Results for “Optimization Under Uncertainty” — Page 8

NASA NTRSDate not supplied

Reduced-order Modeling for Spacecraft Thermal-structural Applications

Leveraging the speed of reduced-order models (ROMs), thermal analysis teams have previously had access to rapid optimization, sensitivity studies, rapid model correlation, and uncertainty quantification, to name a few. An advantage of the developed approach is its relative robustness, which enabled expansion to include structural models in addition to thermal models leading to both rapid thermal-structural and rapid structural-only analyses. This method was tested for a sample thermal-structural application and showed good performance. It was then applied to a complex NASA mission and showed how ROMs could be used to quickly evaluate system uncertainties. Finally, these methods were applied to a structural-only application and used to better optimize and understand the structural design.

Derek Hengeveld↗

NASA NTRS2019

Sizing and Topology Design of an Aeroelastic Wingbox Under Uncertainty

The goals of this work are to use a nested optimizer to conduct simultaneous sizing (inner level) and topology (outer level) design of a wingbox, considering uncertainties in the safety factors used to define the aeroelastic constraints. These uncertainties, propagated via sampling-driven polynomial chaos, are explicitly introduced at the inner level of the method, during gradient-based sizing optimization, resulting in a stochastic optimal sizing distribution. Measures of robustness in the total structural mass are then passed to the outer level, where a global optimizer evolves the topology parameters. The results demonstrate design choices needed to improve robustness in the face of uncertain safety factors, and the various physical mechanisms driving this process.

Stanford, Bret K.↗

NASA NTRS1972

Computerized optimal control system design for reusable and expendable boost vehicles.

An optimization technique has been developed which combines the practical features of hybrid simulation of the dynamic system under study with the systematic approach of modern control theory where a mathematically formulated design criterion is optimized by functional minimization. Standard hybrid computer optimization methods using high-speed repetitive simulations and gradient minimization schemes have been extended to obtain time-varying optimal gain schedules and reduce the sensitivity of the optimized system to parameter and disturbance uncertainties. In this approach the performance index is expressed in meaningful engineering terms that reflect the interactions among all major disciplines, structures, control/actuation system design, aerodynamics and performance. The basic optimization technique is developed and its application to current aerospace control problems including the space shuttle is presented in detail. In the discussion of the application, the controllers resulting from the technique are compared with controllers developed by conventional methods. The paper concludes with a review of the advantages and disadvantages of the technique and plans for future applications.

Connor, C. L.↗

NASA NTRS1986

Design and evaluation of a failure detection and isolation algorithm for restructurable control systems

The use of a decentralized approach to failure detection and isolation for use in restructurable control systems is examined. This work has produced: (1) A method for evaluating fundamental limits to FDI performance; (2) Application using flight recorded data; (3) A working control element FDI system with maximal sensitivity to critical control element failures; (4) Extensive testing on realistic simulations; and (5) A detailed design methodology involving parameter optimization (with respect to model uncertainties) and sensitivity analyses. This project has concentrated on detection and isolation of generic control element failures since these failures frequently lead to emergency conditions and since knowledge of remaining control authority is essential for control system redesign. The failures are generic in the sense that no temporal failure signature information was assumed. Thus, various forms of functional failures are treated in a unified fashion. Such a treatment results in a robust FDI system (i.e., one that covers all failure modes) but sacrifices some performance when detailed failure signature information is known, useful, and employed properly. It was assumed throughout that all sensors are validated (i.e., contain only in-spec errors) and that only the first failure of a single control element needs to be detected and isolated. The FDI system which has been developed will handle a class of multiple failures.

Weiss, Jerold L.↗

NASA NTRS1992

Geopotential models of the Earth from satellite tracking, altimeter and surface gravity observations: GEM-T3 and GEM-T3S

Improved models of the Earth's gravitational field have been developed from conventional tracking data and from a combination of satellite tracking, satellite altimeter and surface gravimetric data. This combination model represents a significant improvement in the modeling of the gravity field at half-wavelengths of 300 km and longer. Both models are complete to degree and order 50. The Goddard Earth Model-T3 (GEM-T3) provides more accurate computation of satellite orbital effects as well as giving superior geoidal representation from that achieved in any previous GEM. A description of the models, their development and an assessment of their accuracy is presented. The GEM-T3 model used altimeter data from previous satellite missions in estimating the orbits, geoid, and dynamic height fields. Other satellite tracking data are largely the same as was used to develop GEM-T2, but contain certain important improvements in data treatment and expanded laser tracking coverage. Over 1300 arcs of tracking data from 31 different satellites have been used in the solution. Reliable estimates of the model uncertainties via error calibration and optimal data weighting techniques are discussed.

Lerch, F. J.↗

NASA NTRS2015

NASA Space Radiation Risk Project: Overview and Recent Results

The NASA Space Radiation Risk project is responsible for integrating new experimental and computational results into models to predict risk of cancer and acute radiation syndrome (ARS) for use in mission planning and systems design, as well as current space operations. The project has several parallel efforts focused on proving NASA's radiation risk projection capability in both the near and long term. This presentation will give an overview, with select results from these efforts including the following topics: verification, validation, and streamlining the transition of models to use in decision making; relative biological effectiveness and dose rate effect estimation using a combination of stochastic track structure simulations, DNA damage model calculations and experimental data; ARS model improvements; pathway analysis from gene expression data sets; solar particle event probabilistic exposure calculation including correlated uncertainties for use in design optimization.

Blattnig, Steve R.↗

NASA NTRS2018

Northern Hemisphere Surface Freeze-Thaw Product from Aquarius L-Band Radiometers

In the Northern Hemisphere, seasonal changes in surface freeze–thaw (FT) cycles are an important component of surface energy, hydrological and eco-biogeochemical processes that must be accurately monitored. This paper presents the weekly polar-gridded Aquarius passive L-band surface freeze–thaw product (FT-AP) distributed on the Equal-Area Scalable Earth Grid version 2.0, above the parallel 50 N, with a spatial resolution of 36 km36 km. The FT-AP classification algorithm is based on a seasonal threshold approach using the normalized polarization ratio, references for frozen and thawed conditions and optimized thresholds. To evaluate the uncertainties of the product, we compared it with another satellite FT product also derived from passive microwave observations but at higher frequency: the resampled 37 GHz FT Earth Science Data Record (FTESDR). The assessment was carried out during the overlapping period between 2011 and 2014. Results show that 77.1% of their common grid cells have an agreement better than 80 %. Their differences vary with land cover type (tundra, forest and open land) and freezing and thawing periods. The best agreement is obtained during the thawing transition and over forest areas, with differences between product mean freeze or thaw onsets of under 0.4 weeks. Over tundra, FT-AP tends to detect freeze onset 2–5 weeks earlier than FT-ESDR, likely due to FT sensitivity to the different frequencies used. Analysis with mean surface air temperature time series from six in situ meteorological stations shows that the main discrepancies between FT-AP and FT-ESDR are related to false frozen retrievals in summer for some regions with FT-AP. The Aquarius product is distributed by the U.S. National Snow and Ice Data Center (NSIDC) at https://nsidc.org/data/aq3_ft/versions/5 with the DOI https://doi.org/10.5067/OV4R18NL3BQR.

Prince, Michael↗

NASA NTRSDate not supplied

Gust Load Alleviation Control and Gust Estimation for a High Aspect Ratio Wing Wind Tunnel Model

This paper presents the gust load alleviation (GLA) study of the aspect ratio 13.5 Common Research Model (CRM) wind-tunnel model. This study details the design of the GLA controller in preparation for wind-tunnel testing in the Transonic Dynamics Tunnel at NASA Langley Research Center. An aeroservolastic (ASE) model was first reduced using a model reduction method that takes advantage of the sinusoidal steady-state response. Then, the reduced model was used to design an extended-state Kalman filter which estimates the states and the sinusoidal gust input. The GLA control was then derived using the optimal control solution to a multi-objective cost function. The results of the GLA controller indicate a 75.6% reduction in wing-root strain while maintaining robust stability margins. The final paper will include performance under sub-optimal conditions, e.g., sensor noise, uncertainty in gust frequency, etc..

Christopher Forte↗

NASA NTRSDate not supplied

Design Under Uncertainty for Conceptual Aircraft Design Leveraging Analytical Gradients

The purpose of this paper is to extend previously demonstrated methodologies for design under uncertainty, leveraging analytical gradients to higher fidelity analysis for use in conceptual aircraft design. Previous work developed methods to generate analytical derivatives through polynomial chaos expansion, eliminating the need to estimate derivatives via complex step or finite difference. In this research, the authors build upon the methods to include physics-based aircraft design codes for aircraft design under uncertainty. This extends the previous work’s case study, which employed analytical aerodynamics and Breguet range estimations for wing design, to a higher fidelity level. In addition, this work extends previous work on interface development between the Uncertainty Quantification with Polynomial Chaos Expansion (UQPCE) software and Model-Based Systems Analysis and Engineering (MBSA&E) frameworks. This paper will discuss the development work necessary to perform multidisciplinary design under uncertainty as well as demonstrate the mechanics of interfacing UQPCE and conceptual aircraft design tools such as NASA’s Aviary code. In a case study, a conceptual aircraft design under uncertainty was conducted and compared against a traditional deterministic design. When given information about the uncertainty space from UQPCE, the optimizer was able to shape the output distribution and produce a more robust design

UQ↗

NASA NTRSDate not supplied

Design Under Uncertainty for Conceptual Aircraft Design Leveraging Analytical Gradients

The purpose of this paper is to extend previously demonstrated methodologies for design under uncertainty, leveraging analytical gradients to higher fidelity analysis for use in conceptual aircraft design. Previous work developed methods to generate analytical derivatives through polynomial chaos expansion, eliminating the need to estimate derivatives via complex step or finite difference. In this research, the authors build upon the methods to include physics-based aircraft design codes for aircraft design under uncertainty. This extends the previous work’s case study, which employed analytical aerodynamics and Breguet range estimations for wing design, to a higher fidelity level. In addition, this work extends previous work on interface development between the Uncertainty Quantification with Polynomial Chaos Expansion (UQPCE) software and Model-Based Systems Analysis and Engineering (MBSA&E) frameworks. This paper will discuss the development work necessary to perform multidisciplinary design under uncertainty as well as demonstrate the mechanics of interfacing UQPCE and conceptual aircraft design tools such as NASA’s Aviary code. In a case study, a conceptual aircraft design under uncertainty was conducted and compared against a traditional deterministic design. When given information about the uncertainty space from UQPCE, the optimizer was able to shape the output distribution and produce a more robust design.

UQ↗

NASA NTRSDate not supplied

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↗

NASA NTRSDate not supplied

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↗

NASA NTRS2013

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

optimal control↗

NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗

NASA NTRS2014

Optimal Design of Calibration Signals in Space Borne Gravitational Wave Detectors

Future space borne gravitational wave detectors will require a precise definition of calibration signals to ensure the achievement of their design sensitivity. The careful design of the test signals plays a key role in the correct understanding and characterization of these instruments. In that sense, methods achieving optimal experiment designs must be considered as complementary to the parameter estimation methods being used to determine the parameters describing the system. The relevance of experiment design is particularly significant for the LISA Pathfinder mission, which will spend most of its operation time performing experiments to characterize key technologies for future space borne gravitational wave observatories. Here we propose a framework to derive the optimal signals in terms of minimum parameter uncertainty to be injected to these instruments during its calibration phase. We compare our results with an alternative numerical algorithm which achieves an optimal input signal by iteratively improving an initial guess. We show agreement of both approaches when applied to the LISA Pathfinder case.

LISA Path_nder mission↗

NASA NTRSDate not supplied

A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty

When allocating redundant effectors to virtual control commands, linear (generalized inverse) allocators have historically been used on aircraft and spacecraft. While simple to implement, generalized inverses are unable to realize a significant portion of the attainable moments. To address this drawback, the control allocation problem can also be formulated as a linear programming or quadratic programming problem and solved using convex optimization based solvers. These approaches have been shown to access a larger set of attainable moments, however, little work has been done to understand the performance of convex optimization-based control allocation in the presence of parametric model uncertainty. This paper seeks to compare the performance of several control allocation approaches, including two forms of generalized inverse allocators, the pseudo inverse and minimum-variance, and the linear programming and quadratic programming approach in the presence of parametric model uncertainty. The performance of these four allocators were tested on an aircraft model in the presence of realistic parametric model uncertainty and the convex optimization approaches were shown to outperform the generalized inverses.

Luke J Miller↗

NASA NTRS2021

Lila: Optimal Dispatching in Probabilistic Temporal Networks using Monte Carlo Tree Search

Executing a Probabilistic Simple Temporal Network (PSTN) amounts at scheduling, i.e. \textit{dispatch}, a set of events under time uncertainty. This constitutes a NP-hard online optimization problem. The right execution time must be dynamically assigned to each event of the PSTN such that the temporal constraints are met, whereas activity durations are progressively observed as the execution unfolds. We propose a dispatching algorithm based on Monte Carlo Tree Search, called Lila, with the following characteristics: (i) it is an anytime algorithm, both offline and online, proven asymptotically optimal; (ii) it returns the current probability of success, either before or at any moment during operations; (iii) it handles any possible continuous or discrete, even non-parametric, probability distributions, as well as inter-dependencies between random variables, exogenous and endogenous uncertainty; and (iv) can be easily extended to handle probabilistic external events, PSTNs with resources, PSTNs with cutoff times and precondition chains, etc. Lila is universal in the sense that it can handle any dispatching protocol, simply by specifying it to the algorithm. It has the unlimited flexibility offered by the simulation paradigm, whilst it asymptotically converges to optimal decisions and/or robustness approximations.

Chien, Steve A.↗

NASA NTRSDate not supplied

Copernicus-LinCov (COPCOV) Software Integration in Support of Robust Trajectory Optimization

Robust trajectory optimization is the process of optimizing a trajectory while accounting for system uncertainty due to a variety of potential error sources. This work highlights the development and features of a novel tool known as CopCov to support robust trajectory optimization efforts. CopCov acts as an interface between Copernicus, a generalized trajectory design and optimization tool, and LinCov, a linear covariance analysis tool. By having a direct interface between these two software packages, Copernicus can receive covariance information from LinCov through a direct feedback loop, thus enabling optimization of a trajectory that is robust to trajectory dispersions and navigation errors. This paper details the architecture of CopCov and its flexibility to operate under varying configurations, including with both tools running locally or alternatively with the tools communicating via a remote connection. Additionally, the CopCov tool is demonstrated on a simple Hohmann transfer reference trajectory with varying numbers of Trajectory Correction Maneuvers (TCMs) and varying problem formulations. This example scenario is used to highlight how the inclusion of the CopCov interface affects burn placement of both major burns and minor burns (i.e., TCMs) in the optimized solution. Results are compared against analytical solutions and against a Genetic Algorithm (GA) optimizer for independent verification and validation.

Copernicus↗