A Liapunov method for the estimation of statistical averages.
Liapunov method for estimating statistical averages of randomly perturbed system
DYNAMICS↗
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Using Finite-Element Analysis In Estimating Reliability
Method of estimating design survivability of structural component incorporates finite-element and probabilistic properties of materials. Involves evaluation of design parameters through direct comparisons of survivability of component expressed in terms of percentages of like components that survive at various lifetimes. Probabilistic properties of materials, given in terms of Weibull parameters, coupled with stress field computed by finite-element analysis to determine fatigue life based on initiation of cracks. Method applied to rotating disk containing bolt holes, representative of disks used in aerospace propulsion turbines. Also used in early stages of design process to optimize life-based designs, reducing testing of full-sized components needed to validate designs.
Zaretsky, Erwin V.↗
Star Tracker Accuracy Improvement and Optimization for Attitude Measurement in Three-Axis
High precision attitude measurement systems obviate the need for the beacon from the receiver making it possible for the spacecraft to beam a laser communications signal to a ground station without the ground station advertising its location. The research presented targets new detection and estimation methods to improve the accuracy in locating stars on a focal plane detector, and an understanding of the effects of changes in the optics design parameters and aberration, including defocus, on the navigation solution itself. This understanding can lead to an optimization of the attitude solution with respect to those optics realm parameter changes. The methodology discussed includes the development of a model of a current star tracker system. Using this model, multiple algorithms are implemented, including a multi-hypothesis method (MHT), to detect and estimate the position of the stars on the focal plane detector. It will be shown that using the MHT for detection and estimation, a greater accuracy can be found for each star estimation from more traditional detection and estimation algorithms. The approach then uses the model to develop statistics of the star tracker and the attitude estimation outputs to understand the accuracy, or variance, of the system's attitude solution. This solution is repeated for a range of defocus aberration, and a lower limit to the variance of the attitude solution is shown. A Cramer Rao lower bound solution is derived for the star tracker system and the results are compared to the Monte Carlo analysis from the model and shown to correlate very well. The approach uses a star image not as a Gaussian spot on the focal plane as done in previous work, and use of an image that includes the effects of aberrations of the optic system, and the effects of under-sampling and noise from the focal plane detector as well. Analysis includes exploring a star tracker's accuracy improvement through the combination of focus error and under-sampling effects alone, possibly contradicting conventional wisdom and approaches.
Lichter, Michael J.↗
Modeling, estimation and identification methods for static shape determination of flexible structures
This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.
Rodriguez, G.↗
A global urban heat island intensity dataset: Generation, comparison, and analysis
The urban heat island (UHI) effect, a phenomenon of local warming over urban areas, is the most well-known impact of urbanization on climate. Globally consistent estimates of the UHI intensity (UHII) are crucial for examining this phenomenon across time and space. However, publicly available UHII datasets are limited and have several constraints: (1) they are for clear-sky surface UHII, not all-sky surface UHII and canopy (air temperature) UHII; (2) the estimation methods often neglect anthropogenic disturbance, introducing uncertainties in the estimated UHII. To address these issues, this study proposes a new dynamic equal-area (DEA) method that can minimize the influence of various confounding factors on UHII estimates through a dynamic cyclic process. Utilizing the DEA method and leveraging various gridded temperature data, we develop a global-scale (>10,000 cities), long-term (over 20 years by month), and multi-faceted (clear-sky surface, all-sky surface, and canopy) UHII dataset. Further, based on these estimates, we provide a comprehensive analysis of the UHII and its trends in global cities. The UHII is found to be greater than zero in >80% of cities, with global annual average magnitudes around 1.0 °C (day) and 0.8 °C (night) for surface UHII, and close to 0.5 °C for canopy UHII. Furthermore, an interannual upward trend in UHII is observed in >60% of cities, with global annual average trends exceeding 0.1 °C/decade (day) and over 0.06 °C/decade (night) for surface UHII, and slightly surpassing 0.03 °C/decade for canopy UHII. Notably, there exists a positive correlation between the magnitude and trend of UHII, suggesting that cities with stronger UHII tend to experience faster growth in UHII. Additionally, discrepancies in UHII are found between different temperature data, stemming not only from distinctions in data types (surface or air temperature) but also from differences in data acquisition times (Terra or Aqua), weather conditions (clear-sky or all-sky), and processing methodologies (with or without gap filling). Overall, our proposed method, dataset, and analysis results have the potential to provide valuable insights for future urban climate studies. The UHII dataset is publicly available at https://doi.org/10.6084/m9.figshare.24821538.
54 ENVIRONMENTAL SCIENCES↗
Aircraft wing weight build-up methodology with modification for materials and construction techniques
An aircraft wing weight estimating method based on a component buildup technique is described. A simplified analytically derived beam model, modified by a regression analysis, is used to estimate the wing box weight, utilizing a data base of 50 actual airplane wing weights. Factors representing materials and methods of construction were derived and incorporated into the basic wing box equations. Weight penalties to the wing box for fuel, engines, landing gear, stores and fold or pivot are also included. Methods for estimating the weight of additional items (secondary structure, control surfaces) have the option of using details available at the design stage (i.e., wing box area, flap area) or default values based on actual aircraft from the data base.
York, P.↗
Reconstructing the Sky Location of Gravitational-Wave Detected Compact Binary Systems: Methodology for Testing and Comparison
The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of equal to or less than 20M solar mass and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor approx. equals 20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor approx. equals 1000 longer processing time.
technique used↗
Estimation of signal-to-noise ratios
Statistical method estimates signal-to-noise ratios in an observed random voltage, such as the output of a telemetry receiver. Signals from a distant transmitting source, overlaid by noise signals, are monitored continuously.
Couvillon, L. A., Jr.↗
Adaptive State Predictor Based Human Operator Modeling on Longitudinal and Lateral Control
Control-theoretic modeling of the human operator dynamic behavior in manual control tasks has a long and rich history. In the last two decades, there has been a renewed interest in modeling the human operator. There has also been significant work on techniques used to identify the pilot model of a given structure. The purpose of this research is to attempt to go beyond pilot identification based on collected experimental data and to develop a predictor of pilot behavior. An experiment was conducted to categorize these interactions of the pilot with an adaptive controller compensating during control surface failures. A general linear in-parameter model structure is used to represent a pilot. Three different estimation methods are explored. A gradient descent estimator (GDE), a least squares estimator with exponential forgetting (LSEEF), and a least squares estimator with bounded gain forgetting (LSEBGF) used the experiment data to predict pilot stick input. Previous results have found that the GDE and LSEEF methods are fairly accurate in predicting longitudinal stick input from commanded pitch. This paper discusses the accuracy of each of the three methods - GDE, LSEEF, and LSEBGF - to predict both pilot longitudinal and lateral stick input from the flight director's commanded pitch and bank attitudes.
Trujillo, Anna C.↗
An Eddy Current Case Study using NASA’s Transfer Function and Limited-Sample Probability of Detection Guidebooks
Probability of detection (POD) requirements for NASA fracture-critical human-rated systems can be met by (1) claiming ‘similarity’ to NASA Standard Nondestructive Evaluation (NDE) flaw sizes or (2) by inspector-specific POD demonstration, known as NASA Special NDE. Standard NDE flaw sizes are intended to represent the detection capability of most qualified inspectors, and were primarily based on POD studies in the development of the Space Shuttle Program Orbiter fracture control plan. However, these Standard NDE flaw sizes were based on fatigue cracks in flat panels of one material alloy over a limited range of panel thicknesses. While the POD study was comprehensive, the inspection conditions are relatively narrow. An evaluation of similarity between the Standard NDE POD study and flight component conditions is required to apply Standard NDE to specific flight component inspections. A similarity evaluation may include differences in materials, surface finish, component geometry (e.g., curvature, corners, welds), and inspection access. Similarity is typically based on a qualitative engineering evaluation. Recently, NASA published a quantitative methodology to assess similarity. If similarity is not supported by test and analysis, then the methodology provides a transfer function of flaw size for Special NDE POD demonstration. NASA recommends that Special POD demonstrations use flaws that are flight-like or more difficult to detect than flight component flaws, which are commonly induced fatigue cracks. Often, it is not feasible to induce fatigue cracks in flight component geometry, and therefore, a simpler representative geometry is used, commonly a flat panel, for POD demonstration. Inducing cracks in simple geometry specimens can be time-consuming and expensive, and thus, minimizing the number of flawed specimens is desired. Traditionally, NASA Special NDE demonstration was limited to MIL-HDBK-1823A methods or the binomial point-estimate method (PEM), commonly known as 29/29. Recently, NASA published a limited-sample POD (LS-POD) methodology for signal-response NDE techniques (e.g., eddy current) that provides POD demonstration with fewer specimens than previous approaches. LS-POD suggests a minimum of 10 flawed specimens, compared to 29 in the PEM and the suggested minimum of 40 from MIL-HDBK-1823A. The methodology also includes new guidance on evaluating the probability of false calls. In this presentation, these new transfer function and LS-POD methodologies are described and illustrated through an eddy current detection capability of far-side flaws on thin welded panels. A geometry-based transfer function is developed using electro-discharge machined (EDM) notches in flight component and simple geometry to estimate the Special NDE flaw size that is representative of the critical initial flaw size required by the fracture analysis. Then, fatigue cracks are induced in simple flat panels of the transferred flaw size, and the LS-POD methodology is used for Special NDE demonstration.
P. A. Parker↗
Distribution System State Estimation Using a Multiple Iteration Extended Kalman Filter Approach
To support the operation of modern distribution systems, operators require real-time visibility into system states. Due to a lack of measurements and unbalanced operation, the state estimation in distribution systems is challenging as compared to transmission systems. This paper proposes the utilization of a Multiple Iteration - Extended Kalman Filter based approach for the distribution system state estimation. This modified version of the baseline extended Kalman filter iterates over the update step multiple times thereby reducing the estimation error. The proposed algorithm along with the auxiliary algorithms such as bad data detection is integrated into a co-simulation environment. Case studies show that the proposed state estimation method can result in a lesser estimation error as compared to the baseline approach.
Bhatti, Bilal Ahmad↗
Time-dependent approximation schemes for some problems of parameter estimation in distributed systems
A parameter estimation method that can be used to estimate functional parameters in delay differential equations and moving boundary problems is discussed. In either problem, the original model equation (which is infinite-dimensional) is approximated by a system of ordinary differential equations that can be solved numerically in an efficient way. The approximation scheme is based on time-dependent spline elements. For the delay equation with time-varying delay, convergence results are presented that indicate the estimates obtained using the approximating system. Numerical test examples converge in some sense to a best-fit parameter for the original system are included by means of which time-varying and state-dependent delays and a time-varying diffusion coefficient in a one-phase, one-dimensional Stefan problem are estimated.
Murphy, K. A.↗
Robust Mosaicking of Stereo Digital Elevation Models from the Ames Stereo Pipeline
Robust estimation method is proposed to combine multiple observations and create consistent, accurate, dense Digital Elevation Models (DEMs) from lunar orbital imagery. The NASA Ames Intelligent Robotics Group (IRG) aims to produce higher-quality terrain reconstructions of the Moon from Apollo Metric Camera (AMC) data than is currently possible. In particular, IRG makes use of a stereo vision process, the Ames Stereo Pipeline (ASP), to automatically generate DEMs from consecutive AMC image pairs. However, the DEMs currently produced by the ASP often contain errors and inconsistencies due to image noise, shadows, etc. The proposed method addresses this problem by making use of multiple observations and by considering their goodness of fit to improve both the accuracy and robustness of the estimate. The stepwise regression method is applied to estimate the relaxed weight of each observation.
Kim, Tae Min↗
Development of an Inertia Relief Method for Aircraft with Dissimilar Engines in LEAPS
Weight estimation is a critical element of the aircraft conceptual design process. The Layered and Extensible Aircraft Performance System (LEAPS) is an aircraft conceptual design tool that is under development by the Systems Analysis and Concepts Directorate (SACD) at the NASA Langley Research Center. LEAPS includes modules that represent aircraft design disciplines. This work presents an update to the LEAPS wing weight estimation method to allow for engine inertia relief to be accurately accounted for when analyzing aircraft with multiple dissimilar engines.
LEAPS↗
Development of an Inertia Relief Method for Aircraft with Dissimilar Engines in LEAPS
Weight estimation is a critical element of the aircraft conceptual design process. The Layered and Extensible Aircraft Performance System (LEAPS) is an aircraft conceptual design tool that is under development by the Systems Analysis and Concepts Directorate (SACD) at the NASA Langley Research Center. LEAPS includes modules that represent aircraft design disciplines. This work presents an update to the LEAPS wing weight estimation method to allow for engine inertia relief to be accurately accounted for when analyzing aircraft with multiple dissimilar engines.
LEAPS↗
Maximum likelihood techniques in QELS
A framework for the analysis of Quasi Elastic Light Scattering (QELS) experiments designed to be used in microgravity environment is derived. Example calculations of the type to be used to design the QELS system are given. The framework for the analysis is based on the concepts of parameter estimation typified by Maximum Likelihood Estimation methods. These methods not only serve as the template for parameter estimation algorithms, but can also be used for optimal design of the experiments. Optimal design of experiments is facilitated by the fact that these methods not only give procedures for parameter estimation, but also estimates of the errors associated with the parameter estimation.
Edwards, Robert V.↗
A concept for adaptive performance optimization on commercial transport aircraft
An adaptive control method is presented for the minimization of drag during flight for transport aircraft. The minimization of drag is achieved by taking advantage of the redundant control capability available in the pitch axis, with the horizontal tail used as the primary surface and symmetric deflection of the ailerons and cruise flaps used as additional controls. The additional control surfaces are excited with sinusoidal signals, while the altitude and velocity loops are closed with guidance and control laws. A model of the throttle response as a function of the additional control surfaces is formulated and the parameters in the model are estimated from the sensor measurements using a least squares estimation method. The estimated model is used to determine the minimum drag positions of the control surfaces. The method is presented for the optimization of one and two additional control surfaces. The adaptive control method is extended to optimize rate of climb with the throttle fixed. Simulations that include realistic disturbances are presented, as well as the results of a Monte Carlo simulation analysis that shows the effects of changing the disturbance environment and the excitation signal parameters.
Jackson, Michael R.↗
Combining Ratio Estimation for Low Density Parity Check (LDPC) Coding
The Low Density Parity Check (LDPC) Code decoding algorithm make use of a scaled receive signal derived from maximizing the log-likelihood ratio of the received signal. The scaling factor (often called the combining ratio) in an AWGN channel is a ratio between signal amplitude and noise variance. Accurately estimating this ratio has shown as much as 0.6 dB decoding performance gain. This presentation briefly describes three methods for estimating the combining ratio: a Pilot-Guided estimation method, a Blind estimation method, and a Simulation-Based Look-Up table. The Pilot Guided Estimation method has shown that the maximum likelihood estimates of signal amplitude is the mean inner product of the received sequence and the known sequence, the attached synchronization marker (ASM) , and signal variance is the difference of the mean of the squared received sequence and the square of the signal amplitude. This method has the advantage of simplicity at the expense of latency since several frames worth of ASMs. The Blind estimation method s maximum likelihood estimator is the average of the product of the received signal with the hyperbolic tangent of the product combining ratio and the received signal. The root of this equation can be determined by an iterative binary search between 0 and 1 after normalizing the received sequence. This method has the benefit of requiring one frame of data to estimate the combining ratio which is good for faster changing channels compared to the previous method, however it is computationally expensive. The final method uses a look-up table based on prior simulated results to determine signal amplitude and noise variance. In this method the received mean signal strength is controlled to a constant soft decision value. The magnitude of the deviation is averaged over a predetermined number of samples. This value is referenced in a look up table to determine the combining ratio that prior simulation associated with the average magnitude of the deviation. This method is more complicated than the Pilot-Guided Method due to the gain control circuitry, but does not have the real-time computation complexity of the Blind Estimation method. Each of these methods can be used to provide an accurate estimation of the combining ratio, and the final selection of the estimation method depends on other design constraints.
Mahmoud, Saad↗