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NASA NTRS1993

Uncertainty relations, zero point energy and the linear canonical group

The close relationship between the zero point energy, the uncertainty relations, coherent states, squeezed states, and correlated states for one mode is investigated. This group-theoretic perspective enables the parametrization and identification of their multimode generalization. In particular the generalized Schroedinger-Robertson uncertainty relations are analyzed. An elementary method of determining the canonical structure of the generalized correlated states is presented.

Sudarshan, E. C. G.↗

NASA NTRS1994

The sensitivity to parametric variation in direct minimization techniques

Solutions of some objective analysis techniques are known to depend upon the subjective values of internal parameters. The change in the solution per change in the parameter is the sensitivity. Parameters with low sensitivity can be varied with large increments during preliminary searches for near-optimal parameter values. Only terms with high sensitivity must be thoroughly investigated once the parameters are determined to be close to optimal. Both absolute and relative sensitivities are discussed and a sensitivity-based definition of the solution uncertainty is proposed. The sensitivity of direct minimization analysis to parametric variation is evaluated using a set of 'response functions' that characterize different aspects of the solution. It is shown that solutions of direct minimization techniques have low absolute sensitivity. Two examples are used to illustrate the usefulness of the technique. Both involved measurements of air-sea quantities (e.g., wind stress and latent heat flux) from a variety of data sources using a direct minimization technique. The examples demonstrate that sensitivity analysis is capable of quantifying regional sensitivities as well as indicating the magnitude and relationship between the various parameters.

Meyers, S. D.↗

NASA NTRS2022

Are Soybean Models Ready for Climate Change Food Impact Assessments?

An accurate estimation of crop yield under climate change scenarios is essential to quantify our ability to feed a growing population and develop agronomic adaptations to meet future food demand. A coordinated evaluation of yield simulations from process-based eco-physiological models for climate change impact assessment is still missing for soybean, the most widely grown grain legume and the main source of protein in our food chain. In this first soybean multi-model study, we used ten prominent models capable of simulating soybean yield under varying temperature and atmospheric CO 2 concentration [CO 2 ] to quantify the uncertainty in soybean yield simulations in response to these factors. Models were first parametrized with high quality measured data from five contrasting environments. We found considerable variability among models in simulated yield responses to increasing temperature and [CO 2 ]. For example, under a + 3 °C temperature rise in our coolest location in Argentina, some models simulated that yield would reduce as much as 24%, while others simulated yield increases up to 29%. In our warmest location in Brazil, the models simulated a yield reduction ranging from a 38% decrease under + 3 °C temperature rise to no effect on yield. Similarly, when increasing [CO 2 ] from 360 to 540 ppm, the models simulated a yield increase that ranged from 6% to 31%. Model calibration did not reduce variability across models but had an unexpected effect on modifying yield responses to temperature for some of the models. The high uncertainty in model responses indicates the limited applicability of individual models for climate change food projections. However, the ensemble mean of simulations across models was an effective tool to reduce the high uncertainty in soybean yield simulations associated with individual models and their parametrization. Ensemble, ensemble mean yield responses to temperature and [CO 2 ] were similar to those reported from the literature. Our study is the first demonstration of the benefits achieved from using an ensemble of grain legume models for climate change food projections, and highlights that further soybean model development with experiments under elevated [CO 2 ] and temperature is needed to reduce the uncertainty from the individual models.

Agricultural Model Inter-comparison and Improvemen↗

NASA NTRS1973

Statistical error model for a solar electric propulsion thrust subsystem

The solar electric propulsion thrust subsystem statistical error model was developed as a tool for investigating the effects of thrust subsystem parameter uncertainties on navigation accuracy. The model is currently being used to evaluate the impact of electric engine parameter uncertainties on navigation system performance for a baseline mission to Encke's Comet in the 1980s. The data given represent the next generation in statistical error modeling for low-thrust applications. Principal improvements include the representation of thrust uncertainties and random process modeling in terms of random parametric variations in the thrust vector process for a multi-engine configuration.

Bantell, M. H.↗

NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 2

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean, the variance, and the range of the model's parameter, thus of the output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, is bounded rigorously.

Crespo, Luis G.↗

NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 1

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean and the variance of the model's parameters, thus of the predicted output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, can be bounded tightly and rigorously.

Crespo, Luis G.↗

NASA NTRS1992

A stochastic damage model for the rupture prediction of a multi-phase solid. I - Parametric studies. II - Statistical approach

A stochastic damage model for predicting the rupture of a brittle multiphase material is developed, based on the microcrack-macrocrack interaction. The model, which incorporates uncertainties in locations, orientations, and numbers of microcracks, characterizes damage by microcracking and fracture by macrocracking. A parametric study is carried out to investigate the change of the stress intensity at the macrocrack tip by the configuration of microcracks. The inherent statistical distribution of the fracture toughness arising from the intrinsic random nature of microcracks is explored using a statistical approach. For this purpose, a computer simulation model is introduced, which incorporates a statistical characterization of geometrical parameters of a random microcrack array.

Lua, Yuan J.↗

NASA NTRS1982

Study of aerodynamic technology for single-cruise engine V/STOL fighter/attack aircraft

A conceptual design analysis is performed on a single engine V/STOL supersonic fighter/attack concept powered by a series flow tandem fan propulsion system. Forward and aft mounted fans have independent flow paths for V/STOL operation and series flow in high speed flight. Mission, combat and V/STOL performance is calculated. Detailed aerodynamic estimates are made and aerodynamic uncertainties associated with the configuration and estimation methods identified. A wind tunnel research program is developed to resolve principal uncertainties and establish a data base for the baseline configuration and parametric variations.

Driggers, H. H.↗

NASA NTRS1992

On slowly varying systems - l-infinity to l-infinity performance and implications to robust adaptive control

The authors present a result on the l-infinity to l-infinity performance of slowly time varying systems. In particular, it is shown that the performance of such systems cannot be much worse than that of the frozen-time systems which are time invariant. This result is used to characterize a class of indirect adaptive controllers that can stabilize a time-invariant system subjected to both parametric and l-infinity to l-infinity bounded unstructured uncertainty. Pertaining to this class of controllers, a particular indirect adaptive scheme is proposed that provides the greatest upper bound on the size of the unstructured uncertainty for which stability is ensured.

Voulgaris, Petros G.↗

NASA NTRS1995

A Globally Optimal Minimax Solution for Spectral Overbounding and Factorization

In this paper, an algorithm is introduced to find a minimum phase transfer function of specified order whose magnitude "tightly" overbounds a specified real-valued nonparametric function of frequency. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments and/or plant modeling) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation).

Scheid, Robert E.↗

NASA NTRS2001

Comparison of Shortwave Cloud Radiative Forcing Derived from ARM SGP Surface and GOES-8 Satellite Measurements During ARESE I and ARESE II

One of the objectives of the ARM Enhanced Shortwave Experiment (ARESE) is to investigate the absorption of solar radiation by clouds over the ARM Southern Great Plains central facility. A variety of techniques employing various combinations Of Surface, aircraft, and satellite data have been used to estimate the absorption empirically. During ARESE-I conducted during fall 1995, conflicting results were produced from different analyses of the combined datasets leading to the need for a more controlled experiment. ARESE-II was conducted during spring 2000. Improved calibrations, different sampling strategies, and broadband satellite data were all available to minimize some of the sources of uncertainty in the data. In this paper, cloud absorption or its parametric surrogates (e.g., Cess et al. 1995) are derived from collocated and coincident surface and satellite radiometer data from both ARESE-I and ARESE-II using the latest satellite and surface instrument calibrations.

Rapp, A. D.↗

NASA NTRS1992

Autonomous Frequency-Domain Indentification

Test and data-processing system determines plant models and uncertainties. Integrated system of methods, digital signal-processing, and algorithms identifies parametric model of large, flexible structures. Experiments in development of system conducted on laboratory model intended to represent large space antenna or flexible spacecraft. Also applicable to many terrestrial systems, robust control of dynamic plants and processes, robust control of systems about which knowledge uncertain or incomplete, decentralized control, and knowledge-based control systems.

Mettler, Edward↗

NASA NTRS1998

Analytical and Experimental Characterization of a Linear-Array Thermopile Scanning Radiometer for Geo-Synchronous Earth Radiation Budget Applications

The Thermal Radiation Group, a laboratory in the department of Mechanical Engineering at Virginia Polytechnic Institute and State University, is currently working towards the development of a new technology for cavity-based radiometers. The radiometer consists of a 256-element linear-array thermopile detector mounted on the wall of a mirrored wedgeshaped cavity. The objective of this research is to provide analytical and experimental characterization of the proposed radiometer. A dynamic end-to-end opto-electrothermal model is developed to simulate the performance of the radiometer. Experimental results for prototype thermopile detectors are included. Also presented is the concept of the discrete Green's function to characterize the optical scattering of radiant energy in the cavity, along with a data-processing algorithm to correct for the scattering. Finally, a parametric study of the sensitivity of the discrete Green's function to uncertainties in the surface properties of the cavity is presented.

Sorensen, Ira J.↗

NASA NTRS2005

Scramjet Development Tests Supporting the Mach 10 Flight of the X-43

The Hyper-X Project s successful third flight of the X-43 at near Mach 10 in 2004 proved the potential for airbreathing propulsion at hypersonic speeds. The engine flowpath used in the X-43 research vehicle was developed and evaluated in a systematic series of ground tests in the NASA HyPulse Shock Tunnel at conditions duplicating Mach 10 flight using a full scale height, partial width engine model of the flight engine. Tests were conducted over a range of equivalence ratios from 0.8 to 1.6 using hydrogen and a mixture of two-percent silane in hydrogen fuels. Silane gas was used as an ignition aid during the short duration of the pulse facility tests. Variation of the engine inflow conditions, pressure, temperature, and Mach number, were parametrically varied during the test entries to broaden the database over the expected uncertainty in the flight conditions. A review of the ground test technique and comparisons of the ground test pressures along with selected flight data are presented.

Rogers, R. C.↗

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 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 NTRS2007

Non-Parametric Collision Probability for Low-Velocity Encounters

An implicit, but not necessarily obvious, assumption in all of the current techniques for assessing satellite collision probability is that the relative position uncertainty is perfectly correlated in time. If there is any mis-modeling of the dynamics in the propagation of the relative position error covariance matrix, time-wise de-correlation of the uncertainty will increase the probability of collision over a given time interval. The paper gives some examples that illustrate this point. This paper argues that, for the present, Monte Carlo analysis is the best available tool for handling low-velocity encounters, and suggests some techniques for addressing the issues just described. One proposal is for the use of a non-parametric technique that is widely used in actuarial and medical studies. The other suggestion is that accurate process noise models be used in the Monte Carlo trials to which the non-parametric estimate is applied. A further contribution of this paper is a description of how the time-wise decorrelation of uncertainty increases the probability of collision.

Carpenter, J. Russell↗

NASA NTRS1976

Search for evidence of a preferred reference frame

Some gravitation theories, in contradiction to general relativity, allow the existence of a universal preferred reference frame. Also allowed in some theories can be a galaxy-induced anisotropy of the gravitation constant. The parametrized post-Newtonian theory predicts that in these cases, there will be anomalous earth-tide amplitudes at specific frequencies. An 18-month earth-tide record obtained with the superconducting gravimeter has been examined for such anomalies. The data allow for the existence of such effects but cannot prove it because of uncertainties concerning geophysical perturbations of the tides. However, an upper limit to the preferred frame parameter of the parametrized post-Newtonian formalism is established at 0.002. The results also set a less rigorous limit on the anisotropy parameter, of the order of 0.001.

Warburton, R. J.↗