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At least 307 records · Page 17

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Starlinger, Alois↗

Optimization of multiparameter radar estimates of rainfall

The estimates of rainfall rate derived from a multiparameter radar based on reflectivity factor (R sub ZH), differential reflectivity (R sub DR), and specific differential propagation phase (R sub DP) have widely varying accuracies over the dynamic range of the natural occurrence of rainfall. This paper presents a framework to optimally combine the three estimates, R sub zH, R sub DR, and R sub DP, to derive the best estimate of rainfall using coherent multiparameter radars. The optimization procedure is demonstrated for application to multiparameter radar measurements at C band.

Chandrasekar, V.↗

Autonomous Component Health Management with Failed Component Detection, Identification, and Avoidance

This paper details a novel scheme for autonomous component health management (ACHM) with failed actuator detection and failed sensor detection, identification, and avoidance. This new scheme has features that far exceed the performance of systems with triple-redundant sensing and voting, yet requires fewer sensors and could be applied to any system with redundant sensing. Relevant background to the ACHM scheme is provided, and the simulation results for the application of that scheme to a single-axis spacecraft attitude control system with a 3rd order plant and dual-redundant measurement of system states are presented. ACHM fulfills key functions needed by an integrated vehicle health monitoring (IVHM) system. It is: autonomous; adaptive; works in realtime; provides optimal state estimation; identifies failed components; avoids failed components; reconfigures for multiple failures; reconfigures for intermittent failures; works for hard-over, soft, and zero-output failures; and works for both open- and closed-loop systems. The ACHM scheme combines a prefilter that generates preliminary state estimates, detects and identifies failed sensors and actuators, and avoids the use of failed sensors in state estimation with a fixed-gain Kalman filter that generates optimal state estimates and provides model-based state estimates that comprise an integral part of the failure detection logic. The results show that ACHM successfully isolates multiple persistent and intermittent hard-over, soft, and zero-output failures. It is now ready to be tested on a computer model of an actual system.

Davis, Robert N.↗

Design of optimal second-order state estimators

The present consideration of the design of online computation-saving second-order state estimators for second-order vector-matrix differential systems proposes a class of such estimators which is proven to possess guaranteed convergence. A class of optimal second-order estimators is then obtained, and the conditions required for optimality are identified. The estimator proposed offers high performance in conjunction with online computation reductions sufficiently great to allow the estimation of the large number of state variables associated with control of large, flexible space structures represented by high-dimensional second-order systems.

Joshi, Suresh M.↗

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗

Development of methodologies for the estimation of thermal properties associated with aerospace vehicles

Thermal stress analyses are an important aspect in the development of aerospace vehicles such as the National Aero-Space Plane (NASP) and the High-Speed Civil Transport (HSCT) at NASA-LaRC. These analyses require knowledge of the temperature within the structures which consequently necessitates the need for thermal property data. The initial goal of this research effort was to develop a methodology for the estimation of thermal properties of aerospace structural materials at room temperature and to develop a procedure to optimize the estimation process. The estimation procedure was implemented utilizing a general purpose finite element code. In addition, an optimization procedure was developed and implemented to determine critical experimental parameters to optimize the estimation procedure. Finally, preliminary experiments were conducted at the Aircraft Structures Branch (ASB) laboratory.

Scott, Elaine P.↗

Lateral control system design for VTOL landing on a DD963 in high sea states

The problem of designing lateral control systems for the safe landing of VTOL aircraft on small ships is addressed. A ship model is derived. The issues of estimation and prediction of ship motions are discussed, using optimal linear linear estimation techniques. The roll motion is the most important of the lateral motions, and it is found that it can be predicted for up to 10 seconds in perfect conditions. The automatic landing of the VTOL aircraft is considered, and a lateral controller, defined as a ship motion tracker, is designed, using optimal control techniqes. The tradeoffs between the tracking errors and the control authority are obtained. The important couplings between the lateral motions and controls are demonstrated, and it is shown that the adverse couplings between the sway and the roll motion at the landing pad are significant constraints in the tracking of the lateral ship motions. The robustness of the control system, including the optimal estimator, is studied, using the singular values analysis. Through a robustification procedure, a robust control system is obtained, and the usefulness of the singular values to define stability margins that take into account general types of unstructured modelling errors is demonstrated. The minimal destabilizing perturbations indicated by the singular values analysis are interpreted and related to the multivariable Nyquist diagrams.

Bodson, M.↗

Validation of a computer code for analysis of subsonic aerodynamic performance of wings with flaps in combination with a canard or horizontal tail and an application to optimization

Extensive correlations of computer code results with experimental data are employed to illustrate the use of a linearized theory, attached flow method for the estimation and optimization of the longitudinal aerodynamic performance of wing-canard and wing-horizontal tail configurations which may employ simple hinged flap systems. Use of an attached flow method is based on the premise that high levels of aerodynamic efficiency require a flow that is as nearly attached as circumstances permit. The results indicate that linearized theory, attached flow, computer code methods (modified to include estimated attainable leading-edge thrust and an approximate representation of vortex forces) provide a rational basis for the estimation and optimization of aerodynamic performance at subsonic speeds below the drag rise Mach number. Generally, good prediction of aerodynamic performance, as measured by the suction parameter, can be expected for near optimum combinations of canard or horizontal tail incidence and leading- and trailing-edge flap deflections at a given lift coefficient (conditions which tend to produce a predominantly attached flow).

Carlson, Harry W.↗

An MME-based attitude estimator using vector observations

In this paper, an optimal batch estimator and filter based on the Minimum Model Error (MME) approach is developed for three-axis stabilized spacecraft. Three different MME algorithms are developed. The first algorithm estimates the attitude of a spacecraft using rate measurements. The second algorithm estimates the attitude without using rate measurements. The absence of rate data may be a result of intentional design or from unexpected failure of existing gyros. The third algorithm determines input-torque modeling error trajectories. All of the algorithms developed in this paper use attitude sensors (e.g., three-axis magnetometers, sun sensors, star trackers, etc.). Results using these new algorithms indicate that an MME-based approach accurately estimates the attitude, rate, and input torque trajectories of an actual spacecraft.

Crassidis, John L.↗

On-Orbit Multi-Field Wavefront Control with a Kalman Filter

A document describes a multi-field wavefront control (WFC) procedure for the James Webb Space Telescope (JWST) on-orbit optical telescope element (OTE) fine-phasing using wavefront measurements at the NIRCam pupil. The control is applied to JWST primary mirror (PM) segments and secondary mirror (SM) simultaneously with a carefully selected ordering. Through computer simulations, the multi-field WFC procedure shows that it can reduce the initial system wavefront error (WFE), as caused by random initial system misalignments within the JWST fine-phasing error budget, from a few dozen micrometers to below 50 nm across the entire NIRCam Field of View, and the WFC procedure is also computationally stable as the Monte-Carlo simulations indicate. With the incorporation of a Kalman Filter (KF) as an optical state estimator into the WFC process, the robustness of the JWST OTE alignment process can be further improved. In the presence of some large optical misalignments, the Kalman state estimator can provide a reasonable estimate of the optical state, especially for those degrees of freedom that have a significant impact on the system WFE. The state estimate allows for a few corrections to the optical state to push the system towards its nominal state, and the result is that a large part of the WFE can be eliminated in this step. When the multi-field WFC procedure is applied after Kalman state estimate and correction, the stability of fine-phasing control is much more certain. Kalman Filter has been successfully applied to diverse applications as a robust and optimal state estimator. In the context of space-based optical system alignment based on wavefront measurements, a KF state estimator can combine all available wavefront measurements, past and present, as well as measurement and actuation error statistics to generate a Maximum-Likelihood optimal state estimator. The strength and flexibility of the KF algorithm make it attractive for use in real-time optical system alignment when WFC alone cannot effectively align the system.

Lou, John↗

The Observed State of the Water Cycle in the Early Twenty-First Century

This study quantifies mean annual and monthly fluxes of Earth's water cycle over continents and ocean basins during the first decade of the millennium. To the extent possible, the flux estimates are based on satellite measurements first and data-integrating models second. A careful accounting of uncertainty in the estimates is included. It is applied within a routine that enforces multiple water and energy budget constraints simultaneously in a variational framework in order to produce objectively determined optimized flux estimates. In the majority of cases, the observed annual surface and atmospheric water budgets over the continents and oceans close with much less than 10% residual. Observed residuals and optimized uncertainty estimates are considerably larger for monthly surface and atmospheric water budget closure, often nearing or exceeding 20% in North America, Eurasia, Australia and neighboring islands, and the Arctic and South Atlantic Oceans. The residuals in South America and Africa tend to be smaller, possibly because cold land processes are negligible. Fluxes were poorly observed over the Arctic Ocean, certain seas, Antarctica, and the Australasian and Indonesian islands, leading to reliance on atmospheric analysis estimates. Many of the satellite systems that contributed data have been or will soon be lost or replaced. Models that integrate ground-based and remote observations will be critical for ameliorating gaps and discontinuities in the data records caused by these transitions. Continued development of such models is essential for maximizing the value of the observations. Next-generation observing systems are the best hope for significantly improving global water budget accounting.

Numerical analysis/modeling↗

Estimation for bilinear stochastic systems

Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed.

Willsky, A. S.↗

Neighboring Optimal Aircraft Guidance in a General Wind Environment

Method and system for determining an optimal route for an aircraft moving between first and second waypoints in a general wind environment. A selected first wind environment is analyzed for which a nominal solution can be determined. A second wind environment is then incorporated; and a neighboring optimal control (NOC) analysis is performed to estimate an optimal route for the second wind environment. In particular examples with flight distances of 2500 and 6000 nautical miles in the presence of constant or piecewise linearly varying winds, the difference in flight time between a nominal solution and an optimal solution is 3.4 to 5 percent. Constant or variable winds and aircraft speeds can be used. Updated second wind environment information can be provided and used to obtain an updated optimal route.

Jardin, Matthew R.↗

Optimal input design for aircraft instrumentation systematic error estimation

A new technique for designing optimal flight test inputs for accurate estimation of instrumentation systematic errors was developed and demonstrated. A simulation model of the F-18 High Angle of Attack Research Vehicle (HARV) aircraft was used to evaluate the effectiveness of the optimal input compared to input recorded during flight test. Instrumentation systematic error parameter estimates and their standard errors were compared. It was found that the optimal input design improved error parameter estimates and their accuracies for a fixed time input design. Pilot acceptability of the optimal input design was demonstrated using a six degree-of-freedom fixed base piloted simulation of the F-18 HARV. The technique described in this work provides a practical, optimal procedure for designing inputs for data compatibility experiments.

Morelli, Eugene A.↗

Optimality of incompletely measurable active and passive attitude control systems

Passive attitude control systems and active systems with incomplete state measurements are only suboptimal systems in the sense of optimal control theory, since optimal systems require complete state measurements or state estimations. An optimal system, then, requires additional hardware (especially in the case of flexible spacecraft) which results in higher costs. Therefore, it is a real engineering problem to determine how much an optimal system exceeds the suboptimal system, or in other words, what is the suboptimal system's degree of optimality. The problem will be treated in three steps: (1) definition of the degree of optimality for linear, time-invariant systems; (2) a computation method using the quadratic cost functional; (3) application to a gravity-gradient stabilized three-body satellite and a spinning flexible satellite.

Schiehlen, W.↗

Theoretical and experimental investigations of sensor location for optimal aeroelastic system state estimation

One of the major concerns in the design of an active control system is obtaining the information needed for effective feedback. This involves the combination of sensing and estimation. A sensor location index is defined as the weighted sum of the mean square estimation errors in which the sensor locations can be regarded as estimator design parameters. The design goal is to choose these locations to minimize the sensor location index. The choice of the number of sensors is a tradeoff between the estimation quality based upon the same performance index and the total costs of installing and maintaining extra sensors. An experimental study for choosing the sensor location was conducted on an aeroelastic system. The system modeling which includes the unsteady aerodynamics model developed by Stephen Rock was improved. Experimental results verify the trend of the theoretical predictions of the sensor location index for different sensor locations at various wind speeds.

Liu, G.↗

Optimal post-experiment estimation of poorly modeled dynamic systems

Recently, a novel strategy for post-experiment state estimation of discretely-measured dynamic systems has been developed. The method accounts for errors in the system dynamic model equations in a more general and rigorous manner than do filter-smoother algorithms. The dynamic model error terms do not require the usual process noise assumptions of zero-mean, symmetrically distributed random disturbances. Instead, the model error terms require no prior assumptions other than piecewise continuity. The resulting state estimates are more accurate than filters for applications in which the dynamic model error clearly violates the typical process noise assumptions, and the available measurements are sparse and/or noisy. Estimates of the dynamic model error, in addition to the states, are obtained as part of the solution of a two-point boundary value problem, and may be exploited for numerous reasons. In this paper, the basic technique is explained, and several example applications are given. Included among the examples are both state estimation and exploitation of the model error estimates.

Mook, D. Joseph↗