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At least 1,117 records · Page 62

The significance of error dynamics in model-following for flight control design

The role of the system error dynamics in model-following control systems is discussed, along with the use of handling quality specifications, actuation bandwidth constraints, stability, and closed-loop performance requirements in flight control design. The model-following problem is formulated using both direct state-space and linear, quadratic, optimization techniques. The results are then demonstrated using several examples involving a generic forward-swept-wing vehicle and a conventional flight vehicle with large parameter uncertainty in order to illustrate the trade-off in closed-loop performance and control law complexity.

Schmidt, David K.↗

A simulation of GPS and differential GPS sensors

The Global Positioning System (GPS) is a revolutionary advance in navigation. Users can determine latitude, longitude, and altitude by receiving range information from at least four satellites. The statistical accuracy of the user's position is directly proportional to the statistical accuracy of the range measurement. Range errors are caused by clock errors, ephemeris errors, atmospheric delays, multipath errors, and receiver noise. Selective Availability, which the military uses to intentionally degrade accuracy for non-authorized users, is a major error source. The proportionality constant relating position errors to range errors is the Dilution of Precision (DOP) which is a function of the satellite geometry. Receivers separated by relatively short distances have the same satellite and atmospheric errors. Differential GPS (DGPS) removes these errors by transmitting pseudorange corrections from a fixed receiver to a mobile receiver. The corrected pseudorange at the moving receiver is now corrupted only by errors from the receiver clock, multipath, and measurement noise. This paper describes a software package that models position errors for various GPS and DGPS systems. The error model is used in the Real-Time Simulator and Cockpit Technology workstation simulations at NASA-LaRC. The GPS/DGPS sensor can simulate enroute navigation, instrument approaches, or on-airport navigation.

Rankin, James M.↗

Q-BEEP: Quantum Bayesian Error Mitigation Employing Poisson Modeling over the Hamming Spectrum

Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processor’s qubit capacity growing. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction (in-situ error mitigation) and Quantum Error Mitigation (post-induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors, increasing the overall fidelity and hence the overall quality of circuit induction. Earlier this year, a pioneering work, namely HAMMER, published in ASPLOS-22 demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they intuitively assumed that errors occur in local clusters, and that at higher average Hamming distances this structure falls away. In this work, we show that such a correlation structure is not only local but extends certain non-local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i.e., calibration statistics) and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the new iterative method, our Q-Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein-Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, the fidelity improvement is up to 17.8%. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to integrate and provide more reliable circuit induction results.

Stein, Samuel A.↗

Battery state of health monitoring by estimation of the number of cyclable Li-ions

Herein this paper introduces a method to monitor battery state of health (SOH) by estimating the number of cyclable Li-ions, a health-relevant electrochemical variable. SOH monitoring is critical to battery management in balancing the trade-off between maximizing system performance and minimizing battery degradation. The decrease of cyclable Li-ions indicates the effect on the SOH of degradation mechanisms that consume cyclable Li-ions. The unavailability of the number of cyclable Li-ions through non-invasive measurements makes its estimation necessary for in-situ SOH monitoring. In this paper, the extended Kalman filter (EKF) is used to estimate the number of cyclable Li-ions as an unknown battery parameter. The single particle model (SPM), a simplified battery electrochemical model, is used as the model in the EKF to achieve a computational complexity suitable for on-line estimation. Simulations are performed under typical electric vehicle current trajectories using an example parameter set for a hybrid-electric-vehicle battery. In the simulations, the battery is represented by the Doyle–Fuller–Newman (DFN) model, an electrochemical model with higher fidelity than the SPM. To comply with the practice, instead of using the same parameters as the DFN model in the SPM, parameterization of the SPM is performed before estimation of the number of cyclable Li-ions. The simulations show high estimation accuracy of the number of cyclable Li-ions using the EKF, even with the structural and parametric differences between the DFN model and the SPM, under both the ideal conditions and various non-ideal conditions (i.e., SOC estimation error, additional modeling error, and measurement noise).

25 ENERGY STORAGE↗

Error enhancement in geomagnetic models derived from scalar data

Models of the main geomagnetic field are generally represented by a scalar potential gamma expanded in a finite number of spherical harmonics. Very accurate observations of F were used, but indications exist that the accuracy of models derived from them is considerably lower. One problem is that F does not always characterize gamma uniquely. It is not clear whether such ambiguity can be encountered in deriving gamma from F in geomagnetic surveys, but there exists a connection, due to the fact that the counterexamples of Backus are related to the dipole field, while the geomagnetic field is dominated by its dipole component. If the models are recovered with a finite error (i.e. they cannot completely fit the data and consequently have a small spurious component), this connection allows the error in certain sequences of harmonic terms in gamma to be enhanced without unduly large effects on the fit of F to the model.

Stern, D. P.↗

Weak charge form factor and radius of 208 Pb through parity violation in electron scattering

We use distorted wave electron scattering calculations to extract the weak charge form factor F W ($\bar{q}$), the weak charge radius R W , and the point neutron radius R n , of 208 Pb from the PREX parity violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer $\bar{q}$ = 0.475 fm -1 . We find F W ($\bar{q}$) = 0.204 ± 0.028(exp) ± 0.001(model). We use the Helm model to infer the weak radius from F W ($\bar{q}$). We find RW = 5.826 ± 0.181(exp) ± 0.027(model) fm. Here the exp error includes PREX statistical and systematic errors, while the model error describes the uncertainty in R W from uncertainties in the surface thickness σ of the weak charge density. The weak radius is larger than the charge radius, implying a 'weak charge skin' where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius R n = 5.751 ± 0.175 (exp) ± 0.026(model) ± 0.005(strange) fm, from R W . Here there is only a very small error (strange) from possible strange quark contributions. We find R n to be slightly smaller than R W because of the nucleon's size. As a result, we find a neutron skin thickness of R n -R p = 0.302 ± 0.175 (exp) ± 0.026 (model) ± 0.005 (strange) fm, where R p is the point proton radius.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Model reduction by trimming for a class of semi-Markov reliability models and the corresponding error bound

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. A model reduction technique called trimming is presented that can be applied to a popular class of systems. Automatic model generation programs were written to help the reliability analyst produce models of complex systems. This method, trimming, is easy to implement and the error bound easy to compute. Hence, the method lends itself to inclusion in an automatic model generator.

White, Allan L.↗

Evaluation of LANDSAT-D Orbit Determination Using a Filter/Smoother (PREFER)

Simulated range and range rate data for five tracking stations were first generated using batch least squares orbit determination (GTDS). Then GTDS was used (in the differential correction mode) to produce a nominal trajectory which was input to PREFER. The GTDS differential correction (DC) run was made using models which differed from those used to produce the simulated data. These model differences were chosen to be fairly realistic approximations to the errors in the models actually used for operational orbit determination. Several different simulation runs were made with different types of model errors in order to determine the sensitivity to these errors. The nominal trajectory and the simulated measurement data were input to PREFER to produce a smoothed ephemeris file. Numerous runs of PREFER were made in which parameters describing the statistics of the model errors were varied. The likelihood function computed by the Kalman filter determined the ""best'' choice of input parameters. There was strong negative correlation between the likelihood function and the errors in the smoothed ephemeris.

Gibbs, B. P.↗

Research Relative to High Spatial Resolution Passive Microwave Sounding Systems

Methods to obtain high resolution passive microwave weather observations, and understanding of their probable impact on numerical weather prediction accuracy were investigated. The development of synthetic aperture concepts for geosynchronous passive microwave sounders were studied. The effects of clouds, precipitation, surface phenomena, and atmospheric thermal fine structure on a scale of several kilometers were examined. High resolution passive microwave sounders (e.g., AMSU) with an increased number of channels will produce initialization data for numerical weather prediction (NWP) models with both increased spatial resolution and coverage. The development of statistical models for error growth in high resolution primitive equation NWP models which permit the consequences of various observing system alternatives, including sensors and assimilation times and procedures is discussed. A high resolution three dimensional primitive equation NWP model to determine parameters in an error growth model similar to that formulated by Lorenz, but with more degrees of freedom is utilized.

Staelin, D. H.↗

Accurate Magnetometer/Gyroscope Attitudes Using a Filter with Correlated Sensor Noise

Magnetometers and gyroscopes have been shown to provide very accurate attitudes for a variety of spacecraft. These results have been obtained, however, using a batch-least-squares algorithm and long periods of data. For use in onboard applications, attitudes are best determined using sequential estimators such as the Kalman filter. When a filter is used to determine attitudes using magnetometer and gyroscope data for input, the resulting accuracy is limited by both the sensor accuracies and errors inherent in the Earth magnetic field model. The Kalman filter accounts for the random component by modeling the magnetometer and gyroscope errors as white noise processes. However, even when these tuning parameters are physically realistic, the rate biases (included in the state vector) have been found to show systematic oscillations. These are attributed to the field model errors. If the gyroscope noise is sufficiently small, the tuned filter 'memory' will be long compared to the orbital period. In this case, the variations in the rate bias induced by field model errors are substantially reduced. Mistuning the filter to have a short memory time leads to strongly oscillating rate biases and increased attitude errors. To reduce the effect of the magnetic field model errors, these errors are estimated within the filter and used to correct the reference model. An exponentially-correlated noise model is used to represent the filter estimate of the systematic error. Results from several test cases using in-flight data from the Compton Gamma Ray Observatory are presented. These tests emphasize magnetometer errors, but the method is generally applicable to any sensor subject to a combination of random and systematic noise.

Sedlak, J.↗

Radial orbit error reduction and sea surface topography determination using satellite altimetry

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Engelis, Theodossios↗

EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on input and model uncertainties, while numerical errors were largely overlooked. Numerical errors can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration of discretization error is mainly due to the difficulty in estimating them. Accurate estimations of discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are difficult to achieve in existing codes. In this work, we will build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verification of spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated via case studies that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties.

42 ENGINEERING↗

Life Prediction Model for Grid-Connected Li-ion Battery Energy Storage System

Lithium-ion (Li-ion) batteries are being deployed on the electrical grid for a variety of purposes, such as to smooth fluctuations in solar renewable power generation. The lifetime of these batteries will vary depending on their thermal environment and how they are charged and discharged. To optimal utilization of a battery over its lifetime requires characterization of its performance degradation under different storage and cycling conditions. Aging tests were conducted on commercial graphite/nickel-manganese-cobalt (NMC) Li-ion cells. A general lifetime prognostic model framework is applied to model changes in capacity and resistance as the battery degrades. Across 9 aging test conditions from 0oC to 55oC, the model predicts capacity fade with 1.4% RMS error and resistance growth with 15% RMS error. The model, recast in state variable form with 8 states representing separate fade mechanisms, is used to extrapolate lifetime for example applications of the energy storage system integrated with renewable photovoltaic (PV) power generation.

25 ENERGY STORAGE↗

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models

The error variance of the process prior multivariate normal distributions of the parameters of the models are assumed to be specified, prior probabilities of the models being correct. A rule for termination of sampling is proposed. Upon termination, the model with the largest posterior probability is chosen as correct. If sampling is not terminated, posterior probabilities of the models and posterior distributions of the parameters are computed. An experiment was chosen to maximize the expected Kullback-Leibler information function. Monte Carlo simulation experiments were performed to investigate large and small sample behavior of the sequential adaptive procedure.

Sidik, S. M.↗

Dynamic response tests of inertial and optical wind-tunnel model attitude measurement devices

Results are presented for an experimental study of the response of inertial and optical wind-tunnel model attitude measurement systems in a wind-off simulated dynamic environment. This study is part of an ongoing activity at the NASA Langley Research Center to develop high accuracy, advanced model attitude measurement systems that can be used in a dynamic wind-tunnel environment. This activity was prompted by the inertial model attitude sensor response observed during high levels of model vibration which results in a model attitude measurement bias error. Significant bias errors in model attitude measurement were found for the measurement using the inertial device during wind-off dynamic testing of a model system. The amount of bias present during wind-tunnel tests will depend on the amplitudes of the model dynamic response and the modal characteristics of the model system. Correction models are presented that predict the vibration-induced bias errors to a high degree of accuracy for the vibration modes characterized in the simulated dynamic environment. The optical system results were uncorrupted by model vibration in the laboratory setup.

Buehrle, R. D.↗

Modal Correction Method For Dynamically Induced Errors In Wind-Tunnel Model Attitude Measurements

This paper describes a method for correcting the dynamically induced bias errors in wind tunnel model attitude measurements using measured modal properties of the model system. At NASA Langley Research Center, the predominant instrumentation used to measure model attitude is a servo-accelerometer device that senses the model attitude with respect to the local vertical. Under smooth wind tunnel operating conditions, this inertial device can measure the model attitude with an accuracy of 0.01 degree. During wind tunnel tests when the model is responding at high dynamic amplitudes, the inertial device also senses the centrifugal acceleration associated with model vibration. This centrifugal acceleration results in a bias error in the model attitude measurement. A study of the response of a cantilevered model system to a simulated dynamic environment shows significant bias error in the model attitude measurement can occur and is vibration mode and amplitude dependent. For each vibration mode contributing to the bias error, the error is estimated from the measured modal properties and tangential accelerations at the model attitude device. Linear superposition is used to combine the bias estimates for individual modes to determine the overall bias error as a function of time. The modal correction model predicts the bias error to a high degree of accuracy for the vibration modes characterized in the simulated dynamic environment.

Buehrle, R. D.↗

Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events

In thist study, we develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives precisely the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) that the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.

97 MATHEMATICS AND COMPUTING↗