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Results for “Optimization Under Uncertainty”

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.

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NASA NTRSDate not supplied

Model Calibration for Cancer Risk Projections According to Uncertain Data

This paper presents forward and inverse formulations for the calibration of computational models according to uncertain data. Uncertainty in the data might be caused by a poor metrology system, measurement noise, missing or uncontrollable input variables, or by the inability to directly measure the inputs and/or outputs of interest. The forward approach performs the calibration in the space of the model’s output thereby requiring repeated model simulations. Conversely, the inverse approach leverages an ensemble of solutions to an inverse problem in order to perform the calibration in the space of the model’s parameters. As such, the computational demands of the inverse approach are considerably lower. These strategies are applied to the calibration of a radiation model that in-forms cancer risk projections for future deep space missions.

uncertainty quantification↗
NASA NTRS2006

Accommodating Sensor Uncertainty in the Cones Method: Polycones and Fuzzycones

The "cones method" is an analytical algorithm to combine a pair of angle observations into a common vector. Two new algorithms have been developed to optimize the "cones method" solutions when more than two observation angles are available and when estimates of measurement uncertainties can be made. The polycones algorithm consists of determining a simple weighted average of the solution vectors over all possible pairs of measurements with the weights determined from the measurement uncertainty. The Fuzzycones method finds the vector of maximum probability. Both of these methods have been implemented and tested and both reduce errors in computed vector positions.

Hashmall, Joseph A.↗
NASA NTRS2004

Radiometer Design Analysis Based Upon Measurement Uncertainty

This paper introduces a method for predicting the performance of a radiometer design based on calculating the measurement uncertainty. The variety in radiometer designs and the demand for improved radiometric measurements justify the need for a more general and comprehensive method to assess system performance. Radiometric resolution, or sensitivity, is a figure of merit that has been commonly used to characterize the performance of a radiometer. However when evaluating the performance of a calibration design for a radiometer, the use of radiometric resolution has limited application. These limitations are overcome by considering instead the measurement uncertainty. A method for calculating measurement uncertainty for a generic radiometer design including its calibration algorithm is presented. The result is a generalized technique by which system calibration architectures and design parameters can be studied to optimize instrument performance for given requirements and constraints. Example applications demonstrate the utility of using measurement uncertainty as a figure of merit.

Racette, Paul E.↗
NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗
NASA NTRS1976

Reduced state feedback gain computation

Because application of conventional optimal linear regulator theory to flight controller design requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. Therefore, a stochastic linear model that was developed is presented which accounts for aircraft parameter and initial uncertainty, measurement noise, turbulence, pilot command and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Kaufman, H.↗
NASA NTRS1998

Sliding Mode Thermal Control System for Space Station Furnace Facility

The decoupled control of the nonlinear, multiinput-multioutput, and highly coupled space station furnace facility (SSFF) thermal control system is addressed. Sliding mode control theory, a subset of variable-structure control theory, is employed to increase the performance, robustness, and reliability of the SSFF's currently designed control system. This paper presents the nonlinear thermal control system description and develops the sliding mode controllers that cause the interconnected subsystems to operate in their local sliding modes, resulting in control system invariance to plant uncertainties and external and interaction disturbances. The desired decoupled flow-rate tracking is achieved by optimization of the local linear sliding mode equations. The controllers are implemented digitally and extensive simulation results are presented to show the flow-rate tracking robustness and invariance to plant uncertainties, nonlinearities, external disturbances, and variations of the system pressure supplied to the controlled subsystems.

Jackson Mark E.↗
NASA NTRS1989

Autonomous frequency domain identification: Theory and experiment

The analysis, design, and on-orbit tuning of robust controllers require more information about the plant than simply a nominal estimate of the plant transfer function. Information is also required concerning the uncertainty in the nominal estimate, or more generally, the identification of a model set within which the true plant is known to lie. The identification methodology that was developed and experimentally demonstrated makes use of a simple but useful characterization of the model uncertainty based on the output error. This is a characterization of the additive uncertainty in the plant model, which has found considerable use in many robust control analysis and synthesis techniques. The identification process is initiated by a stochastic input u which is applied to the plant p giving rise to the output. Spectral estimation (h = P sub uy/P sub uu) is used as an estimate of p and the model order is estimated using the produce moment matrix (PMM) method. A parametric model unit direction vector p is then determined by curve fitting the spectral estimate to a rational transfer function. The additive uncertainty delta sub m = p - unit direction vector p is then estimated by the cross spectral estimate delta = P sub ue/P sub uu where e = y - unit direction vectory y is the output error, and unit direction vector y = unit direction vector pu is the computed output of the parametric model subjected to the actual input u. The experimental results demonstrate the curve fitting algorithm produces the reduced-order plant model which minimizes the additive uncertainty. The nominal transfer function estimate unit direction vector p and the estimate delta of the additive uncertainty delta sub m are subsequently available to be used for optimization of robust controller performance and stability.

Yam, Yeung↗
NASA NTRS1990

A Boltzmann machine for the organization of intelligent machines

A three-tier structure consisting of organization, coordination, and execution levels forms the architecture of an intelligent machine using the principle of increasing precision with decreasing intelligence from a hierarchically intelligent control. This system has been formulated as a probabilistic model, where uncertainty and imprecision can be expressed in terms of entropies. The optimal strategy for decision planning and task execution can be found by minimizing the total entropy in the system. The focus is on the design of the organization level as a Boltzmann machine. Since this level is responsible for planning the actions of the machine, the Boltzmann machine is reformulated to use entropy as the cost function to be minimized. Simulated annealing, expanding subinterval random search, and the genetic algorithm are presented as search techniques to efficiently find the desired action sequence and illustrated with numerical examples.

Moed, Michael C.↗
NASA NTRS1993

Robust neighboring extremal guidance for the advanced launch system

With the availability of modern flight computers, realtime neighboring extremal guidance seems feasible. To overcome sensitivity to unknown system parameters and environmental uncertainties, a robust neighboring extremal guidance scheme is proposed. About the optimal trajectory, the accessory problem in the calculus of variations is formed, generating a quadratic cost criterion in the perturbed states and controls. By formulating a disturbance attenuation problem based upon the second variation cost criterion, a differential game is formulated. The game theoretic cost criterion is minimized with respect to the perturbed control but maximized with respect to the unknown parameters in the linearized dynamics. The resulting differential game problem gives rise to a two-point boundary-value problem solved using the sweep method. The sweep method solution provides a linear robust neighboring extremal guidance scheme that is applied to the Advanced Launch System.

Bain, John↗
NASA NTRS1999

Systematic Differences between Satellite-Based Presipitation Climatologies over the Tropical Oceans

Since the beginning of the World Climate Research Program's Global Precipitation Climatology Project (GPCP) satellite remote sensing of precipitation has made dramatic improvements, particularly for tropical regions. Data from microwave and infrared sensors now form the most critical input to precipitation data sets and can be calibrated with surface gauges to so that the strengths of each data source can be maximized in some statistically optimal sense. It is clear however that there still remain significant uncertainties with satellite precipitation retrievals which limit their usefulness for many purposes. Systematic differences i'A tropical precipitation estimates have been brought to light in comparison activities such as the GPCP Algorithm Intercomparison Project and more recent Wetnet Precipitation Intercomparison Project 3. These uncertainties are assuming more importance because of the demands for validation associated with global climate modeling and data assimilation methodologies. The objective of the present study is to determine the physical basis for systematic differences in spatial structure of tropical precipitation as portrayed by several different satellite-based data sets. The study is limited to oceanic regions only and deals primarily with aspects of spatial variability. We are specifically interested in why MSU channel 1 and GPI precipitation differences are so striking over the Eastern Pacific ITCZ and why they both differ from other microwave emission-based precipitation estimates from SSM/I and a scattering-based deep convective ice index from MSU channel 2. Our results to date have shown that MSU channel I precipitation estimates are biased high over the Eastern Pacific ITCZ because of two factors: (1) the hypersensitivity of this frequency to cloud water in contrast to falling rain drops, and (2) unaccounted for scattering effects by precipitation-size ice which depresses the signal of the liquid water emission. Likewise, cold cloud top climatologies such as the GPI show an excess (a deficit) in estimated rainfall over the E. Pacific ITCZ (Warm Pool region). We show that these algorithms need to account for regionally varying heights (or temperatures) at which tropical convection detrains to form cirrus shields. A second objective we pursue is to identify variations in the macroscale cloud physical and thermodynamic properties of precipitation regimes" and relate these differences to tropical dynamical mechanisms of tropical heat and moisture balance. Finally, we interpret the algorithm differences and their associations with tropical dynamics in terms of WCRP GPCP goals for constructing precipitation climatologies.

Robertson, Frankin R.↗
NASA NTRS2003

Response Surface Methods for Spatially-Resolved Optical Measurement Techniques

Response surface methods (or methodology), RSM, have been applied to improve data quality for two vastly different spatial ly-re solved optical measurement techniques. In the first application, modern design of experiments (MDOE) methods, including RSM, are employed to map the temperature field in a direct-connect supersonic combustion test facility at NASA Langley Research Center. The laser-based measurement technique known as coherent anti-Stokes Raman spectroscopy (CARS) is used to measure temperature at various locations in the combustor. RSM is then used to develop temperature maps of the flow. Even though the temperature fluctuations at a single point in the flowfield have a standard deviation on the order of 300 K, RSM provides analytic fits to the data having 95% confidence interval half width uncertainties in the fit as low as +/-30 K. Methods of optimizing future CARS experiments are explored. The second application of RSM is to quantify the shape of a 5-meter diameter, ultra-light, inflatable space antenna at NASA Langley Research Center.

Danehy, P. M.↗
NASA NTRS2014

Extravehicular Activity Asteroid Exploration and Sample Collection Capability

One of the challenging primary objectives associated with NASA's Asteroid Redirect Crewed Mission (ARCM) is to demonstrate deep space Extravehicular Activity (EVA) and tools and to obtain asteroid samples to return to Earth for further study. Prior Shuttle and International Space Station (ISS) spacewalks have benefited from engineered EVA interfaces which have been designed and manufactured on Earth. Rigid structurally mounted handrails, and tools with customized interfaces and restraints optimize EVA performance. For ARCM, EVA complexity increases due to the uncertainty of the asteroid properties. The variability of rock size, shape and composition, as well as behavior of the asteroid capture mechanism will complicate EVA translation, tool restraint, and body stabilization. The unknown asteroid hardness and brittleness will complicate tool use. The rock surface will introduce added safety concerns for cut gloves and debris control. Feasible solutions to meet ARCM EVA objectives were identified using experience gained during Apollo, Shuttle, and ISS EVAs, terrestrial mountaineering practices, NASA Extreme Environment Mission Operations (NEEMO) 16 mission, and during Neutral Buoyancy Laboratory testing in the Modified Advanced Crew Escape Suit (MACES) suit. This paper will summarize the overall operational concepts for conducting EVAs for the ARCM mission including translation paths and body restraint methods, potential tools used to extract the samples, design implications for the Asteroid Redirect Vehicle (ARV) for EVA, and the results of early development testing of potential EVA tasks.

Sipila, Stephanie A.↗
NASA NTRS2014

Extravehicular Activity Asteroid Exploration and Sample Collection Capability

One of the challenging primary objectives associated with NASA's Asteroid Redirect Crewed Mission (ARCM) is to demonstrate deep space Extravehicular Activity (EVA) and tools and to obtain asteroid samples to return to Earth for further study. Prior Shuttle and International Space Station (ISS) spacewalks have benefited from engineered EVA interfaces which have been designed and manufactured on Earth. Rigid structurally mounted handrails, and tools with customized interfaces and restraints optimize EVA performance. For ARCM, EVA complexity increases due to the uncertainty of the asteroid properties. The variability of rock size, shape and composition, as well as behavior of the asteroid capture mechanism will complicate EVA translation, tool restraint, and body stabilization. The unknown asteroid hardness and brittleness will complicate tool use. The rock surface will introduce added safety concerns for cut gloves and debris control. Feasible solutions to meet ARCM EVA objectives were identified using experience gained during Apollo, Shuttle, and ISS EVAs, terrestrial mountaineering practices, NASA Extreme Environment Mission Operations (NEEMO) 16 mission, and during Neutral Buoyancy Laboratory testing in the Modified Advanced Crew Escape Suit (MACES) suit. This paper will summarize the overall operational concepts for conducting EVAs for the ARCM mission including translation paths and body restraint methods, potential tools used to extract the samples, design implications for the Asteroid Redirect Vehicle (ARV) for EVA, and the results of early development testing of potential EVA tasks.

Sipila, Stephanie A.↗
NASA NTRS2021

Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model

The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. The combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.

Robert S. Schrom↗
NASA NTRS2008

Science Goals in Radiation Protection for Exploration

Space radiation presents major challenges to future missions to the Earth s moon or Mars. Health risks of concern include cancer, degenerative and performance risks to the central nervous system, heart and lens, and the acute radiation syndromes. The galactic cosmic rays (GCR) contain high energy and charge (HZE) nuclei, which have been shown to cause qualitatively distinct biological damage compared to terresterial radiation, such as X-rays or gamma-rays, causing risk estimates to be highly uncertain. The biological effects of solar particle events (SPE) are similar to terresterial radiation except for their biological dose-rate modifiers; however the onset and size of SPEs are difficult to predict. The high energies of GCR reduce the effectiveness of shielding, while SPE s can be shielded however the current gap in radiobiological knowledge hinders optimization. Methods used to project risks on Earth must be modified because of the large uncertainties in projecting health risks from space radiation, and thus impact mission requirements and costs. We describe NASA s unique approach to radiation safety that applies probabilistic risk assessments and uncertainty based criteria within the occupational health program for astronauts and to mission design. The two terrestrial criteria of a point estimate of maximum acceptable level of risk and application of the principle of As Low As Reasonably Achievable (ALARA) are supplemented by a third requirement that protects against risk projection uncertainties using the upper 95% confidence level (CL) in radiation risk projection models. Exploration science goals in radiation protection are centered on ground-based research to achieve the necessary biological knowledge, and in the development of new technologies to improve SPE monitoring and optimize shielding. Radiobiology research is centered on a ground based program investigating the radiobiology of high-energy protons and HZE nuclei at the NASA Space Radiation Laboratory (NSRL) located at DoE s Brookhaven National Laboratory in Upton, NY. We describe recent NSRL results that are closing the knowledge gap in HZE radiobiology and improving exploration risk estimates. Linking probabilistic risk assessment to research goals makes it possible to express risk management objectives in terms of quantitative metrics, which include the number of days in space without exceeding a given risk level within well defined confidence limits, and probabilistic assessments of the effectiveness of design trade spaces such as material type, mass, solar cycle, crew selection criteria, and biological countermeasures. New research in SPE alert and risk assessment, individual radiation sensitivity, and biological countermeasure development are described.

Cucinotta, Francs A.↗
NASA NTRS2018

Development of a Multi-Phase Mission Planning Tool for NASA X-57 Maxwell

The physical design and operation of electric aircraft like NASA Maxwell X-57 are significantly different than conventionally fueled aircraft. Operational optimization will require close coupling of aerodynamics, propulsion, and power. To address the uncertainty of electric aircraft operation, a system level Mission Planning Tool is developed to simulate all aircraft trajectory phases: taxi, motor run-up, takeoff, climb, cruise, and descent. The Mission Planning Tool captures performance parameters at each point of the trajectory including battery state of charge, the temperatures of components in the electrical system, and propulsion system thrust. This work describes the modeling of each mission phase, and compares the results of simulating a user-specified trajectory, and using a collocated optimal control approach to determine an optimal trajectory. The results show that optimization of the mission show a significant increase in the final battery state of charge over the user- specified simulation strategy. These results will inform the operation of the NASA Maxwell X-57 test flights that will take place this year.

Schnulo, Sydney L.↗
NASA NTRS2008

Risk Analysis for Resource Planning Optimization

The main purpose of this paper is to introduce a risk management approach that allows planners to quantify the risk and efficiency tradeoff in the presence of uncertainties, and to make forward-looking choices in the development and execution of the plan. Demonstrate a planning and risk analysis framework that tightly integrates mathematical optimization, empirical simulation, and theoretical analysis techniques to solve complex problems.

resource planning optimization↗
NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗