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The classical LQG stochastic control law is reformulated using the matrix factorization S equals UDU super T. This method yields a statistical guidance analysis algorithm that is numerically superior to the classical solution yet requires negligible additional computation and storage. Moreover, experience with U-D algorithms has shown them to be adaptable and easy to implement on a variety of problems.
An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.
The subject of this paper is the application of extremal field guidance to the covariance analysis of low thrust retargeting guidance. The general procedure for low thrust navigation analysis is briefly reviewed. The basic equations of trajectory optimization and extremal field guidance are presented with emphasis on the low thrust problem. The adopted formulation includes thruster on-off times as control variables and accounts for the effects of model parameter variations. A method of solution of the guidance equations is outlined; and the application of the solution in a covariance analysis, including a procedure for the treatment of model parameter variations as either biases or first order Gauss-Markov stochastic processes, is discussed.
The processing, mission planning, and support requirements were defined for the HL-20 lifting-body configuration that can serve as a Personnel Launch System. These requirements were based on the assumption of an operating environment that incorporates aircraft and airline support methods and techniques that are applicable to operations. The study covered the complete turnaround process for the HL-20, including landing through launch, and mission operations, but did not address the support requirements of the launch vehicle except for the integrated activities. Support is defined in terms of manpower, staffing levels, facilities, ground support equipment, maintenance/sparing requirements, and turnaround processing time. Support results were drawn from two contracted studies, plus an in-house analysis used to define the maintenance manpower. The results of the contracted studies were used as the basis for a stochastic simulation of the support environment to determine the sufficiency of support and the effect of variance on vehicle processing. Results indicate the levels of support defined for the HL-20 through this process to be sufficient to achieve the desired flight rate of eight flights per year.
Innovative organizational complexity and product quality models applicable to performance metrics for NASA-MSFC's Systems Analysis and Integration Laboratory (SAIL) missions and objectives are presented. An intensive research effort focuses on the synergistic combination of stochastic process modeling, nodal and spatial decomposition techniques, organizational and computational complexity, systems science and metrics, chaos, and proprietary statistical tools for accelerated risk assessment. This is followed by the development of a preliminary model, which is uniquely applicable and robust for quantitative purposes. Exercise of the preliminary model using a generic system hierarchy and the AXAF-I architectural hierarchy is provided. The Kendall test for positive dependence provides an initial verification and validation of the model. Finally, the research and development of the innovation is revisited, prior to peer review. This research and development effort results in near-term, measurable SAIL organizational and product quality methodologies, enhanced organizational risk assessment and evolutionary modeling results, and 91 improved statistical quantification of SAIL productivity interests.
The future Communication, Navigation, and Surveillance/Air Traffic Management (CNS/ATM) System will rely on global satellite navigation, and ground-based and satellite based communications via Multi-Protocol Networks (e.g. combined Aeronautical Telecommunications Network (ATN)/Internet Protocol (IP)) to bring about needed improvements in efficiency and safety of operations to meet increasing levels of air traffic. This paper will discuss the development of an approach that completely describes optimal data link architecture configuration and behavior to meet the multiple conflicting objectives of concurrent and different operations functions. The practical application of the approach enables the design and assessment of configurations relative to airspace operations phases. The approach includes a formal taxonomic classification, an architectural analysis methodology, and optimization techniques. The formal taxonomic classification provides a multidimensional correlation of data link performance with data link service, information protocol, spectrum, and technology mode; and to flight operations phase and environment. The architectural analysis methodology assesses the impact of a specific architecture configuration and behavior on the local ATM system performance. Deterministic and stochastic optimization techniques maximize architectural design effectiveness while addressing operational, technology, and policy constraints.
This paper presents an uncertainty analysis of the stagnation-point calibration probe surface predictions for conditions that span the performance envelope of the Hypersonic Materials Environmental Test System facility located at NASA Langley Research Center. A second-order stochastic expansion was constructed over 47 uncertain parameters to evaluate the sensitivities, identify the most significant uncertain variables, and quantify the uncertainty in the stagnation-point heat flux and pressure predictions of the calibration probe for a low- and high-enthalpy test condition. A sensitivity analysis showed that measurement bias uncertainty is the most significant contributor to the stagnation-point pressure and heat flux variance for the low-enthalpy condition. For the high-enthalpy condition, a paradigm shift in sensitivities revealed the computational fluid dynamics model input uncertainty as the main contributor. A comparison between the prediction and measurement of the stagnation-point conditions under uncertainty showed that there was evidence of statistical disagreement. A validation metric was proposed and applied to the prediction uncertainty to account for the statistical disagreement when compared to the possible stagnation-point heat flux and pressure measurements.
This work analyses activation calculations for dosimetry materials during a steady-state irradiation in the Transient Reactor Test (TREAT) reactor core. Hence, we developed a workflow based on the Monte Carlo code OpenMC alongside a custom depletion solver. The irradiation-induced activity as a function of time is computed, and several sensitivity studies are performed to evaluate uncertainty. This study has shown activity computations are sensitive to flux amplitude, irradiation time, atoms quantity and microscopic cross sections. Stochastic uncertainties have been propagated to evaluate the activity uncertainty for each dosimetry material. Most uncertainties are below our target of 3%, which demonstrates OpenMC as a powerful predictive and analysis tool. The precise results obtained through this newly developed computation scheme will be used in future experiments to characterize quantities of interest when operating the TREAT reactor in new configurations.
This work analyses activation calculations for dosimetry materials during a steady-state irradiation in the Transient Reactor Test (TREAT) reactor core. Hence, we developed a workflow based on the Monte Carlo code OpenMC alongside a custom depletion solver. The irradiation-induced activity as a function of time is computed, and several sensitivity studies are performed to evaluate uncertainty. This study has shown activity computations are sensitive to flux amplitude, irradiation time, atoms quantity and microscopic cross sections. Stochastic uncertainties have been propagated to evaluate the activity uncertainty for each dosimetry material. Most uncertainties are below our target of 3%, which demonstrates OpenMC as a powerful predictive and analysis tool. The precise results obtained through this newly developed computation scheme will be used in future experiments to characterize quantities of interest when operating the TREAT reactor in new configurations.
Structural components produced from laminated CMC (ceramic matrix composite) materials are being considered for a broad range of aerospace applications that include various structural components for the national aerospace plane, the space shuttle main engine, and advanced gas turbines. Specifically, these applications include segmented engine liners, small missile engine turbine rotors, and exhaust nozzles. Use of these materials allows for improvements in fuel efficiency due to increased engine temperatures and pressures, which in turn generate more power and thrust. Furthermore, this class of materials offers significant potential for raising the thrust-to-weight ratio of gas turbine engines by tailoring directions of high specific reliability. The emerging composite systems, particularly those with silicon nitride or silicon carbide matrix, can compete with metals in many demanding applications. Laminated CMC prototypes have already demonstrated functional capabilities at temperatures approaching 1400 C, which is well beyond the operational limits of most metallic materials. Laminated CMC material systems have several mechanical characteristics which must be carefully considered in the design process. Test bed software programs are needed that incorporate stochastic design concepts that are user friendly, computationally efficient, and have flexible architectures that readily incorporate changes in design philosophy. The CCARES (Composite Ceramics Analysis and Reliability Evaluation of Structures) program is representative of an effort to fill this need. CCARES is a public domain computer algorithm, coupled to a general purpose finite element program, which predicts the fast fracture reliability of a structural component under multiaxial loading conditions.
Analysis of the responses of rising or falling spherical wind sensors to atmospheric wind perturbations on the wind profile in the vertical, using Fourier transform techniques. The linearized equations of motion of a sensor that is subject to drag and gravitational body forces are developed by perturbing a sensor about an equilibrium uniform motion with wind fluctuations which have vertical variations. The wind environment and sensor velocities are decomposed with stochastic Fourier-Stieltjes integrals, and the linearized equations of motion are used to derive the response functions and phase angles of the sensor motions. The results of the analysis are used to analyze the response properties of the Jimsphere balloon wind sensor. It is shown that, in general, the transfer functions associated with the horizontal sensor motions are smaller than the transfer functions associated with the vertical sensor motions in the omega times T product range from zero to infinity, omega being the wind perturbation frequency and T a time constant of the system. Thus, the sensor is more responsive to vertical than to horizontal air motions.
The Annular Core Research Reactor (ACRR) Monte Carlo N-Particle (MCNP) model is used by ACRR reactor operators and experiment designers at Sandia National Laboratories for a variety of computational calculations ranging from reactor kinetics parameter estimates and safety analyses to experimental planning. To understand the dominant source of uncertainty within the MCNP model, perturbations in temperature were applied to individual ACRR MCNP fuel rods. Fuel rod temperatures were randomly sampled from a uniform distribution from operational temperatures to quantify temperature-related uncertainty effects. Stochastic mixing was used to blend the cross sections of the desired temperatures using the MCNP continuous and Thermal Neutron Scattering Treatment [S(α,β)] libraries in ENDF/B-VII.1. Furthermore, this uncertainty analysis produced a 640 row × 640 column correlation and covariance matrix of the neutron energy spectra. Positive covariance was produced around the 1-MeV region and the 0.2-eV region. Correlation was found in the thermal and fast energy regions, but no correlation was observed in the slowing-down energy region because interactions in this region are not dominated by fuel.
The L–H transition power threshold PLH is observed to increase with applied n = 3 resonant magnetic perturbations (RMP) in ITER-similar-shape plasmas with balanced neutral beam torque injection in DIII-D. The increase is most pronounced with added electron–cyclotron heating: PLH increases with decreasing edge plasma collisionality as PLH/PLH-08 ~ (ν*)−0.5, where PLH-08 is the 2008 ITPA multi-machine power threshold scaling. This result raises concerns for H-mode access at low edge collisionality in ITER, where RMP may have to be applied before the L–H transition to safely suppress the first edge-localized mode. Non-axisymmetric modifications with RMP include a simultaneous reduction of the radial electric field (Er) well depth and E × B shear. This can be attributed to increasing edge toroidal co-current rotation, and is consistent with substantially increased local long-wavelength turbulence (measured via beam emission spectroscopy). At high RMP perturbation strength the edge electric field Er reverses sign locally (becomes positive), with changes in dominant turbulence modes. Edge magnetic stochasticity provides an attractive explanation of the observed modifications, and the observed changes in toroidal rotation and Er are consistent with a simple fluid model describing radial electron current flow along stochastic fieldlines. The observed collisionality dependence of the L-mode edge electric field with applied RMP is also qualitatively consistent with this model. Reflectometry data indicate a significant reduction of the normalized L-mode radial density gradient a/Ln at high RMP field with simultaneous increase in radial particle flux and electron thermal flux from power balance analysis. We conjecture that the increase of PLH with RMP results from the combined effects of reduced E × B flow shear (increasing turbulent transport levels) and toroidal/poloidal flow modulation due to edge stochasticity. Initial experiments indicate that non-resonant n = 3 magnetic perturbations lead only to relatively small changes in Er, E × B shear and fluctuation characteristics, and have less impact on the L–H transition power threshold. This motivates further exploration of the RMP spectrum dependence of PLH for possible mitigation of the observed threshold increase.
Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. So an important question remains, where does the information originate? In this paper, we examine this question using stochastic simulations of earthquake catalogs. Our catalog simulations are computed using an Earthquake Rescaled Aftershock Seismicity (“ERAS”) stochastic model. This model is similar in many ways to other stochastic seismicity simulations, but has the advantage that the model has only 2 free parameters to be set, one for the aftershock (Omori-Utsu) time decay, and one for the aftershock spatial migration away from the epicenter. Generating a simulation catalog and fitting the two parameters to the observed catalog such as California takes only a few minutes of wall clock time. While clustering can arise from random, Poisson statistics, we show that significant information in the simulation catalogs arises from the “non-Poisson” power-law aftershock clustering, implying that the practice of de-clustering observed catalogs may remove information that would otherwise be useful in forecasting and nowcasting. We also show that the nowcasting method provides similar results with the ERAS model as it does with observed seismicity.
Elemental abundances (C6, N7, O8, Na11, Mg12, Al3, P15, S16, Cl17, K19, Ca20, Ti22, Mn25, Fe26, and Ni28) were obtained for a set of terrestrial fossils and the rock matrix surrounding them. Principal Component Analysis extracted five factors accounting for the 92.5% of the data variance, i.e. information content, of the elemental abundance data. Hierarchical Cluster Analysis provided unsupervised sample classification distinguishing fossil from matrix samples on the basis of either raw abundances or PCA input that agreed strongly with visual classification. A stochastic, non-linear Artificial Neural Network produced a Bayesian probability of correct sample classification. The results provide a quantitative probabilistic methodology for discriminating terrestrial fossils from the surrounding rock matrix using chemical information. To demonstrate the applicability of these techniques to the assessment of meteoritic samples or in situ extraterrestrial exploration, we present preliminary data on samples of the Orgueil meteorite. In both systems an elemental signature produces target classification decisions remarkably consistent with morphological classification by a human expert using only structural (visual) information. We discuss the possibility of implementing a complexity analysis metric capable of automating certain image analysis and pattern recognition abilities of the human eye using low magnification optical microscopy images and discuss the extension of this technique across multiple scales.
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.
Plant cell signaling often relies on the cellular organization of receptor-like kinases (RLKs) within membrane nanodomains to enhance signaling specificity and efficiency. Thus, nanometer-scale quantitative analysis of spatial organizations of RLKs could provide new understanding of mechanisms underlying plant responses to environmental stress. Here, we used stochastic optical reconstruction fluorescence microscopy (STORM) to quantify the colocalization of the flagellin-sensitive-2 (FLS2) receptor and the nanodomain marker, remorin, within Arabidopsis thaliana root hair cells. We found that recovery of FLS2 and remorin in the plasma membrane, following ligand-induced internalization by bacterial-flagellin-peptide (flg22), reached ~85% of their original membrane density after ~90 min. The pairs colocalized at the membrane at greater frequencies, compared with simulated randomly distributed pairs, except for directly after recovery, suggesting initial uncoordinated recovery followed by remorin and FLS2 pairing in the membrane. The purinergic receptor, P2K1, colocalized with remorin at similar frequencies as FLS2, while FLS2 and P2K1 colocalization occurred at significantly lower frequencies, suggesting that these RLKs mostly occupy distinct nanodomains. The chitin elicitor receptor, CERK1, colocalized with FLS2 and remorin at much lower frequencies, suggesting little coordination between CERK1 and FLS2. These findings emphasize STORM’s capacity to observe distinct nanodomains and degrees of coordination between plant cell receptors, and their respective immune pathways.
A probabilistic fracture mechanics approach for predicting the failure life distribution due to subcritical crack growth is presented. A state-of-the-art crack propagation method is used in a Monte Carlo simulation to generate a distribution of failure lives. The crack growth failure model expresses failure life as a function of stochastic parameters including environment, loads, material properties, geometry, and model specification errors. A stochastic crack growth rate model that considers the uncertainties due to scatter in the data and mode misspecification is proposed. The rationale for choosing a particular type of probability distribution for each stochastic input parameter and for specifying the distribution parameters is presented. The approach is demonstrated through a probabilistic crack growth failure analysis of a welded tube in the Space Shuttle Main Engine. A discussion of the results from this application of the methodology is given.