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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 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 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 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 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.↗
NASA NTRS1980

Evaluation of composite bolometers at 0.4 Kelvin

Composite bolometer structures have provided the most sensitive IR detectors for operation at helium-4 temperatures of 1.5K. Below 1.5K the electrical and thermal properties change significantly and the performance characteristics cannot be accurately extrapolated for composite bolometers at helium-3 temperatures of 0.4K. The paper deals with experimentally assessed performance of composite bolometers at 0.4K. It is found that sensitivity estimates derived from electrical or load curve properties can overestimate the responsivity to radiation by several orders of magnitude depending upon a particular material behavior. For many near-millimeter applications background power levels are several nanowatts and the associated photon noise plus Johnson and phonon noise components impose a fundamental detection limit of about 5 x 10 to the -15thW/Hz to the -1/2. We have successfully fabricated composite bolometers which at 0.4 K and millimeter wavelengths achieve a noise equivalent power of 7 x 10 to the -15thW/Hz to the -1/2 coupled with a large absorbing area (0.3 sq cm) and a fast response time (2 msec.).

El-Ataway, S.↗
NASA NTRS1981

Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system

Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.

Tsang, W. L.↗
NASA NTRS1984

An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities

An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method 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 with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.

Murphy, P. C.↗
NASA NTRS1974

Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations

This paper discusses numerical aspects of computing maximum likelihood estimates for linear dynamical systems in state-vector form. Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined. The problems due to singular Hessian or singular information matrix that are common in practice are discussed in detail and methods for their solution are proposed. New results on the calculation of state sensitivity functions via reduced order models are given. Several methods for speeding convergence and reducing computation time are also discussed.

Gupta, N. K.↗
NASA NTRS1982

Sensitivity analysis of add-on price estimate for select silicon wafering technologies

The cost of producing wafers from silicon ingots is a major component of the add-on price of silicon sheet. Economic analyses of the add-on price estimates and their sensitivity internal-diameter (ID) sawing, multiblade slurry (MBS) sawing and fixed-abrasive slicing technique (FAST) are presented. Interim price estimation guidelines (IPEG) are used for estimating a process add-on price. Sensitivity analysis of price is performed with respect to cost parameters such as equipment, space, direct labor, materials (blade life) and utilities, and the production parameters such as slicing rate, slices per centimeter and process yield, using a computer program specifically developed to do sensitivity analysis with IPEG. The results aid in identifying the important cost parameters and assist in deciding the direction of technology development efforts.

Mokashi, A. R.↗
NASA NTRS1989

A Monte Carlo/response surface strategy for sensitivity analysis: application to a dynamic model of vegetative plant growth

We describe the application of a strategy for conducting a sensitivity analysis for a complex dynamic model. The procedure involves preliminary screening of parameter sensitivities by numerical estimation of linear sensitivity coefficients, followed by generation of a response surface based on Monte Carlo simulation. Application is to a physiological model of the vegetative growth of soybean plants. The analysis provides insights as to the relative importance of certain physiological processes in controlling plant growth. Advantages and disadvantages of the strategy are discussed.

Non-NASA Center↗
NASA NTRS1985

A sensitivity analysis of the Shuttle Orbiter heating

A procedure for estimating relative sensitivities in Space Shuttle Orbiter entry heating due to variations from nominal flight parameters is presented. Ballpark values are provided for assessing heating changes caused by off-nominal variations in anglle of attack and Reynolds number for laminar flow conditions. Also, a procedure for scaling heating data obtained on subscale models tested at low-enthalpy wind-tunnel test conditions to high-enthalpy flight conditions using simplified flow analysis techniques is presented and verified with flight and wind-tunnel data. In addition, data are presented illustrating that a significant increase in heating was experienced on the fifth Orbiter flight. The increase was possibly caused by changes in the catalytic properties of the Orbiter thermal protection system surface.

Williams, S. D.↗