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At least 595 records · Page 33

Optimal controllers for finite wordlength implementation

When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exists realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the Linear Quadratic Gaussian (LQG) theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision the separation principle does not hold.

Liu, K.↗

Optimal controllers for finite wordlength implementation

There exist realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take into account the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the LQG (linear quadratic Gaussian) theory since they reduce to the standard LQG controller when infinite-precision computation is used, but for finite precision the separation principle does not hold.

Liu, K.↗

Vertical detachment energies of ammonia cluster anions using self-interaction-corrected methods

Systems with weakly bound extra electrons impose great challenges to semilocal density functional approximations (DFAs), which suffer from self-interaction errors. Small ammonia clusters are one such example of weakly bound anions where the extra electron is weakly bound. We applied two self-interaction correction (SIC) schemes, viz., the well-known Perdew–Zunger and the recently developed locally scaled SIC (LSIC) with the local spin density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA), and the SCAN meta-GGA functionals to calculate the vertical detachment energies (VDEs) of small ammonia cluster anions (NH3)n–. Our results show that the LSIC significantly reduces the errors in calculations of VDE with LSDA and PBE-GGA functionals leading to better agreement with the reference values calculated with coupled cluster singles and doubles with perturbative triples [CCSD(T)]. Accurate prediction of VDE as an absolute of the highest occupied molecular orbital (HOMO) is challenging for DFAs. Our results show that VDEs estimated from the negative of HOMO eigenvalues with the LSIC-LSDA and Perdew–Zunger SIC-PBE are within 11 meV of the reference CCSD(T) results. Here, the LSIC method performs consistently well for the VDE estimates, from both the total energy differences and the absolute HOMO eigenvalues.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Estimating Climatological Bias Errors for the Global Precipitation Climatology Project (GPCP)

A procedure is described to estimate bias errors for mean precipitation by using multiple estimates from different algorithms, satellite sources, and merged products. The Global Precipitation Climatology Project (GPCP) monthly product is used as a base precipitation estimate, with other input products included when they are within +/- 50% of the GPCP estimates on a zonal-mean basis (ocean and land separately). The standard deviation s of the included products is then taken to be the estimated systematic, or bias, error. The results allow one to examine monthly climatologies and the annual climatology, producing maps of estimated bias errors, zonal-mean errors, and estimated errors over large areas such as ocean and land for both the tropics and the globe. For ocean areas, where there is the largest question as to absolute magnitude of precipitation, the analysis shows spatial variations in the estimated bias errors, indicating areas where one should have more or less confidence in the mean precipitation estimates. In the tropics, relative bias error estimates (s/m, where m is the mean precipitation) over the eastern Pacific Ocean are as large as 20%, as compared with 10%-15% in the western Pacific part of the ITCZ. An examination of latitudinal differences over ocean clearly shows an increase in estimated bias error at higher latitudes, reaching up to 50%. Over land, the error estimates also locate regions of potential problems in the tropics and larger cold-season errors at high latitudes that are due to snow. An empirical technique to area average the gridded errors (s) is described that allows one to make error estimates for arbitrary areas and for the tropics and the globe (land and ocean separately, and combined). Over the tropics this calculation leads to a relative error estimate for tropical land and ocean combined of 7%, which is considered to be an upper bound because of the lack of sign-of-the-error canceling when integrating over different areas with a different number of input products. For the globe the calculated relative error estimate from this study is about 9%, which is also probably a slight overestimate. These tropical and global estimated bias errors provide one estimate of the current state of knowledge of the planet's mean precipitation.

Global Precipitation Climatology Project (GPCP)↗

Screening actuator locations for static shape control

Correction of shape distortion due to zero-mean normally distributed errors in structural sizes which are random variables is examined. A bound on the maximum improvement in the expected value of the root-mean-square shape error is obtained. The shape correction associated with the optimal actuators is also characterized. An actuator effectiveness index is developed and shown to be helpful in screening actuator locations in the structure. The results are specialized to a simple form for truss structures composed of nominally identical members. The bound and effectiveness index are tested on a 55-m radiometer antenna truss structure. It is found that previously obtained results for optimum actuators had a performance close to the bound obtained here. Furthermore, the actuators associated with the optimum design are shown to have high effectiveness indices. Since only a small fraction of truss elements tend to have high effectiveness indices, the proposed screening procedure can greatly reduce the number of truss members that need to be considered as actuator sites.

Haftka, Raphael T.↗

An algorithm for the estimation of bounds on the emissivity and temperatures from thermal multispectral airborne remotely sensed data

The effective flux incident upon the detectors of a thermal sensor, after it has been corrected for atmospheric effects, is a function of a non-linear combination of the emissivity of the target for that channel and the temperature of the target. The sensor system cannot separate the contribution from the emissivity and the temperature that constitute the flux value. A method that estimates the bounds on these temperatures and emissivities from thermal data is described. This method is then tested with remotely sensed data obtained from NASA's Thermal Infrared Multispectral Scanner (TIMS) - a 6 channel thermal sensor. Since this is an under-determined set of equations i.e. there are 7 unknowns (6 emissivities and 1 temperature) and 6 equations (corresponding to the 6 channel fluxes), there exist theoretically an infinite combination of values of emissivities and temperature that can satisfy these equations. Using some realistic bounds on the emissivities, bounds on the temperature are calculated. These bounds on the temperature are refined to estimate a tighter bound on the emissivity of the source. An error analysis is also carried out to quantitatively determine the extent of uncertainty introduced in the estimate of these parameters. This method is useful only when a realistic set of bounds can be obtained for the emissivities of the data. In the case of water the lower and upper bounds were set at 0.97 and 1.00 respectively. Five flights were flown in succession at altitudes of 2 km (low), 6 km (mid), 12 km (high), and then back again at 6 km and 2 km. The area selected with the Ross Barnett reservoir near Jackson, Mississippi. The mission was flown during the predawn hours of 1 Feb. 1992. Radiosonde data was collected for that duration to profile the characteristics of the atmosphere. Ground truth temperatures using thermometers and radiometers were also obtained over an area of the reservoir. The results of two independent runs of the radiometer data averaged 7.03 plus or minus .70 for the first run and 7.31 plus or minus .88 for the second run. The results of the algorithm yield a temperature of 7.68 for the low altitude data to 8.73 for the high altitude data.

Jaggi, S.↗

Time-Critical Coordination of UAS with Non-Ideal Autopilots under Lossy Communication Networks

In this presentation we will explore several distributed consensus algorithms developed to maintain coordination among a fleet of heterogeneous UAS subject to external disturbances. An overview of the network assumptions and autopilot performance bounds required to meet the coordination objective will be provided. In particular, we will leverage passivity-based stability conditions for bidirectional networks that require the communication graph to be connected in an integral sense, but may fail to connect pointwise in time during the entire mission. Non-ideal autopilots that can only track a desired speed profile with a prescribed precision induce an error in vehicle coordination. The autopilot performance bounds will be propagated through the coordination dynamics to understand the limits introduced by autopilots.

conensus↗

The Dolinar Receiver in an Information Theoretic Framework

Optical communication at the quantum limit requires that measurements on the optical field be maximally informative, but devising physical measurements that accomplish this objective has proven challenging. The Dolinar receiver exemplifies a rare instance of success in distinguishing between two coherent states: an adaptive local oscillator is mixed with the signal prior to photodetection, which yields an error probability that meets the Helstrom lower bound with equality. Here we apply the same local-oscillator-based architecture with aninformation-theoretic optimization criterion. We begin with analysis of this receiver in a general framework for an arbitrary coherent-state modulation alphabet, and then we concentrate on two relevant examples. First, we study a binary antipodal alphabet and show that the Dolinar receiver's feedback function not only minimizes the probability of error, but also maximizes the mutual information. Next, we study ternary modulation consistingof antipodal coherent states and the vacuum state. We derive an analytic expression for a near-optimal local oscillator feedback function, and, via simulation, we determine its photon information efficiency (PIE). We provide the PIE versus dimensional information efficiency (DIE) trade-off curve and show that this modulation and the our receiver combination performs universally better than (generalized) on-off keying plus photoncounting, although, the advantage asymptotically vanishes as the bits-per-photon diverges towards infinity.

optical communications↗

A concatenated coding scheme for error control

A concatenated coding scheme for error control in data communications is analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. The probability of undetected error of the above error control scheme is derived and upper bounded. Two specific exmaples are analyzed. In the first example, the inner code is a distance-4 shortened Hamming code with generator polynomial (X+1)(X(6)+X+1) = X(7)+X(6)+X(2)+1 and the outer code is a distance-4 shortened Hamming code with generator polynomial (X+1)X(15+X(14)+X(13)+X(12)+X(4)+X(3)+X(2)+X+1) = X(16)+X(12)+X(5)+1 which is the X.25 standard for packet-switched data network. This example is proposed for error control on NASA telecommand links. In the second example, the inner code is the same as that in the first example but the outer code is a shortened Reed-Solomon code with symbols from GF(2(8)) and generator polynomial (X+1)(X+alpha) where alpha is a primitive element in GF(z(8)).

Lin, S.↗

Exploiting Measurement Uncertainty Estimation in Evaluation of GOES-R ABI Image Navigation Accuracy Using Image Registration Techniques

In evaluating GOES-R Advanced Baseline Imager (ABI) image navigation quality, upsampled sub-images of ABI images are translated against downsampled Landsat 8 images of localized, high contrast earth scenes to determine the translations in the East-West and North-South directions that provide maximum correlation. The native Landsat resolution is much finer than that of ABI, and Landsat navigation accuracy is much better than ABI required navigation accuracy and expected performance. Therefore, Landsat images are considered to provide ground truth for comparison with ABI images, and the translations of ABI sub-images that produce maximum correlation with Landsat localized images are interpreted as ABI navigation errors. The measured local navigation errors from registration of numerous sub-images with the Landsat images are averaged to provide a statistically reliable measurement of the overall navigation error of the ABI image. The dispersion of the local navigation errors is also of great interest, since ABI navigation requirements are specified as bounds on the 99.73rd percentile of the magnitudes of per pixel navigation errors. However, the measurement uncertainty inherent in the use of image registration techniques tends to broaden the dispersion in measured local navigation errors, masking the true navigation performance of the ABI system. We have devised a novel and simple method for estimating the magnitude of the measurement uncertainty in registration error for any pair of images of the same earth scene. We use these measurement uncertainty estimates to filter out the higher quality measurements of local navigation error for inclusion in statistics. In so doing, we substantially reduce the dispersion in measured local navigation errors, thereby better approximating the true navigation performance of the ABI system.

navigation performance↗

Trajectory Control of Rendezvous with Maneuver Target Spacecraft

In this paper, a nonlinear trajectory control algorithm of rendezvous with maneuvering target spacecraft is presented. The disturbance forces on the chaser and target spacecraft and the thrust forces on the chaser spacecraft are considered in the analysis. The control algorithm developed in this paper uses the relative distance and relative velocity between the target and chaser spacecraft as the inputs. A general formula of reference relative trajectory of the chaser spacecraft to the target spacecraft is developed and applied to four different proximity maneuvers, which are in-track circling, cross-track circling, in-track spiral rendezvous and cross-track spiral rendezvous. The closed-loop differential equations of the proximity relative motion with the control algorithm are derived. It is proven in the paper that the tracking errors between the commanded relative trajectory and the actual relative trajectory are bounded within a constant region determined by the control gains. The prediction of the tracking errors is obtained. Design examples are provided to show the implementation of the control algorithm. The simulation results show that the actual relative trajectory tracks the commanded relative trajectory tightly. The predicted tracking errors match those calculated in the simulation results. The control algorithm developed in this paper can also be applied to interception of maneuver target spacecraft and relative trajectory control of spacecraft formation flying.

Zhou, Zhinqiang↗

Semirigorous bounds for the dipole moments and transition moments of the LiH molecule

Semirigorous error limits for the dipole moments and transition moments of LiH at R = 3.015 bohr are reported. Weinhold's formula for the upper and lower bounds to transition moments is extended to include transitions between states of the same symmetry, and Chong's (1976) semirigorous expression for the lower bound to the overlap between the approximate and the true wavefunctions is applied to the calculation. The semirigorous theory of Chong was also generalized in the sense that the zeroth-order wavefunction was allowed to contain many configuration state functions instead of just the Hartree-Fock or first natural configuration state function.

Langhoff, S. R.↗

Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout

We show that the lowest quantum Cramér-Rao bound achievable in interferometry with a one-axis twisted spin coherent state is saturated by the asymptotic method of moments error of a protocol that uses one call to the one-axis twisting, one call to time-reversed one-axis twisting, and a final total spin measurement (i.e., a twist-untwist protocol). The result is derived by first showing that the metrological phase diagram for one-axis twisting is asymptotically characterized by a single quantum Fisher information value N(N + 1)/2 for all times, then constructing a twist-untwist protocol having a method of moments error that saturates this value. The case of finite-range one-axis twisting is similarly analyzed, and a simple functional form for the metrological phase diagram is found in both the short-range and long-range interaction regimes. Numerical evidence suggests that the finite-range analogues of twist-untwist protocols can exhibit a method of moments error that asymptotically saturates the lowest quantum Cramér-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times.

36 MATERIALS SCIENCE↗

Risk-Based Dispatch Bound Calculator

This calculator outputs time-varying lower and upper bounds (matrices), called dispatch bounds, for the controllable portions of the power injections at each node in a distribution network to guarantee that the voltage magnitudes stay within prescribed bounds with at least a given probability for any set of power injections that are within their dispatch bounds. The calculator is meant to be a tool for a central controller of a distribution network to set dispatch bounds for each node that allows each node to independently decide their actual power injection within their dispatch bound. The user can choose whether to assume the forecast errors of the uncontrollable power injections are gaussian or are worst-case (distributionally robust). The user can choose whether the dispatch bounds include the controllable reactive power or just the active power under a constant power factor assumption.

Comden, Joshua↗

Bias Characterization, Vertical Interpolation, and Horizontal Interpolation for Distributed Wind Siting Using Mesoscale Wind Resource Estimates

Much like their counterparts in utility-scale wind energy, developers of industrial, small-scale and distributed wind turbine deployments need to understand and accurately characterize the wind resource to properly assess the power generation and financial ramifications during siting and planning. National Renewable Energy Laboratory’s WIND (Wind Integration National Dataset) Toolkit (WTK) provides a best-in-class wind resource dataset generated using the Weather Research and Forecasting (WRF) model. This dataset includes parameters such as the wind speed, wind direction, and temperature at various heights, plus atmospheric stability near the surface. This data is available at 2-km spatial resolution and five-minute temporal resolution across 7 years, from 2007 to 2013 through a publicly accessible API interface. The Tools Assessing Performance (TAP) project seeks to extend this dataset to allow long term resource estimates and leverage it to better equip distributed wind equipment manufacturers, owner-operators, and installation professionals with better tools for practical siting applications. In this report, we present the results from our investigation within the TAP project focused on characterization of bias in WTK-based wind speed estimates and evaluation of vertical and horizontal interpolation techniques. We discuss the tradeoffs between different techniques and their combinations, as well as describe the lower bounds we determine for the studied validation errors. While the specific estimates we present are specific to WTK and the validation dataset we have chosen for this investigation (NREL's Wind Resource Meteorological Database), the overall analysis and the studied techniques are general enough to be applied to a broader set of wind datasets, both simulation-based and observational.

17 WIND ENERGY↗

Analysis of the Trusted Inertial Terrain-Aided Navigation Measurement Function

The trusted inertial terrain-aided navigation (TITAN) algorithm leverages an airborne vertical synthetic aperture radar to measure the range to the closest ground points along several prescribed iso-Doppler contours. These TITAN minimum-range, prescribed-Doppler measurements are the result of a constrained nonlinear optimization problem whose optimization function and constraints both depend on the radar position and velocity. Owing to the complexity of this measurement definition, analysis of the TITAN algorithm is lacking in prior work. This publication offers such an analysis, making the following three contributions: (1) an analytical solution to the TITAN constrained optimization measurement problem, (2) a derivation of the TITAN measurement function Jacobian, and (3) a derivation of the Cramér-Rao lower bound on the estimated position and velocity error covariance. These three contributions are verified via Monte Carlo simulations over synthetic terrain, which further reveal two remarkable properties of the TITAN algorithm: (1) the along-track positioning errors tend to be smaller than the cross-track positioning errors, and (2) the cross-track positioning errors are independent of the terrain roughness.

TITAN↗

Optical receivers using rough reflectors

This report examines the possible use of rough, or nondiffraction-limited, reflectors for collecting optical signals. It is shown that in the absence of background radiation, the reflector's surface quality has little effect on the performance of a properly designed receiver, but that the presence of even small amounts of background radiation can lead to severe performance degradation. Techniques are suggested for improving receiver performance in high-background environments, and bounds and approximations to the exact error-probability expressions are derived.

Vilnrotter, V. A.↗

Evaluation of detectability and distinguishability of aircraft control element failures using flight test data

This paper examines the detectability and distinguishability of control element failures on the B-737 aircraft. The results of Weiss (1985) are used to define decentralized residuals from analytic redundancy relationships, and the results of Weiss et al. (1984) are used to define the probabilistic distance measures which provide bounds on the minimum achievable probabilities or error. The residual signals are then generated using data which were recorded during a landing approach of the NASA-Langley Advanced Transport Operations (ATOPS) transportation systems research vehicle (TSRV). The distance measures are computed using estimates of the statistics of these residual signals.

Weiss, J. L.↗