Random differential equations in control theory
Control processes and optimization problems solutions by stochastic differential equations, discussing dynamic models and programming, linear filtering and optimal feedback
Wonham, W. M.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Application of stochastic optimal reduced state feedback gain computation procedures to the design of aircraft gust alleviation controllers
A stochastic linear model that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs was used to determine feedback gains useful for reducing the vertical acceleration which results from the presence of a vertical wind gust. Considered in the study were the influence of various feedback configurations, the effects of sensor noise, flight condition changes, and initialization procedures. Results showed that for sixth order linearized longitudinal motion, a controller with feedback on three states could be designed for effective gust alleviation taking into account both sensor noise and flight condition variation.
Sobel, K.↗
Structure of particle-laden jets - Measurements and predictions
Measurements of mean and fluctuating velocities of both phases as well as particle mass fluxes were completed in turbulent, particle-laden jets containing monodisperse particles with well-defined initial and boundary conditions. The new measurements were used to evaluate a stochastic separated flow model of the process which treated effects of interphase slip and turbulent dispersion using random-walk computations for particle motion. The continuous phase was treated using a modified k-epsilon model allowing for direct contributions of interphase transport to both mean and turbulence properties. The model performed reasonably well over the new data base, with all empirical parameters fixed from earlier work. In contrast, simplified models ignoring either interphase slip or turbulent dispersion yielded poor agreement with the measurements.
Shuen, J.-S.↗
A statistical model of carbon/carbon composite failure
A failure model which considers the stochastic nature of the damage accumulation process is essential to assess reliability and to accurately scale the results from standard test specimens to composite structures. A superior filamentary composite for high temperature applications is composed of carbon fibers in a carbon matrix. Carbon-carbon composites are the strongest known material at very high temperatures. Since there appears to be a significant randomness in C-C material strength which cannot be controlled or detected with current technology, a better model of the material failure based upon statistical principles should be used. Simple applications of the model based upon the limited data provide encouraging results that indicate that better design of test specimens would provide a substantially higher prediction for the design strength of C-C composites. An A-basis strength for the C-C tensile rings from a first stage D-5 billets was estimated. A statistical failure model was developed for these rings which indicates that this strength may be very conservative for larger C-C parts. The analysis may be improved by use of a heterogeneous/noncontinuum finite element approach on the minimechanical level.
Slattery, Kerry T.↗
Remote sensing science for the Nineties; Proceedings of IGARSS '90 - 10th Annual International Geoscience and Remote Sensing Symposium, University of Maryland, College Park, May 20-24, 1990. Vols. 1, 2, & 3
Various papers on remote sensing (RS) for the nineties are presented. The general topics addressed include: subsurface methods, radar scattering, oceanography, microwave models, atmospheric correction, passive microwave systems, RS in tropical forests, moderate resolution land analysis, SAR geometry and SNR improvement, image analysis, inversion and signal processing for geoscience, surface scattering, rain measurements, sensor calibration, wind measurements, terrestrial ecology, agriculture, geometric registration, subsurface sediment geology, radar modulation mechanisms, radar ocean scattering, SAR calibration, airborne radar systems, water vapor retrieval, forest ecosystem dynamics, land analysis, multisensor data fusion. Also considered are: geologic RS, RS sensor optical measurements, RS of snow, temperature retrieval, vegetation structure, global change, artificial intelligence, SAR processing techniques, geologic RS field experiment, stochastic modeling, topography and Digital Elevation model, SAR ocean waves, spaceborne lidar and optical, sea ice field measurements, millimeter waves, advanced spectroscopy, spatial analysis and data compression, SAR polarimetry techniques. Also discussed are: plant canopy modeling, optical RS techniques, optical and IR oceanography, soil moisture, sea ice back scattering, lightning cloud measurements, spatial textural analysis, SAR systems and techniques, active microwave sensing, lidar and optical, radar scatterometry, RS of estuaries, vegetation modeling, RS systems, EOS/SAR Alaska, applications for developing countries, SAR speckle and texture.
Source record↗
Multifrequency studies of bright radio supernova remnants. 2: W49B
We report radio observations of the supernova remnant W49B using the Very Large Array (VLA) of the NRAO at 90, 20, and 6 cm. This work continues the study of the properties of young, bright supernova remnants (SNRs) begun with 3C 391 (Moffett & Reynolds 1994). Here we present high-resolution images of total intensity, polarization, and spectral index of W49B. In large-scale morphology it is basically a box-shaped remnant expanding into an apparently inhomogeneous medium, but we also find small-scale structures, arcs and filaments, which lie interior to the outer shell in projection. The actual spatial position of the filaments is unknown, though we suspect that they are in the remnant interior rather than on the front or back face of the blast wave. In addition, their distribution in two dimensions suggests the projection of a helical structure. The shell edge, sharply rising in brightness for at least 3/4 of its circumference, still remains unresolved at our highest resolution (4 sec). This for our assumed distance of 8 kpc, the width of the region in which the emission appears is less than 0.16 pc, indicating short mean free paths for shock-accelerated electrons and high levels of MHD turbulence presumably causing the scattering. We find no polarized flux at 90 or 20 cm, with 3 sigma upper limits in polarized intensity of 36 mJy at 90 cm (45 sec resolution) and 7.2 mJy at 20 cm (5 sec resolution), or 22 micro-Jy/sq arcsec and 370 micro-jy/sq arcsec, respectively, for any emission extended on those scales. Polarized flux is present at 6 cm, but at a very low mean polarized fraction (total polarized flux divided by total flux) of 0.44% +/- 0.06%, which, as for 3C 391, is much lower than typical for bright SNRs at this frequency. The morphology in polarized intensity is poorly correlated with that in total intensity. We see excursions in the polarized fraction up to at least 10% in a few locations, but even where polarization is seen, typical levels are a few percent. Tangled or disordered magnetic fields in the emitting region of the radio shell may be responsible for depolarizing the radio synchrotron radiation, but some form of internal Faraday depolarization may also occur. We estimate the foreground Faraday rotation measure to be about -450 rad/sq m, similar to that found for 3C 391, which is also the Galactic plane and just about as distant. Spectral index images created from the total intensity images show that the spectral index across W49B is constant to within about Delta alpha approximately 0.1 in bright regions. This result weakly supports a common origin of the radio-emitting electrons, as in the blast wave, rather than in inhomogeneous turbulent regions of differing properties due to the stochastic (second-order Fermi) acceleration process. Variations at the level of Delta alpha approximately 0.1 are seen, but their significance is doubtful. New observations at 90 cm, using experimental three-dimensional imaging technology, may improve on this limit.
Moffett, David A.↗
Dynamical Evolution of Planetary Embryos
During the past decade, progress has been made by relating the 'standard model' for the formation of planetary systems to computational and observational advances. A significant contribution to this has been provided by this grant. The consequence of this is that the rigor of the physical modeling has improved considerably. This has identified discrepancies between the predictions of the standard model and recent observations of extrasolar planets. In some cases, the discrepancies can be resolved by recognition of the stochastic nature of the planetary formation process, leading to variations in the final state of a planetary system. In other cases, it seems more likely that there are major deficiencies in the standard model, requiring our identifying variations to the model that are not so strongly constrained to our Solar System.
Wetherill, George W.↗
The Short-Term Prediction of Universal Time and Length-Of-Day Using Atmospheric Angular Momemtum
Methods to combine the diverse set of geodetic measurements of Earth orientation that are currently available, and to interpolate and extrapolate these data to generate an optimal estimate of Earth orientation, have been under development at JPL for a number of years. The strategy currently in use is a Kalman filtering scheme based on Earth orentation parameters and their excitation functions that incorporates stochastic models of the important physical processes and takes into account the variable form, quality, and temporal density of the data provided by diffent measurement services.
Universal Time↗
Knowledge-based processing for aircraft flight control
This Contractor Report documents research in Intelligent Control using knowledge-based processing in a manner dual to methods found in the classic stochastic decision, estimation, and control discipline. Such knowledge-based control has also been called Declarative, and Hybid. Software architectures were sought, employing the parallelism inherent in modern object-oriented modeling and programming. The viewpoint adopted was that Intelligent Control employs a class of domain-specific software architectures having features common over a broad variety of implementations, such as management of aircraft flight, power distribution, etc. As much attention was paid to software engineering issues as to artificial intelligence and control issues. This research considered that particular processing methods from the stochastic and knowledge-based worlds are duals, that is, similar in a broad context. They provide architectural design concepts which serve as bridges between the disparate disciplines of decision, estimation, control, and artificial intelligence. This research was applied to the control of a subsonic transport aircraft in the airport terminal area.
Painter, John H.↗
Neural chaos: A spectral stochastic neural operator
Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.
Polynomial chaos expansion↗
Evaluation of Improved Pushback Forecasts Derived from Airline Ground Operations Data
Accurate and timely predictions of airline pushbacks can potentially lead to improved performance of automated decision-support tools for airport surface traffic, thus reducing the variability and average duration of costly airline delays. One factor which affects the realization of these benefits is the level of uncertainty inherent in the turn processes. To characterize this inherent uncertainty, three techniques are developed for predicting time-to-go until pushback as a function of available ground-time; elapsed ground-time; and the status (not-started/in-progress/completed) of individual turn processes (cleaning, fueling, etc.). These techniques are tested against a large and detailed dataset covering approximately l0(exp 4) real-world turn operations obtained through collaboration with Deutsche Lufthansa AG. Even after the dataset is filtered to obtain a sample of turn operations with minimal uncertainty, the standard deviation of forecast error for all three techniques is lower-bounded away from zero, indicating that turn operations have a significant stochastic component. This lower-bound result shows that decision-support tools must be designed to incorporate robust mechanisms for coping with pushback demand stochasticity, rather than treating the pushback demand process as a known deterministic input.
Carr, Francis↗
Integrated Arrival and Departure Schedule Optimization Under Uncertainty
In terminal airspace, integrating arrivals and departures with shared waypoints provides the potential of improving operational efficiency by allowing direct routes when possible. Incorporating stochastic evaluation as a post-analysis process of deterministic optimization, and imposing a safety buffer in deterministic optimization, are two ways to learn and alleviate the impact of uncertainty and to avoid unexpected outcomes. This work presents a third and direct way to take uncertainty into consideration during the optimization. The impact of uncertainty was incorporated into cost evaluations when searching for the optimal solutions. The controller intervention count was computed using a heuristic model and served as another stochastic cost besides total delay. Costs under uncertainty were evaluated using Monte Carlo simulations. The Pareto fronts that contain a set of solutions were identified and the trade-off between delays and controller intervention count was shown. Solutions that shared similar delays but had different intervention counts were investigated. The results showed that optimization under uncertainty could identify compromise solutions on Pareto fonts, which is better than deterministic optimization with extra safety buffers. It helps decision-makers reduce controller intervention while achieving low delays.
stochastic optimization↗
Time-dependent behavior of active galactic nuclei with pair production
We study the properties of coupled partial differential equations describing the time-dependent behavior of the photon and electron occupation numbers for conditions likely to be found near active galactic nuclei (AGN). The processes governing electron acceleration are modeled by a stochastic accelerator, and we include acceleration by Alfvenic and whistler turbulence. The acceleration of electrons is limited by Compton and synchrotron losses, and the number density of electrons depends on pair production and annihilation processes. We also treat particle escape from the system. We examine the steady, (possibly) oscillatory, and unstable solutions that arise for various choices of parameters. We examine instabilities related to pair production and trapping and consider the formation of pair jets.
Li, H.↗
Stochastic Simulation of Mudcrack Damage Formation in an Environmental Barrier Coating
The FEAMAC/CARES program, which integrates finite element analysis (FEA) with the MAC/GMC (Micromechanics Analysis Code with Generalized Method of Cells) and the CARES/Life (Ceramics Analysis and Reliability Evaluation of Structures / Life Prediction) programs, was used to simulate the formation of mudcracks during the cooling of a multilayered environmental barrier coating (EBC) deposited on a silicon carbide substrate. FEAMAC/CARES combines the MAC/GMC multiscale micromechanics analysis capability (primarily developed for composite materials) with the CARES/Life probabilistic multiaxial failure criteria (developed for brittle ceramic materials) and Abaqus (Dassault Systèmes) FEA. In this report, elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio elements enabled the formation of crack boundaries, leading to development of mudcrack-patterned damage. Finite element models of a disk-shaped three-dimensional specimen and a twodimensional model of a through-the-thickness cross section subjected to progressive cooling from 1,300 °C to an ambient temperature of 23 °C were made. Mudcrack damage in the coating resulted from the buildup of residual tensile stresses between the individual material constituents because of thermal expansion mismatches between coating layers and the substrate. A two-parameter Weibull distribution characterized the coating layer stochastic strength response and allowed the effect of the Weibull modulus on the formation of damage and crack segmentation lengths to be studied. The spontaneous initiation of cracking and crack coalescence resulted in progressively smaller mudcrack cells as cooling progressed, consistent with a fractal-behaved fracture pattern. Other failure modes such as delamination, and possibly spallation, could also be reproduced. The physical basis assumed and the heuristic approach employed, which involves a simple stochastic cellular automaton methodology to approximate the crack growth process, are described. The results ultimately show that a selforganizing mudcrack formation can derive from a Weibull distribution that is used to describe the stochastic strength response of the bulk brittle ceramic material layers of an EBC.
Nemeth, Noel N.↗
Requirements for theoretical models of outflows
Recent observational and theoretical investigations of astrophysical mass outflows are reviewed, with a focus on the basic physical principles. Specific limitations on the observational data and their interpretation are listed and discussed. Modeling problems considered include the role of the critical point in determining the mass-loss rate and terminal velocity, the physical processes controlling density at the critical point, the possible coexistence of multiple mass-loss mechanisms, time scales, instabilities and phase changes, multiphase atmospheres and winds, the definition of geometries, the role of the environment, explosive transient events, stochastic phenomena, mode-mode coupling and damping processes, departures from ionization equilibrium, and nonthermal phenomena.
Linsky, Jeffrey L.↗
Probability Density Function Control of Frequency Fluctuations in Renewable-Rich Power Systems
The stochastic nature of renewable energy sources (RESs) necessitates treating power system frequency response as a random process with a nonstationary probability density function (PDF). Here, based upon the stochastic distribution control theory originated by the second author, this paper proposes a novel stochastic controller to improve the frequency PDF in power grids when integrating a large amount of RESs, thereby minimizing the effects of uncertainties and enhancing overall system stability. The key idea is to manipulate the controllable power generation resources so that the frequency PDF is make to follow a target PDF by using the stochastic distribution control theory originated by the second author. The proposed method can easily be plugged into existing automatic generation controls for multi-area transmission grids. The proposed method is validated via a modified Kundar's two area system and 240-bus Western Electricity Coordinating Council systems. The simulation results show that the proposed control shapes the frequency PDF narrower and sharper, leading to a notable improvement toward minimizing the effects of randomness and uncertainty during grid operation.
frequency↗
Utilizing remote sensing of thematic mapper data to improve our understanding of estuarine processes and their influence on the productivity of estuarine-dependent fisheries
A stochastic spatial computer model addressing coastal resource problems in Lousiana is being refined and validated using thematic mapper (TM) imagery. The TM images of brackish marsh sites were processed and data were tabulated on spatial parameters from TM images of the salt marsh sites. The Fisheries Image Processing Systems (FIPS) was used to analyze the TM scene. Activities were concentrated on improving the structure of the model and developing a structure and methodology for calibrating the model with spatial-pattern data from the TM imagery.
Browder, Joan A.↗
Automated Flight Routing Using Stochastic Dynamic Programming
Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.
Ng, Hok K.↗