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NASA NTRS1978

On-line parameter estimation using a high sensitivity estimator

An on-line parameter identification method is presented. The method is based on a recursive formulation of the maximum likelihood method, with a significant modification on the gains of the state estimator. In the conventional maximum likelihood method, the Kalman gains are used in the state estimator. This produces unbiased, minimum variance parameter estimates in the presence of process noise and measurement noise, but it also slows the convergence rate when the identification is done on-line. Here we suggest choosing the gains to maximize a measure of the sensitivities of the state estimates to parameter variations. One such criterion is to minimize the trace of the inverse information matrix. This increases the convergence rate significantly. After one or two time constants, the gains are switched to the Kalman values to assure unbiased, minimum-variance estimates. The state estimate will initially be nonoptimal, and may not be adequate for control purposes. In this case, a parallel Kalman filter which uses the identifier's parameter estimates can be used. This method is applied here for the identification of a simple first-order system, and for the identification of short-period stability derivatives of an F-8 aircraft from simulated data.

Mishne, D.↗
NASA NTRS1970

Estimating sensitivity of vacuum gages

Gage sensitivity for a particular gas is estimated using the known performance of the gage with a reference gas /nitrogen/ and employing several empirical rules which have usable accuracy. Relative gage sensitivities have been estimated for over 100 gases and vapors.

Summers, R. L.↗
NASA NTRS2020

Comparison of Equilibrium Climate Sensitivity Estimates From Slab Ocean, 150‐Year, and Longer Simulations

We compare equilibrium climate sensitivity (ECS) estimates from pairs of long (≥ 800‐year) control and abruptly quadrupled CO2 simulations with shorter (150, 300 year) coupled atmosphere‐ocean simulations and Slab Ocean Models (SOM). Consistent with previous work, ECS estimates from shorter coupled simulations based on annual averages for years 1‐150 underestimate those from SOM (‐8% ± 13%) and long (‐14% ± 8%) simulations. Analysis of only years 21‐150 improved agreement with SOM (‐2% ± 14%) and long (‐8% ± 10%) estimates. Use of pentadal averages for years 51‐150 results in improved agreement with long simulations (‐4% ± 11%). While ECS estimates from current generation US models based on SOM and coupled annual averages of years 1‐150 range from 2.6°C to 5.3°C, estimates based longer simulations of the same models range from 3.2°C to 7.0°C. Such variations between methods argues for caution in comparison and interpretation of ECS estimates across models.

Climate sensitivity↗
NASA NTRS2019

Equilibrium Climate Sensitivity Estimated by Equilibrating Climate Models

The methods to quantify equilibrium climate sensitivity are still debated. We collect millennial length simulations of coupled climate models and show that the global mean equilibrium warming is higher than those obtained using extrapolation methods from shorter simulations. Specifically, 27 simulations with 15 climate models forced with a range of CO2 concentrations show a median 17% larger equilibrium warming than estimated from the first 150 years of the simulations. The spatial patterns of radiative feedbacks change continuously, in most regions reducing their tendency to stabilizing the climate. In the equatorial Pacific, however, feedbacks become more stabilizing with time. The global feedback evolution is initially dominated by the tropics, with eventual substantial contributions from the midlatitudes. Time dependent feedbacks underscore the need of a measure of climate sensitivity that accounts for the degree of equilibration, so that models, observations, and paleo proxies can be adequately compared and aggregated to estimate future warming.

Maria Rugenstein↗
NASA NTRS1989

An investigation of new methods for estimating parameter sensitivities

The method proposed for estimating sensitivity derivatives is based on the Recursive Quadratic Programming (RQP) method and in conjunction a differencing formula to produce estimates of the sensitivities. This method is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RQP algorithm. Initial testing on a test set with known sensitivities demonstrates that the method can accurately calculate the parameter sensitivity.

Beltracchi, Todd J.↗
NASA NTRS1988

An investigation of new methods for estimating parameter sensitivities

Parameter sensitivity is defined as the estimation of changes in the modeling functions and the design variables due to small changes in the fixed parameters of the formulation. There are currently several methods for estimating parameter sensitivities requiring either difficult to obtain second order information, or do not return reliable estimates for the derivatives. Additionally, all the methods assume that the set of active constraints does not change in a neighborhood of the estimation point. If the active set does in fact change, than any extrapolations based on these derivatives may be in error. The objective here is to investigate more efficient new methods for estimating parameter sensitivities when the active set changes. The new method is based on the recursive quadratic programming (RQP) method and in conjunction a differencing formula to produce estimates of the sensitivities. This is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RPQ algorithm. Inital testing on a test set with known sensitivities demonstrates that the method can accurately calculate the parameter sensitivity. To handle changes in the active set, a deflection algorithm is proposed for those cases where the new set of active constraints remains linearly independent. For those cases where dependencies occur, a directional derivative is proposed. A few simple examples are included for the algorithm, but extensive testing has not yet been performed.

Beltracchi, Todd J.↗
NASA NTRS1975

Bayesian estimation - A sensitivity analysis

The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by assuming the existence of a true prior which is different in form from that of the assigned prior distribution. By using mean-squared error as a measure of performance, the ensuing Bayes decision function is compared to the corresponding minimum variance unbiased estimator. Results indicate that the Bayes estimator is largely robust to deviations from the assigned prior and remains squared-error superior to the MVU type within a broad region.

Canavos, G. C.↗
NASA NTRS1971

A parametric study of motor starting for a 2- to 10-kilowatt Brayton power system

A study of the motor starting of a Brayton cycle power system was conducted to provide estimates of system sensitivity to several controllable parameters. These sensitivity estimates were used as a basis for selection of an optimum motor-start scheme to be implemented on the 2- to 10-kilowatt Brayton power system designed and presently under test. The studies were conducted with an analog simulation of the Brayton power system and covered a range of frequencies from 400 Hz (33 percent design) to 1200 Hz (design), voltage-to-frequency ratios of 0.050 (50 percent design) to 0.100 (design), turbine-inlet temperatures of 800 K (1440 R, 70 percent design) to 1140 K (2060 deg R, design), and prestart pressure levels of 14.5 psia to 29.0 psia. These studies have shown the effect of selected system variables on motor starting. The final selection of motor-start variables can therefore be made on the basis of motor-start inverter complexity, battery size and weight, desired steady-state pressure level after startup, and other operational limitations. In general, the study showed the time required for motor starting to be inversely proportional to motor frequency, voltage, turbine-inlet temperature, and pressure level. An increase in any of these parameters decreases startup time.

Cantoni, D. A.↗
NASA NTRSDate not supplied

Science Yield Estimates and Sensitivities With the AstroPIC Integrated Photonic Coronagraph for the Habitable Worlds Observatory

The Habitable Worlds Observatory (HWO) flagship has a goal to survey ~100 of the nearest stellar systems and their habitable zones in order to detector and spectroscopically characterize ~25 potentially “Earth-like planets” (or “Exoearths”). The HWO telescope will feature a >6-m diameter aperture and a coronagraph that will suppress starlight by ten orders of magnitude to enable the detection and characterization of Earth analogues in the habitable zone. Three Exploratory Analytic Cases (EACs) are currently considering different aperture configurations for HWO including on-axis and off-axis apertures and both different hexagonal and keystone segmentation configurations. Photonic Integrated Circuits (PICs) offer a path to miniaturize traditional, bulk optics coronagraph functionality reducing risk margins and increasing mission science exoearth yields for the HWO mission. We have developed a simulation pipeline that enables evaluation of the AstroPIC photonic integrated coronagraph through to estimates mission yields. We present sensitivities to aberrations for different types of segmentation and low-order aberrations for HWO EACs demonstrating that AstroPIC is suitable for both on-axis and off-axis configurations. We perform a parametric sweep of the exoearth science yield sensitivities in terms of key coronagraph parameters including coronagraphic end-to-end throughput, inner working angle, robustness to aberrations, and bandwidth. We consider both a hybrid and a pure photonic architecture; a pure integrated photonic architecture provides the greatest potential in science yield improvements, although a hybrid PIC limited in its numbers of modes can provide complementary science to a traditional, bulk-optic coronagraph and increasing the estimated science yield when operated jointly.

Photonics↗
NASA NTRS1989

An investigation of using an RQP based method to calculate parameter sensitivity derivatives

Estimation of the sensitivity of problem functions with respect to problem variables forms the basis for many of our modern day algorithms for engineering optimization. The most common application of problem sensitivities has been in the calculation of objective function and constraint partial derivatives for determining search directions and optimality conditions. A second form of sensitivity analysis, parameter sensitivity, has also become an important topic in recent years. By parameter sensitivity, researchers refer to the estimation of changes in the modeling functions and current design point due to small changes in the fixed parameters of the formulation. Methods for calculating these derivatives have been proposed by several authors (Armacost and Fiacco 1974, Sobieski et al 1981, Schmit and Chang 1984, and Vanderplaats and Yoshida 1985). Two drawbacks to estimating parameter sensitivities by current methods have been: (1) the need for second order information about the Lagrangian at the current point, and (2) the estimates assume no change in the active set of constraints. The first of these two problems is addressed here and a new algorithm is proposed that does not require explicit calculation of second order information.

Beltracchi, Todd J.↗
NASA NTRS1984

Maximum likelihood algorithm using an efficient scheme for computing sensitivities and parameter confidence intervals

Improved techniques for estimating airplane stability and control derivatives and their standard errors are presented. A maximum likelihood estimation algorithm is developed which relies on an optimization scheme referred to as a modified Newton-Raphson scheme with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared to integrating the analytically-determined sensitivity equations or using a finite difference scheme. An aircraft estimation problem is solved using real flight data to compare MNRES with the commonly used modified Newton-Raphson technique; MNRES is found to be faster and more generally applicable. Parameter standard errors are determined using a random search technique. The confidence intervals obtained are compared with Cramer-Rao lower bounds at the same confidence level. It is observed that the nonlinearity of the cost function is an important factor in the relationship between Cramer-Rao bounds and the error bounds determined by the search technique.

Murphy, P. C.↗
NASA NTRS2015

Implications for Climate Sensitivity from the Response to Individual Forcings

Climate sensitivity to doubled CO2 is a widely-used metric of the large-scale response to external forcing. Climate models predict a wide range for two commonly used definitions: the transient climate response (TCR: the warming after 70 years of CO2 concentrations that riseat 1 per year), and the equilibrium climate sensitivity (ECS: the equilibrium temperature change following a doubling of CO2 concentrations). Many observational datasets have been used to constrain these values, including temperature trends over the recent past 16, inferences from paleo-climate and process-based constraints from the modern satellite eras. However, as the IPCC recently reported different classes of observational constraints produce somewhat incongruent ranges. Here we show that climate sensitivity estimates derived from recent observations must account for the efficacy of each forcing active during the historical period. When we use single forcing experiments to estimate these efficacies and calculate climate sensitivity from the observed twentieth-century warming, our estimates of both TCR and ECS are revised upward compared to previous studies, improving the consistency with independent constraints.

Sensitivity↗
NASA NTRS1991

Constant frequency pulsed phase-locked-loop instrument for measurement of ultrasonic velocity

A new instrument based on a constant-frequency pulsed phase-locked-loop (CFPPLL) concept has been developed to accurately measure the ultrasonic wave velocity in liquids and changes in ultrasonic wave velocity in solids and liquids. An analysis of the system shows that it is immune to many of the frequency-dependent effects that plague other techniques. Measurements of the sound velocity in ultrapure water are used to confirm the analysis. The results are in excellent agreement with values from the literature, and establish that the CFPPLL provides a reliable, accurate way to measure velocities, as well as for monitoring small changes in velocity without the sensitivity to frequency-dependent phase shifts common to other measurement systems. The estimated sensitivity to phase changes is better than a few parts in 10 to the 7th.

Yost, William T.↗
NASA NTRS2018

Internal Variability and Disequilibrium Confound Estimates of Climate Sensitivity from Observations

An emerging literature suggests that estimates of equilibrium climate sensitivity (ECS) derived from recent observations and energy balance models are biased low because models project more positive climate feedback in the far future. Here we use simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5) to show that across models, ECS inferred from the recent historical period (1979-2005) is indeed almost uniformly lower than that inferred from simulations subject to abrupt increases in CO2-radiative forcing. However, ECS inferred from simulations in which sea surface temperatures are prescribed according to observations is lower still. ECS inferred from simulations with prescribed sea surface temperatures is strongly linked to changes to tropical marine low clouds. However, feedbacks from these clouds are a weak constraint on long-term model ECS. One interpretation is that observations of recent climate changes constitute a poor direct proxy for long-term sensitivity.

Marvel, Kate↗
NASA NTRS2001

Interferometric Characterization of the Earth's Atmosphere from Lagrange Point 2

Part of the NASA plans for future Earth Science missions calls for observations using novel vantage points that can produce science products otherwise unobtainable. Observations of the Earth from the Lagrange-2 point, L-2, (1.5 million km behind the Earth on the Earth-Sun line) affords a unique vantage point for atmospheric science. Spectral observation of the Earth's atmosphere using solar occultation techniques in the near infrared (1 to 4 microns) provides one of the most accurate methods of passively sensing attitude profiles of the major species (CO2, O3, O2, CH4, H2O N2O). While traditional polar orbiting occultation measurements can obtain about 14 measurements per day (2 per orbit), solar occultation observations from the Lagrange-2 point will yield hourly profile measurements at all latitudes. The expected spatial resolution is 2 km in altitude, 0.5 degrees in latitude, and 2 degrees in longitude. The result from 24 hours of observations will be a three-dimensional map of atmospheric composition. To accomplish this task from L-2 requires the development of a large moderate spectral resolution instrument whose entrance aperture is about 10 meters. Use of a standard telescope design with a 10-meter circular mirror or a 10-meter strip mirror would be prohibitively expensive and excessively massive. Instead, we are proposing the development of a 10-meter linear interferometer coupled to a Fourier transform imaging spectrometer. The result will be a highly efficient design with sufficient sensitivity, while having both spatial and spectral resolution to produce the desired results. Preliminary calculations show that seven species (CO2, O3, O2, CH4, H2O N2O) have clearly separated spectral features in the I to 4 microns range with sufficient absorption to produce profile information from near the Earth's surface to the middle stratosphere. For CO2 the estimated sensitivity to change is 0.33% or 1 part in 330. This should be sufficient to detect changes that are significant for the carbon cycle studies. Initial instrument design studies are underway to determine the optimum optical design for the interferometer-spectrometer as well as the necessary highly stable mechanical designs. Separate design studies are being conducted for the spacecraft. shuttle launch facility, low-light solar power design, thermal control, and unique navigation requirements to reach and maintain the tight halo orbit about L-2.

Herman, Jay R.↗
NASA NTRS1974

The UCSD/MIT hard X-ray and low energy gamma ray experiment for HEAO-A

An HEAO-A spacecraft is described which is scheduled for launch in April 1977 to survey the sky in the 0.15 keV to 10 MeV range of X-rays with improved sensitivity and angular resolution. The spectral and time variations of discrete sources, and the spectrum and isotropy of the diffuse component will be measured. A hard X-ray and low energy gamma ray experiment is described which will use as an array of seven (NaI)(Tl)/CsI(Na) phoswich detectors and eight large CsI(Na) shields. Detector events are pulse-height analyzed with a selectable time resolution of 0.1, 0.005, or 0.00002 sec. The instrument background is expected to be comprised of approximately equal parts of diffuse gamma rays entering the aperture, radioactive decay of spallation products, and gamma ray leakage through the shields. Detailed background predictions are presented, and sensitivity estimates indicate that the Crab nebula should be detected up to approximately 5 MeV. Approximate 1% isotropy limits for the diffuse component of cosmic gamma rays should be achieved, and its spectrum measured with improved precision.

Matteson, J. L.↗
NASA NTRS1978

Simulation studies of wide and medium field of view earth radiation data analysis

A parameter estimation technique is presented to estimate the radiative flux distribution over the earth from radiometer measurements at satellite altitude. The technique analyzes measurements from a wide field of view (WFOV), horizon to horizon, nadir pointing sensor with a mathematical technique to derive the radiative flux estimates at the top of the atmosphere for resolution elements smaller than the sensor field of view. A computer simulation of the data analysis technique is presented for both earth-emitted and reflected radiation. Zonal resolutions are considered as well as the global integration of plane flux. An estimate of the equator-to-pole gradient is obtained from the zonal estimates. Sensitivity studies of the derived flux distribution to directional model errors are also presented. In addition to the WFOV results, medium field of view results are presented.

Green, R. N.↗