and pre-dawn soil surface temperature, termed Apparent Thermal Inertia (I(sub A)), was used to identify days when E was negligible, and thus, ET=T. For other days, a three-step procedure based on energy balance equations was used to estimate Qe contributions of daily E and T to total daily ET. The method was tested at Walnut Gulch Experimental Watershed in southeast Arizona based on Bowen ratio estimates of ET and continuous measurements of surface temperature with an infrared thermometer (IRT) from 2004- 2005, and a second dataset of Bowen ratio, IRT and stem-flow gage measurements in 2003. Results showed that reasonable estimates of daily T were obtained for a multi-year period with ease of operation and minimal cost. With known season-long daily T, E and ET, it is possible to determine the soil water availability associated with grass- and shrub-dominated sites and better understand the hydrologic impact of regional woody plant encroachment.

Moran, M. Susan↗

Atmospheric Aerosol Properties and Climate Impacts

This report critically reviews current knowledge about global distributions and properties of atmospheric aerosols, as they relate to aerosol impacts on climate. It assesses possible next steps aimed at substantially reducing uncertainties in aerosol radiative forcing estimates. Current measurement techniques and modeling approaches are summarized, providing context. As a part of the Synthesis and Assessment Product in the Climate Change Science Program, this assessment builds upon recent related assessments, including the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4, 2007) and other Climate Change Science Program reports. The objectives of this report are (1) to promote a consensus about the knowledge base for climate change decision support, and (2) to provide a synthesis and integration of the current knowledge of the climate-relevant impacts of anthropogenic aerosols for policy makers, policy analysts, and general public, both within and outside the U.S government and worldwide.

Chin, Mian↗

TOWARD A METHOD FOR SCALING HUMAN BODY MODELS IN AN IMU-BASED WORKFLOW

BACKGROUND Scaled biomechanical models can more accurately inform crew health decisions when tailored to the wide range of astronaut sizes. One component to improve scaling of existing models to better represent each unique astronaut’s size is the individual length scaling of limbs. Traditionally, these lengths are determined by motion capture or manual measurement. A new method is herein proposed for length scaling which can be done by measuring linear and angular accelerations at a desired point during isolated motion around a point of rotation, then calculating the distance between the desired point and point of rotation. When an Inertial Measurement Unit (IMU) device is placed at the distal point of a limb, the isolated motion is about that limb’s proximal joint. For example, to measure forearm length, an IMU is placed at the wrist, the point of rotation is at the elbow, and the isolated motion is forearm flexion and extension. These calculated lengths are then used to scale models to each unique astronaut’s size, thereby improving the applicability of the model. This method of scaling limb segments can be used for any limb that has an easily defined proximal joint for the limb to rotate around including hands, arms, legs, feet. Utilizing IMUs for data collection also provides the synergistic ability to record data without a dedicated space in a room with many cameras, therefore reducing the data collection footprint, or record data where optical motion capture is not possible, such as inside a spacesuit. METHODS AND RESULTS To test this method, upper body data collection was performed with 5 Xsens DOT IMUs on a single subject. IMUs consist of an accelerometer, a gyroscope, and a magnetometer which collect linear acceleration, angular velocity, and magnetic fluctuations, respectively. Before any ground-based laboratory collection, the magnetic fluctuations are used to correct the heading of the IMU in space relative to the Earth’s magnetic field. The direct measurement of angular velocity is integrated to calculate angular acceleration. Then the linear acceleration ( a ) and angular acceleration (α) are solved using r = at/α to calculate the radius, which in this case is the distance between the IMU and the point of rotation (i.e., segment length). The IMU must be placed at the most distal point of the limb being measured (i.e., ankle if measuring lower leg length) and the test plan must consist of an isolated motion about that limb’s proximal joint (i.e., knee flexion and extension if measuring lower leg length). The distances (radii) calculated at every time interval were filtered (bandpass filter keeping 5th-90th percentile data) to eliminate outliers and spurious data that occur when the isolated motion was stopped or nearly stopped. The remaining distances were averaged, resulting in the calculated limb length. Scaling factors were then computed by dividing the calculated limb length by the unscaled model’s length. These scale factors are plugged into the Scale Tool in OpenSim [1,2] to apply the scaling to the OpenSim Full Body Rajagopal Model [3,4]. Manual measurements of limb lengths were taken before data collection started and used for comparing against the calculated lengths. The Anthropometric Survey of US Army Personnel (ANSUR II) [5] was also used as a third source of reference for limb length measurements. The following measurements were retrieved from the subject before data collection: 34.5 cm from L1 to C7 (thorax), 25.7 cm from C7 Joint Center (JC) to head vertex (neck and head), 36.3 cm from shoulder JC to elbow JC (humerus), 29.5 cm from elbow JC to wrist JC (forearm), and 16.2 cm from clavicle to acromion (clavicle). Of those five, forearm and humerus lengths were calculated using this proposed method to obtain preliminary results. The forearm length after filtering and averaging was calculated to be 37.6 cm. This is a 28% overestimation from the measured forearm length (29.5 cm). The humerus length after filtering and averaging was calculated to be 47.8 cm. This is a 31% difference from the measured subject length (36.3 cm). Sources of error include imperfect isolated motion (method currently expects that motion should be perfectly circular in a 2D plane, include no rotation of the IMU, and be relatively smooth; a more secure IMU attachment method will help), unrefined filter techniques (removed highest and lowest values with 20% high and low pass filters and no smoothing filters), arbitrary removal of stopped or near stopped data (kept data for only a short range before and after the angular velocity peaking), and a more representative method for removing gravitational acceleration is needed (current method is to zero all accelerations against a baseline taken just before the isolated motion which does not account for the gravitational acceleration changed due to IMU rotation during movement). Addressing these error sources will improve the accuracy of the limb length calculation. Next steps include creating a method for whole-body scaling estimation using individual limb scale factors. Continued pursuit of these techniques is expected to enable acquiring anthropometric information using only IMUs in real-time.

E. K. Marecki↗

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben D Phillips↗

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben Phillips↗