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NASA NTRSDate not supplied

Path Planning: Differential Dynamic Programming and Model Predictive Path Integral Control on VTOL Aircraft

This paper explores two optimal control approaches, widely used in robotics, to establish their viability as real-time trajectory planners for vehicle configurations envisioned for the emerging aviation sector of Urban Air Mobility (UAM). Differential Dynamic Programming (DDP) enables planning over highly nonlinear dynamics using second-order approximations along a nominal trajectory, and displays quadratic convergence to a local solution. Model Predictive Path Integral (MPPI) is a stochastic sampling-based algorithm that can optimize for general cost criteria, including potentially highly nonlinear formulations, and supports parallel computation through the use of modern GPU hardware. In this work, DDP and MPPI were implemented using model predictive control (MPC), and the results indicate they are able to successfully transition the aircraft over different flight envelopes and generate trajectories unique to UAM vehicles.

Differential Dynamic Programming↗

NASA NTRS1972

Control theory for random systems

A survey is presented of the current knowledge available for designing and predicting the effectiveness of controllers for dynamic systems which can be modeled by ordinary differential equations. A short discussion of feedback control is followed by a description of deterministic controller design and the concept of system state. The need for more realistic disturbance models led to the use of stochastic process concepts, in particular the Gauss-Markov process. A compensator controlled system, with random forcing functions, random errors in the measurements, and random initial conditions, is treated as constituting a Gauss-Markov random process; hence the mean-square behavior of the controlled system is readily predicted. As an example, a compensator is designed for a helicopter to maintain it in hover in a gusty wind over a point on the ground.

Bryson, A. E., Jr.↗

NASA NTRS1973

Suboptimal stochastic controller for an n-body spacecraft

The problem is studied of determining a stochastic optimal controller for an n-body spacecraft. The approach used in obtaining the stochastic controller involves the application, interpretation, and combination of advanced dynamical principles and the theoretical aspects of modern control theory. The stochastic controller obtained for a complicated model of a spacecraft uses sensor angular measurements associated with the base body to obtain smoothed estimates of the entire state vector, can be easily implemented, and enables system performance to be significantly improved.

Larson, V.↗

NASA NTRS1973

A guidance and navigation system for continuous low thrust vehicles

A midcourse guidance and navigation system for continuous low thrust vehicles is described. A set of orbit elements, known as the equinoctial elements, are selected as the state variables. The uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time nominal trajectory is defined and the equation of motion and the measurement equation are linearized about this nominal trajectory. An exponential cost criterion is constructed and a linear feedback guidance law is derived to control the thrusting direction of the engine. Using this guidance law, the vehicle will fly in a trajectory neighboring the nominal trajectory. The extended Kalman filter is used for state estimation. Finally a short mission using this system is simulated. The results indicate that this system is very efficient for short missions.

Tse, C. J. C.↗

NASA NTRS1973

A guidance and navigation system for continuous low-thrust vehicles

A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.

Jack-Chingtse, C.↗

NASA NTRS1985

Composite Loads Spectra for Select Space Propulsion Structural Components: Probabilistic Load Model Development

This effort is in support of the development of the expert system of computer codes to predict the loads on select structural components of a space propulsion engine. The development will be based primarily on the space shuttle main engine (SSME) test data base. Because of random variations of the many different sources of the loadings on the selected structural components and transients, a probabilistic approach to the problems was adopted. The goal of this task is to characterize all of the individual sources of loads at critical structural locations, such as the turbine blades, the transfer ducts, and liquid oxygen posts, using state-of-the-art probabilistic methods with varying levels of sophistication. The second phase of this work is the development of a composite load model based on a probabilistic synthesis of the individual load model previously developed. This model will be based on the stochastic combination of the load variables and not on the physical process for the combination of the individual loads to the composite load seen by the selected structural components.

Kurth, R.↗

NASA NTRS1985

Cometary impacts, molecular clouds, and the motion of the sun perpendicular to the galactic plane

The stochastic nature of the mass extinction model of Rampino and Stothers (1984), based on the vertical oscillation of the solar system about the plane of the Galaxy, can accommodate a few events with large phase discrepancies. The degree of modulation is crucial in that it depends on the scale height of the population of molecular clouds relative to the amplitude of the solar system and tends to zero if this ratio is large and encounters are entirely random. Here data are presented here from CO surveys of molecular clouds both within and beyond the solar circle which permit explicit calculation of the strength of the modulation. The cloud layer near the sun it too extended and, as a consequence, the modulation of cloud encounters is too weak for a statistically significant period to be extracted from the nine extinctions analyzed by Rampino and Stothers.

Thaddeus, P.↗

NASA NTRS1990

Performance evaluation of a Doppler radar system for wind shear detection

Nonlinear stochastic differential equations are used to model wind shear, and extended Kalman filters are used to generate state estimates from measurements received from a Doppler radar onboard an aircraft. Likelihood-ratio tests are then used to detect the presence of wind shear. The performance of the system is evaluated by deriving theoretical expressions for the false alarm and miss error probabiilties. The approach uses a Fokker-Planck equation. The overall methodology is general and should be of interest in other applications.

Khalaf, Camille S.↗

NASA NTRS1993

Bifurcation analysis of a simple analytic model of self-propagating star formation

We investigate the structure and stability of rotationally symmetric nonhomogeneous time-independent solutions derived from a simple analytic model of self-propagating star formation. For this purpose we employ two methodologies: We use bifurcation theoretical methods to prove the existence of nonhomogeneous axisymmetric stationary solutions of an appropriate nonlinear evolution equation for the stellar density. We show that the nonhomogeneous solution branch bifurcates from the homogeneous one at a critical parameter value of the star formation rate. Further, the analytical theory allows us to show that the new solution set is stable in the weakly nonlinear regime near the bifurcation point. To follow the solution branch further, we use numerical methods. The numerical calculation shows the structure and stability of these solutions. We conclude that no periodic time-dependent solutions of this special model exist, and no further bifurcations can be found. The same results have been found in simulations of stochastic self-propagating star formation based on similar models. Therefore, our findings provide a natural explanation, why long-lived large-scale structure have not been found in those simulations.

Neukirch, Thomas↗

NASA NTRS2002

Health Monitoring for Airframe Structural Characterization

This study established requirements for structural health monitoring systems, identified and characterized a prototype structural sensor system, developed sensor interpretation algorithms, and demonstrated the sensor systems on operationally realistic test articles. Fiber-optic corrosion sensors (i.e., moisture and metal ion sensors) and low-cycle fatigue sensors (i.e., strain and acoustic emission sensors) were evaluated to validate their suitability for monitoring aging degradation; characterize the sensor performance in aircraft environments; and demonstrate placement processes and multiplexing schemes. In addition, a unique micromachined multimeasure and sensor concept was developed and demonstrated. The results show that structural degradation of aircraft materials could be effectively detected and characterized using available and emerging sensors. A key component of the structural health monitoring capability is the ability to interpret the information provided by sensor system in order to characterize the structural condition. Novel deterministic and stochastic fatigue damage development and growth models were developed for this program. These models enable real time characterization and assessment of structural fatigue damage.

Munns, Thomas E.↗

NASA NTRS2007

A Black-Scholes Approach to Satisfying the Demand in a Failure-Prone Manufacturing System

The goal of this paper is to use a financial model and a hedging strategy in a systems application. In particular, the classical Black-Scholes model, which was developed in 1973 to find the fair price of a financial contract, is adapted to satisfy an uncertain demand in a manufacturing system when one of two production machines is unreliable. This financial model together with a hedging strategy are used to develop a closed formula for the production strategies of each machine. The strategy guarantees that the uncertain demand will be met in probability at the final time of the production process. It is assumed that the production efficiency of the unreliable machine can be modeled as a continuous-time stochastic process. Two simple examples illustrate the result.

Chavez-Fuentes, Jorge R.↗

NASA NTRS2008

The Mock LISA Data Challenge Round 3: New and Improved Sources

The Mock LISA Data Challenges are a program to demonstrate and encourage the development of data-analysis capabilities for LISA. Each round of challenges consists of several data sets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information they can infer about the source parameters. The challenges are being released in rounds of increasing complexity and realism. Challenge 3. currently in progress, brings new source classes, now including cosmic-string cusps and primordial stochastic backgrounds, and more realistic signal models for supermassive black-hole inspirals and galactic double white dwarf binaries.

Baker, John↗

NASA NTRS2011

A Statistical Model of Tropical Cyclone Tracks in the Western North Pacific with ENSO-Dependent Cyclogenesis

A new statistical model for western North Pacific Ocean tropical cyclone genesis and tracks is developed and applied to estimate regionally resolved tropical cyclone landfall rates along the coasts of the Asian mainland, Japan, and the Philippines. The model is constructed on International Best Track Archive for Climate Stewardship (IBTrACS) 1945-2007 historical data for the western North Pacific. The model is evaluated in several ways, including comparing the stochastic spread in simulated landfall rates with historic landfall rates. Although certain biases have been detected, overall the model performs well on the diagnostic tests, for example, reproducing well the geographic distribution of landfall rates. Western North Pacific cyclogenesis is influenced by El Nino-Southern Oscillation (ENSO). This dependence is incorporated in the model s genesis component to project the ENSO-genesis dependence onto landfall rates. There is a pronounced shift southeastward in cyclogenesis and a small but significant reduction in basinwide annual counts with increasing ENSO index value. On almost all regions of coast, landfall rates are significantly higher in a negative ENSO state (La Nina).

Yonekura, Emmi↗

NASA NTRS2011

Calibrated Noise Measurements with Induced Receiver Gain Fluctuations

The lack of well-developed techniques for modeling changing statistical moments in our observations has stymied the application of stochastic process theory in science and engineering. These limitations were encountered when modeling the performance of radiometer calibration architectures and algorithms in the presence of non stationary receiver fluctuations. Analyses of measured signals have traditionally been limited to a single measurement series. Whereas in a radiometer that samples a set of noise references, the data collection can be treated as an ensemble set of measurements of the receiver state. Noise Assisted Data Analysis is a growing field of study with significant potential for aiding the understanding and modeling of non stationary processes. Typically, NADA entails adding noise to a signal to produce an ensemble set on which statistical analysis is performed. Alternatively as in radiometric measurements, mixing a signal with calibrated noise provides, through the calibration process, the means to detect deviations from the stationary assumption and thereby a measurement tool to characterize the signal's non stationary properties. Data sets comprised of calibrated noise measurements have been limited to those collected with naturally occurring fluctuations in the radiometer receiver. To examine the application of NADA using calibrated noise, a Receiver Gain Modulation Circuit (RGMC) was designed and built to modulate the gain of a radiometer receiver using an external signal. In 2010, an RGMC was installed and operated at the National Institute of Standards and Techniques (NIST) using their Noise Figure Radiometer (NFRad) and national standard noise references. The data collected is the first known set of calibrated noise measurements from a receiver with an externally modulated gain. As an initial step, sinusoidal and step-function signals were used to modulate the receiver gain, to evaluate the circuit characteristics and to study the performance of a variety of calibration algorithms. The receiver noise temperature and time-bandwidth product of the NFRad are calculated from the data. Statistical analysis using temporal-dependent calibration algorithms reveals that the natural occurring fluctuations in the receiver are stationary over long intervals (100s of seconds); however the receiver exhibits local non stationarity over the interval over which one set of reference measurements are collected. A variety of calibration algorithms have been applied to the data to assess algorithms' performance with the gain fluctuation signals. This presentation will describe the RGMC, experiment design and a comparative analysis of calibration algorithms.

Racette, Paul↗

NASA NTRSDate not supplied

Probing Sensitivity of Discharge Characteristics to Model Selection using Uncertainty Quantification in an aprotic Li-Oxygen Battery

Currently, there are several models in the literature, such as kinetic models, microstructural models, and mass transport models that describe a Li-air battery's discharge behavior. Many of these models are calibrated and tested at low current densities and cannot be easily transferred to high current densities. Even at low current densities, there is no quantitative method for a researcher to choose a reaction kinetic model such as classical Butler-Volmer and its derivatives, and modified Marcus-Hush-Chidsey, a resistance model for lithium peroxide such as electron transport via tunneling or linear resistivity, a surface coverage model (lithium peroxide growth) such as partial coverage or full coverage, and mass transport model (discussed in Ref. [1]). Also, it is time-consuming to test different models at high current density (1C) due to a lack of well-tested models and well-calibrated model parameters. For this presentation, we will develop an analytical model, which acts as a surrogate model for a sophisticated finite element model to predict discharge time and discharge voltage. Next, we use an uncertainty quantifying technique called reduced-order stochastic optimization [2, 3] to determine the uncertainty in model parameters for rate kinetics, lithium peroxide resistivity, and parasitic resistance. Finally, a finite element simulation is performed to determine the error introduced by the surrogate model and its influence on the uncertainty in the model parameters.

M Mehta↗

NASA NTRS2017

Predicting Cell Death and Mutation Frequency for a Wide Spectrum of LET by Assuming DNA Break Clustering Inside Repair Domains

The high relative biological effectiveness (RBE) of high charged and energy (HZE) particles for cell death, DNA mutations and cancer remain based on experimental data. In this work, we propose that the existence of DNA repair domains is sufficient to predict both cell death and mutation frequencies for any LET by only taking into account experimental data from low-LET, offering one mechanism for RBE across LET. We hypothesize that whenever multiple DNA double-strand breaks (DSBs) are generated within the same DNA repair domain, DSBs are actively regrouped for more efficient repair [1]. This hypothesis has been supported by the low-LET sublinear dose response observed at doses greater than ~1Gy for 53BP1 radiation-induced foci (RIF) reflecting increasing DSB/RIF with dose [2]. Previously, we modeled radiation-induced cell death of human breast cells by first inferring the size of these domains from the dose dependence of low-LET RIF, and by associating a lethality factor to the number of pairs of DSBs in each RIF [1]. In this work, we first integrate the new NASA computer models RITCARD (Relativistic Ion Tracks, Chromosome Aberrations, Repair, and Damage) [3] and BDSTracks (Biological Damage by Stochastic Tracks) for a more accurate microdosimetry and a better model of the nuclear organization to predict the location of DSBs. A large array of particles and energy are simulated, covering more than three orders of magnitude for LET (~1-1000 keV/Âµm). Next, we extend our previous model to predict mutation frequencies by assuming that clustered DSBs increase mutation probability, which is formalized by the mutation frequency being linearly dependent on both the number of DSBs and the number of pairs of DSBs inside individual RIF. Linear coefficients are estimated so that simulations predict accurately mutation frequencies observed in Chinese hamster cells exposed to low-LET. Keeping these coefficients unchanged, we then predict mutation frequencies induced by HZE by simulating DSBs and obtain RBEs for mutations and cell death following the expected experimental bell shape for LET dependence. We also observe an orientation effect that needs to be confirmed, showing different RBE depending on the angle of the HZE beam hitting the main axis of the cell.

Plante, Ianik↗

NASA NTRS1983

Identification and stochastic control of helicopter dynamic modes

A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.

Molusis, J. A.↗

NASA NTRS1993

A review of chemically reactive turbulent flow mixing mechanisms and a new design for a low NO(x) combustor

A review of chemically reactive flow analysis is presented. Key studies are reviewed. The approaches to modeling chemically reactive flows that are discussed are PDF, conserved PDF, conserved scalar, stochastic, and mixing length. Turbulent mixing mechanisms are also discussed and a model is formulated that could be used for optimizing non-premixed gas reacting systems. Consequently, a re-examination of the NO(x) reduction concepts for nonpremixed reactants are suggested together with two new designs for low NO(x) subsonic combustor research.

Mcbeath, Giorgio↗