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NASA NTRS1982

An adaptive tracking observer for failure-detection systems

The design problem of adaptive observers applied to linear, constant and variable parameters, multi-input, multi-output systems, is considered. It is shown that, in order to keep the observer's (or Kalman filter) false-alarm rate (FAR) under a certain specified value, it is necessary to have an acceptable proper matching between the observer (or KF) model and the system parameters. An adaptive observer algorithm is introduced in order to maintain desired system-observer model matching, despite initial mismatching and/or system parameter variations. Only a properly designed adaptive observer is able to detect abrupt changes in the system (actuator, sensor failures, etc.) with adequate reliability and FAR. Conditions for convergence for the adaptive process were obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors and accurate and fast parameter identification, in both deterministic and stochastic cases.

Sidar, M.↗

NASA NTRS1982

Design of analytical failure detection using secondary observers

The problem of designing analytical failure-detection systems (FDS) for sensors and actuators, using observers, is addressed. The use of observers in FDS is related to the examination of the n-dimensional observer error vector which carries the necessary information on possible failures. The problem is that in practical systems, in which only some of the components of the state vector are measured, one has access only to the m-dimensional observer-output error vector, with m or = to n. In order to cope with these cases, a secondary observer is synthesized to reconstruct the entire observer-error vector from the observer output error vector. This approach leads toward the design of highly sensitive and reliable FDS, with the possibility of obtaining a unique fingerprint for every possible failure. In order to keep the observer's (or Kalman filter) false-alarm rate under a certain specified value, it is necessary to have an acceptable matching between the observer (or Kalman filter) models and the system parameters. A previously developed adaptive observer algorithm is used to maintain the desired system-observer model matching, despite initial mismatching or system parameter variations. Conditions for convergence for the adaptive process are obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors, while accurate and fast parameter identification, in both deterministic and stochastic cases, is obtained.

Sisar, M.↗

NASA NTRS2003

Subgrid Combustion Modeling for the Next Generation National Combustion Code

In the first year of this research, a subgrid turbulent mixing and combustion methodology developed earlier at Georgia Tech has been provided to researchers at NASA/GRC for incorporation into the next generation National Combustion Code (called NCCLES hereafter). A key feature of this approach is that scalar mixing and combustion processes are simulated within the LES grid using a stochastic 1D model. The subgrid simulation approach recovers locally molecular diffusion and reaction kinetics exactly without requiring closure and thus, provides an attractive feature to simulate complex, highly turbulent reacting flows of interest. Data acquisition algorithms and statistical analysis strategies and routines to analyze NCCLES results have also been provided to NASA/GRC. The overall goal of this research is to systematically develop and implement LES capability into the current NCC. For this purpose, issues regarding initialization and running LES are also addressed in the collaborative effort. In parallel to this technology transfer effort (that is continuously on going), research has also been underway at Georgia Tech to enhance the LES capability to tackle more complex flows. In particular, subgrid scalar mixing and combustion method has been evaluated in three distinctly different flow field in order to demonstrate its generality: (a) Flame-Turbulence Interactions using premixed combustion, (b) Spatially evolving supersonic mixing layers, and (c) Temporal single and two-phase mixing layers. The configurations chosen are such that they can be implemented in NCCLES and used to evaluate the ability of the new code. Future development and validation will be in spray combustion in gas turbine engine and supersonic scalar mixing.

Menon, Suresh↗

NASA NTRS2008

A Globally Optimal Particle Tracking Technique for Stereo Imaging Velocimetry Experiments

An important phase of any Stereo Imaging Velocimetry experiment is particle tracking. Particle tracking seeks to identify and characterize the motion of individual particles entrained in a fluid or air experiment. We analyze a cylindrical chamber filled with water and seeded with density-matched particles. In every four-frame sequence, we identify a particle track by assigning a unique track label for each camera image. The conventional approach to particle tracking is to use an exhaustive tree-search method utilizing greedy algorithms to reduce search times. However, these types of algorithms are not optimal due to a cascade effect of incorrect decisions upon adjacent tracks. We examine the use of a guided evolutionary neural net with simulated annealing to arrive at a globally optimal assignment of tracks. The net is guided both by the minimization of the search space through the use of prior limiting assumptions about valid tracks and by a strategy which seeks to avoid high-energy intermediate states which can trap the net in a local minimum. A stochastic search algorithm is used in place of back-propagation of error to further reduce the chance of being trapped in an energy well. Global optimization is achieved by minimizing an objective function, which includes both track smoothness and particle-image utilization parameters. In this paper we describe our model and present our experimental results. We compare our results with a nonoptimizing, predictive tracker and obtain an average increase in valid track yield of 27 percent

McDowell, Mark↗

NASA NTRS1997

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗

NASA NTRSDate not supplied

NESC GN&C TDT Workshop on 2D Image Motion Optical Transfer Functions, Pointing Performance Analysis, and Requirements

What You Will Learn: The focus is on payload imaging performance due to pointing motion. Some historical background on pointing performance analysis is given. The Optical Transfer Function (OTF) and Modulation Transfer Function (MTF) are defined. The imaging performance due to pointing motion is measured by image motion optical transfer functions (IM OTF). IM OTFs are defined for displacement, smear, and jitter motions, which are all rigorously defined. Deterministic and Statistical IM OTFs are briefly derived and graphically illustrated and compared. The IM OTFs are parameterized by pointing error metrics(PEM), which are means and covariances of displacement, smear, and jitter. Emphasis is on procedures and algorithms to evaluate the image motion optical transfer functions and pointing error metrics. Three procedures are covered, which depend on whether the pointing error data is from time-domain simulation, frequency-domain analysis, or stochastic modeling. A method to evaluate the relative contribution of disturbance sources and to identify the most significant contributors is presented. The presentation includes pertinent discussion of flexible structures and control-structure interaction. No single book can adequately cover this subject, so a book is not required for the course. A list of selected articles, reports, documents, and books is provided for reference and further study. Mathis kept to the minimum necessary to convey principles; lengthy derivations are left to the reference material. Graphics are used to illustrate concepts. As with any such learning endeavor, the knowledge gained will be retained and strengthened through actual practice.c©2019–2021 Mark E. Pittelkau— 5

NASA Engineering and Safety Center (NESC)↗

NASA NTRS1993

Numerical experiments with model monophyletic and paraphyletic taxa

The problem of how accurately paraphyletic taxa versus monophyletic (i.e., holophyletic) groups (clades) capture underlying species patterns of diversity and extinction is explored with Monte Carlo simulations. Phylogenies are modeled as stochastic trees. Paraphyletic taxa are defined in an arbitrary manner by randomly choosing progenitors and clustering all descendants not belonging to other taxa. These taxa are then examined to determine which are clades, and the remaining paraphyletic groups are dissected to discover monophyletic subgroups. Comparisons of diversity patterns and extinction rates between modeled taxa and lineages indicate that paraphyletic groups can adequately capture lineage information under a variety of conditions of diversification and mass extinction. This suggests that these groups constitute more than mere "taxonomic noise" in this context. But, strictly monophyletic groups perform somewhat better, especially with regard to mass extinctions. However, when low levels of paleontologic sampling are simulated, the veracity of clades deteriorates, especially with respect to diversity, and modeled paraphyletic taxa often capture more information about underlying lineages. Thus, for studies of diversity and taxic evolution in the fossil record, traditional paleontologic genera and families need not be rejected in favor of cladistically-defined taxa.

Non-NASA Center↗

NASA NTRS1971

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Parrish, R. V.↗

NASA NTRS1994

Stochastic solution to quantum dynamics

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

John, Sarah↗

NASA NTRS1975

Adaptive statistical pattern classifiers for remotely sensed data

A technique for the adaptive estimation of nonstationary statistics necessary for Bayesian classification is developed. The basic approach to the adaptive estimation procedure consists of two steps: (1) an optimal stochastic approximation of the parameters of interest and (2) a projection of the parameters in time or position. A divergence criterion is developed to monitor algorithm performance. Comparative results of adaptive and nonadaptive classifier tests are presented for simulated four dimensional spectral scan data.

Gonzalez, R. C.↗

NASA NTRS1982

On-line methods for rotorcraft aeroelastic mode identification

The requirements for the on-line identification of rotorcraft aeroelastic blade modes from random response test data are presented. A recursive maximum likelihood (RML) technique is used in conjunction with a bandpass filter to identify isolated blade mode damping and frequency. The RML technique is demonstrated to have excellent convergence characteristics in random measurement noise and random process noise excitation. The RML identification technique uses an ARMA representation for the aeroelastic stochastic system and requires virtually no user interaction while providing accurate confidence bands on the parameter estimates. Comparisons are made with an off-line Newton type maximum likelihood algorithm which uses a state variable model representation. Results are presented from simulation random response data which quantify the identifed parameter convergence behavior for various levels of random excitation which is typical of wind tunnel turbulence levels. The RML technique is applied to hingless rotor test data from the NASA Langley Research Center Helicopter Hover Facility.

Molusis, J. A.↗

NASA NTRS2013

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.

Ono, Masahiro↗

NASA NTRS1978

The augmentation algorithm and molecular phylogenetic trees

Moore's (1977) augmentation procedure is discussed, and it is concluded that the procedure is valid for obtaining estimates of the total number of fixed nucleotide substitutions both theoretically and in practice, for both simulated and real data, and in agreement, for experimentally dense data sets, with stochastic estimates of the divergence, provided the restrictions on codon mutability resulting from natural selection are explicitly allowed for. Tateno and Nei's (1978) critique that the augmentation procedure has a systematic bias toward overestimation of the total number of nucleotide replacements is disputed, and a data analysis suggests that ancestral sequences inferred by the method of parsimony contain a large number of incorrectly assigned nucleotides.

Holmquist, R.↗

NASA NTRS1980

Stochastic analysis of multiple-passband spectral classifications systems affected by observation errors

The classification of targets viewed by a pushbroom type multiple band spectral scanner by algorithms suitable for implementation in high speed online digital circuits is considered. A class of algorithms suitable for use with a pipelined classifier is investigated through simulations based on observed data from agricultural targets. It is shown that time distribution of target types is an important determining factor in classification efficiency.

Tsokos, C. P.↗

NASA NTRS2018

An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes

Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere.

vegetation remote sensing; stochastic radiative tr↗

NASA NTRS1987

Algorithmic commonalities in the parallel environment

The ultimate aim of this project was to analyze procedures from substantially different application areas to discover what is either common or peculiar in the process of conversion to the Massively Parallel Processor (MPP). Three areas were identified: molecular dynamic simulation, production systems (rule systems), and various graphics and vision algorithms. To date, only selected graphics procedures have been investigated. They are the most readily available, and produce the most visible results. These include simple polygon patch rendering, raycasting against a constructive solid geometric model, and stochastic or fractal based textured surface algorithms. Only the simplest of conversion strategies, mapping a major loop to the array, has been investigated so far. It is not entirely satisfactory.

Mcanulty, Michael A.↗

NASA NTRS1983

A separated bias identification and state estimation algorithm for nonlinear systems

A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.

Caglayan, A. K.↗

NASA NTRS2022

Coupling Carbon Oxidation and Surface Recession in Direct-Simulation Monte Carlo Code, SPARTA

Ablative thermal protection system (TPS) materials for spacecraft are composites that are often made out of carbon-based reinforcement and a polymeric matrix. They endure high-temperature oxidation and surface recession when re-entering Earth’s atmosphere. Ablation is the result of many coupled and competing thermal, mechanical, and chemical phenomena, and it is difficult to isolate the role of each on the overall degradation of the TPS. Here we develop an ablation model for material recession coupled explicitly to finite rate carbon oxidation in complex microstructures. In this work, Stochastic PArallel Rarified-gas Time-accurate Analyzer (SPARTA), a direct-simulation Monte Carlo (DSMC) code, is modified to allow oxidation-driven ablation of implicitly defined carbon surfaces. In SPARTA, implicit surfaces are generated from the grid corner point values via a marching cubes algorithm, therefore creating a new set of surface elements every time ablation is performed. The finite-rate oxidation model developed by Gopalan et. al, was adapted to tally surface reactions and other surface data on a per-grid cell basis. The ablation functionality was also adjusted so once the reactions have occurred, the number of reactions leading to CO formation can be converted to corner point reduction values; therefore, carbon removal is directly proportional to surface recession. We also develop robust algorithms which handle the evolution of the flow cells and solid material regions, including split cells (flow cell divided in two by a solid surface). Finally, we demonstrate our implicit chemistry model for 2D and 3D geometries by producing reaction statistics and detailed visualization of oxidation-induced material recession at the microscale.

V Arias↗