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NASA NTRS2013

Advanced Methods for Determining Prediction Uncertainty in Model-Based Prognostics with Application to Planetary Rovers

Prognostics is centered on predicting the time of and time until adverse events in components, subsystems, and systems. It typically involves both a state estimation phase, in which the current health state of a system is identified, and a prediction phase, in which the state is projected forward in time. Since prognostics is mainly a prediction problem, prognostic approaches cannot avoid uncertainty, which arises due to several sources. Prognostics algorithms must both characterize this uncertainty and incorporate it into the predictions so that informed decisions can be made about the system. In this paper, we describe three methods to solve these problems, including Monte Carlo-, unscented transform-, and first-order reliability-based methods. Using a planetary rover as a case study, we demonstrate and compare the different methods in simulation for battery end-of-discharge prediction.

prognosis↗

NASA NTRS1995

A steady-state Kalman filter for assimilating data from a single polar orbiting satellite

A steady-state scheme for data assimilation in the context of a single, short period (relative to a day), sun-synchronous, polar-orbiting satellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predictions together, are steady in time. For a linear system forced by random noise, the optimal steady-state gains (Wiener gains) are equivalent to those of a Kalman filter. Computing the Kalman gains increases the computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using prior estimates of the gains to assimilate simulated observations of one run of the model, termed 'truth' into another run termed 'prediction'. At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four iterations. Further simplification is achieved by making the gains depend on longitudinal distance from the observation point, not on absolute longitude. For a single-layer primitive equation model, the scheme works well even if only the mass field is observed but not the velocity field. Although the scheme was developed for Mars Observer, it should be applicable to data retrieved from Earth atmosphere satellites, for example, UARS.

Banfield, Don↗

NASA NTRS2024

Performance of Two Battery Prognostic Applications used by Two Octocopters for Safe Low Altitude Autonomous Flight Operations

This paper addresses the problem of building trust in online predictions of the remaining available flying time for two different electric Unmanned Aerial Vehicles (eUAVs) powered by lithium-ion-polymer batteries. Flight tests for various automation research missions for the two vehicles were monitored using two on-board battery health management applications to make predictions of the remaining flying time (RFT) for each eUAV and to predict the state of the battery. Playback of the voltage, current and temperature profiles of the battery discharge were used to assess the accuracy of the estimation of the voltage and the charge states of the models as well as the estimate of the RFT. The reference ground truth values were the observed landing time and the measured battery pack resting pack voltage 20 minutes after the flight. The predicted RFT, state of charge (SoC), and state of energy (SoE) were compared with the observed results. Noise values of one standard deviation from the mean values of the internal charge states of the battery model during a reference run were used to vary the states during simulation. One application used an equivalent circuit model of the electrical dynamics of the battery pack, and the other application used a reduced-order electrochemistry model. The variation of the model state components was compared to the variation in the estimate of the RFT and the variation in the SoE to estimate a confidence factor. Variation in the estimates caused by factors affecting the off-line laboratory parameter identification experiments is considered. Variation in the estimates due to environmental factors are discussed.

Assurance↗

NASA NTRS1982

Software for the grouped optimal aggregation technique

The grouped optimal aggregation technique produces minimum variance, unbiased estimates of acreage and production for countries, zones (states), or any designated collection of acreage strata. It uses yield predictions, historical acreage information, and direct acreage estimate from satellite data. The acreage strata are grouped in such a way that the ratio model over historical acreage provides a smaller variance than if the model were applied to each individual stratum. An optimal weighting matrix based on historical acreages, provides the link between incomplete direct acreage estimates and the total, current acreage estimate.

Brown, P. M.↗

NASA NTRS2012

Wavefront Compensation Segmented Mirror Sensing and Control

The primary mirror of very large submillimeter-wave telescopes will necessarily be segmented into many separate mirror panels. These panels must be continuously co-phased to keep the telescope wavefront error less than a small fraction of a wavelength, to ten microns RMS (root mean square) or less. This performance must be maintained continuously across the full aperture of the telescope, in all pointing conditions, and in a variable thermal environment. A wavefront compensation segmented mirror sensing and control system, consisting of optical edge sensors, Wavefront Compensation Estimator/Controller Soft ware, and segment position actuators is proposed. Optical edge sensors are placed two per each segment-to-segment edge to continuously measure changes in segment state. Segment position actuators (three per segment) are used to move the panels. A computer control system uses the edge sensor measurements to estimate the state of all of the segments and to predict the wavefront error; segment actuator commands are computed that minimize the wavefront error. Translational or rotational motions of one segment relative to the other cause lateral displacement of the light beam, which is measured by the imaging sensor. For high accuracy, the collimator uses a shaped mask, such as one or more slits, so that the light beam forms a pattern on the sensor that permits sensing accuracy of better than 0.1 micron in two axes: in the z or local surface normal direction, and in the y direction parallel to the mirror surface and perpendicular to the beam direction. Using a co-aligned pair of sensors, with the location of the detector and collimated light source interchanged, four degrees of freedom can be sensed: transverse x and y displacements, as well as two bending angles (pitch and yaw). In this approach, each optical edge sensor head has a collimator and an imager, placing one sensor head on each side of a segment gap, with two parallel light beams crossing the gap. Two sets of optical edge sensors are used per segment-to-segment edge, separated by a finite distance along the segment edge, for four optical heads, each with an imager and a collimator. By orienting the beam direction of one edge sensor pair to be +45 away from the segment edge direction, and the other sensor pair to be oriented -45 away from the segment edge direction, all six degrees of freedom of relative motion between the segments can be measured with some redundancy. The software resides in a computer that receives each of the optical edge sensor signals, as well as telescope pointing commands. It feeds back the edge sensor signals to keep the primary mirror figure within specification. It uses a feed-forward control to compensate for global effects such as decollimation of the primary and secondary mirrors due to gravity sag as the telescope pointing changes to track science objects. Three segment position actuators will be provided per segment to enable controlled motions in the piston, tip, and tilt degrees of freedom. These actuators are driven by the software, providing the optical changes needed to keep the telescope phased.

Redding, David C.↗

NASA NTRS2017

An 8-Year, High-Resolution Reanalysis of Atmospheric CO2 Mixing Ratios Based on OCO-2 and GOSAT-ACOS Retrievals

The NASA GMAO (Global Modeling and Assimilation Office) reanalysis blends OCO-2 (Orbiting Carbon Observatory 2) and GOSAT-ACOS (Greenhouse Gases Observing Satellite-Atmospheric Carbon Observations from Space) retrievals (top) with GEOS (Goddard Earth Observing System) model predictions (bottom) to estimate the full 3D (three-dimensional) state of CO2 every 3 hours (middle). This poster describes monthly atmospheric growth rates derived from the reanalysis and an application to aircraft data with the potential to aid bias correction.

GEOS-Carb↗

NASA NTRS1990

Adaptive state estimation for control of flexible structures

This paper proposes a new approach of obtaining adaptive state estimation of a system in the presence of unknown system disturbances and measurement noise. In the beginning, a non-optimal Kalman filter with arbitrary initial guess for the process and measurement noises is implemented. At the same time, an adaptive transversal predictor (ATP) based on the recursive least-squares (RLS) algorithm is used to yield optimal one- to p- step-ahead output predictions using the previous input/output data. Referring to these optimal predictions the Kalman filter gain is updated and the performance of the state estimation is thus improved. If forgetting factor is implemented in the recursive least-squares algorithm, this method is also capable of dealing with the situation when the noise statistics are slowly time-varying. This feature makes this new approach especially suitable for the control of flexible structures. A numerical example demonstrates the feasibility of this real time adaptive state estimation method.

Chen, Chung-Wen↗

NASA NTRS2012

Method and apparatus for autonomous, in-receiver prediction of GNSS ephemerides

Methods and apparatus for autonomous in-receiver prediction of orbit and clock states of Global Navigation Satellite Systems (GNSS) are described. Only the GNSS broadcast message is used, without need for periodic externally-communicated information. Earth orientation information is extracted from the GNSS broadcast ephemeris. With the accurate estimation of the Earth orientation parameters it is possible to propagate the best-fit GNSS orbits forward in time in an inertial reference frame. Using the estimated Earth orientation parameters, the predicted orbits are then transformed into Earth-Centered-Earth-Fixed (ECEF) coordinates to be used to assist the GNSS receiver in the acquisition of the signals. GNSS satellite clock states are also extracted from the broadcast ephemeris and a parameterized model of clock behavior is fit to that data. The estimated modeled clocks are then propagated forward in time to enable, together with the predicted orbits, quicker GNSS signal acquisition.

Bar-Sever, Yoaz E.↗

NASA NTRS1996

Durability and Damage Tolerance of High Temperature Polymeric Composites

Modern durability and damage tolerance predictions for composite material systems rely on accurate estimates of the local stress and material states for each of the constituents, as well as the manner in which the constituents interact. In this work, an number of approaches to estimating the stress states and interactions are developed. First, an elasticity solution is presented for the problem of a penny-shaped crack in an N-phase composite material system opened by a prescribed normal pressure. The stress state around such a crack is then used to estimate the stress concentrations due to adjacent fiber fractures in composite materials. The resulting stress concentrations are then used to estimate the tensile strength of the composite. The predicted results are compared with experimental values. In addition, a cumulative damage model for fatigue is presented. Modifications to the model are made to include the effects of variable amplitude loading. These modifications are based upon the use of remaining strength as a damage metric and the definition of an equivalent generalized time. The model is initially validated using results from the literature. Also, experimental data from APC-2 laminates and IM7/K3B laminates are used in the model. The use of such data for notched laminates requires the use of an effective hole size, which is calculated based upon strain distribution measurements. Measured remaining strengths after fatigue loading are compared with the predicted values for specimens fatigued at room temperature and 350 F (177 C).

Case, Scott W.↗

NASA NTRS1986

Spline-based distributed system identification with application to large space antennas

A parameter and state estimation technique for distributed models is demonstrated through the solution of a problem generic to large space antenna system identification. Assuming the position of the reflective surface of the maypole (hoop/column) antenna to be approximated by the static two-dimensional, stretched-membrane partial differential equation with variable-stiffness coefficient functions, a spline-based approximation procedure is described that estimates the shape and stiffness functions from data set observations. For given stiffness functions, the Galerkin projection with linear spline-based functions is applied to project the distributed problem onto a finite-dimensional subspace wherein algebraic equations exist for determining a static shape (state) prediction. The stiffness functions are then parameterized by cubic splines and the parameters estimated by an output error technique. Numerical results are presented for data descriptive of a 100-m-diameter maypole antenna.

Banks, H. T.↗

NASA NTRSDate not supplied

Flight Mechanics Analysis of Low-Earth Orbit Flight Test of an Inflatable Decelerator

The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) successfully demonstrated the capability of an inflatable aeroshell. Prior to launch, flight mechanics analysis was conducted to better understand the predicted splashdown point of the re-entry vehicle and ejectable data recorder. Best estimated trajectory separation states were utilized to understand the LOFTID trajectory over the entire 36 minute launch window. Weather forecasting model were integrated into the simulation to improve trajectory prediction accuracy. Automation tools were developed to facilitate the rapid generation of trajectory predictions during operations. The resulting improvements to the flight mechanics modeling and simulation allowed for pre-launch splashdown point to be within 3 nautical miles of the actual splashdown point.

Rohan G Deshmukh↗

NASA NTRSDate not supplied

Flight Mechanics Analysis of Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID)

Rohan Deshmukh↗

NASA NTRS2011

Geomagnetic Variability and Predictability

The Earth's magnetic field varies on time scales from seconds to millions of years. These variations can be measured directly by ground observatories and satellites, and indirectly through laboratories. They are from different electromagnetic processes in magnetosphere and ionosphere (external), ocean and crust (surface), and deep in the Earth's fluid outer core (internal). Of the measured magnetic signals, 95% is from the core, and is called the core field, or internal field. Variation of the core field, often called the geomagnetic secular variation (SV), is the manifestation of the magnetohydrodynamic processes in the core. Therefore, SV provides rich information on the core dynamical state that is then critical for understanding the geophysical mechanisms of the SV, the core-mantle interactions, and contribution of mass transport inside the core on Earth's gravity variation. Traditionally, the core state is probed via two independent methodologies: core flow inversion from the observed SV, and pure numerical dynamo simulation. The former is driven by observations, but does not include necessary interactions among physical variables; the latter is dynamically consistent, but is not constrained by any observation. Therefore, both are very limited in providing appropriate estimates of the core state. To avoid these limitations, a new approach, geomagnetic data assimilation, appears recently. In this approach, simulation results (model forecasts) are constantly corrected with observations, the corrected solutions (analysis), are then used as the initial conditions to make more accurate forecasts of future. Recent studies have demonstrated successfully that assimilation solutions are different from those of free running models. These new solutions are better estimates of the core state, and have been used to provide accurate prediction of SV for the period from 2010 to 2015. This prediction is part of the IGRF field model for international community applications.

Kuang, Weijia↗

NASA NTRS2020

A Digital Twin Feasibility Study (Part II):Non-Deterministic Predictions of Fatigue Life Using In-Situ Diagnostics and Prognostics

The Digital Twin (DT) concept has the potential to revolutionize the way systems and their components are designed, managed, maintained, and operated across a vast number of fields from engineering to healthcare. The focus of this work is the implementation of DT for the health management of fatigue critical structures. This paper is the second part of a two-part series. The first of the series demonstrated the use of multi-scale, initiation-to-failure crack growth modeling to form non-deterministic predictions of fatigue life. In this second part, a general method for reducing uncertainty in fatigue life predictions is presented that couples in-situ diagnostics and prognostics in a probabilistic framework. Monte Carlo methods and high-fidelity finite element models are used to (i) generate probabilistic estimates of crack state throughout the life of the same geometrically complex test specimen and (ii) predict fatigue life with decreasing uncertainty as more of these diagnoses are obtained. The ability to predict accurately and in the presence of uncertainty is demonstrated, suggesting that the proposed DT method is feasible for fatigue life prognosis and should be pursued further with a focus on increasing application realism.

Patrick E Leser↗

NASA NTRS1991

New Secondary Batteries Utilizing Electronically Conductive Polypyrrole Cathode

To gain a better understanding of the dynamic behavior in electronically conducting polypyrroles and to provide guidance toward designs of new secondary batteries based on these polymers, two mathematical models are developed; one for the potentiostatically controlled switching behavior of polypyrrole film, and one for the galvanostatically controlled charge/discharge behavior of lithium/polypyrrole secondary battery cell. The first model is used to predict the profiles of electrolyte concentrations, charge states, and electrochemical potentials within the thin polypyrrole film during switching process as functions of applied potential and position. Thus, the detailed mechanisms of charge transport and electrochemical reaction can be understood. Sensitivity analysis is performed for independent parameters, describing the physical and electrochemical characteristic of polypyrrole film, to verify their influences on the model performance. The values of independent parameters are estimated by comparing model predictions with experimental data obtained from identical conditions. The second model is used to predict the profiles of electrolyte concentrations, charge state, and electrochemical potentials within the battery system during charge and discharge processes as functions of time and position. Energy and power densities are estimated from model predictions and compared with existing battery systems. The independent design criteria on the charge and discharge performance of the cell are provided by studying the effects of design parameters.

Yeu, Taewhan↗

NASA NTRS1984

A numerical simulation of barotropic instability. I Wave-mean flow interaction

A numerical model is used to study the evolution of the barotropic point jet instability as it interacts with the mean flow. The linearized instability solution agrees well with the recent analytical solutions of Lindzen. Stabilization of the point jet instability occurs as the mean flow is modified by wave vorticity transport. Assuming stabilization occurs when the meridional gradient of the zonal mean vorticity is no longer negative, the maximum integrated wave enstrophy can be predicted. In addition, an estimate of the integrated wave enstrophy at steady state can be made by balancing the generation of vorticity against dissipation. These limits are found to be in good agreement with the numerical results.

Schoeberl, M. R.↗

NASA NTRS1988

Experimental studies in system identification of helicopter rotor dynamics

Recent experiments investigating the system identification of helicopter rotor dynamics are described. The identification makes use of a two-pass procedure that estimates the rotor dynamic states prior to estimation of the dynamic equation parameters. Estimation of the rotor states is made possible through use of the predictive information contained in blade-mounted accelerometers combined with a specialized processing scheme utilizing these signals. Descriptions of the experimental hardware and the system identification technique are given, as well as implementation issues for using the procedure on other similarly instrumented rotor blades. Finally, comparisons with other identification techniques using the same data are presented. It is demonstrated that the approach is an attractive one for measurement of a helicopter rotor's dynamic behavior.

Mckillip, Robert, Jr.↗

NASA NTRS1998

On-Orbit Model Refinement for Controller Redesign

High performance control design for a flexible space structure is challenging since high fidelity plant models are difficult to obtain a priori. Uncertainty in the control design models typically require a very robust, low performance control design which must be tuned on-orbit to achieve the required performance. A new procedure for refining a multivariable open loop plant model based on closed-loop response data is presented. Using a minimal representation of the state space dynamics, a least squares prediction error method is employed to estimate the plant parameters. This control-relevant system identification procedure stresses the joint nature of the system identification and control design problem by seeking to obtain a model that minimizes the difference between the predicted and actual closed-loop performance. This paper presents an algorithm for iterative closed-loop system identification and controller redesign along with illustrative examples.

Whorton, Mark S.↗