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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.
The effects of turbulence modulation on the evaporating spray characteristics of a liquid fuel jet are numerically investigated. Two modulation models are implemented into the k-epsilon two-equation model. The gas phase is solved by a pressure-based method on a Eulerian frame and droplets are solved by a stochastic discrete particle technique based on Lagrangian formulation. The k-epsilon models are used to characterize the time and length scales of the gas phase turbulence for droplet dispersions and droplet/turbulence interactions. The modulation models are found to have significant effects on gas phase dynamics, and are less important for the droplet dynamics. Numerical predictions are compared with the experimental data of Drallemier and Peters (1990).
The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.
Because of the extreme variability of rain rate in space and time and the difficulties with remote sensing methods of measuring rain rates, accurate determination of rainfall over large areas and time periods has long been a problem for hydrologists, meteorogists, and climatologists. A number of statistical models of rain have been developed in order to investigate the impact of rain variability on satellite remote sensing methods, validation of satellite rain products, and generation of rain maps with accompanying error estimates. These models may be useful in examining 'sub-grid scale' issues in representing precipitation in numerical mdoels. A stochastic model will first be described which can generate time-dependent high-resolution spatial rain fields with space and time correlations similar to those seen in rain data, as well as representing the presence of areas with zero rain rate and log-normally distributed rain rates where there is rain. A simpler model derived from this, formulated in the spectral domain, seems to imply fractal-like rain statistics at small scales when fit to rain data.
The PSAM (Probabilistic Structural Analysis Methods) program is developing a probabilistic structural risk assessment capability for the SSME components. An advanced probabilistic structural analysis software system, NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), is being developed as part of the PSAM effort to accurately simulate stochastic structures operating under severe random loading conditions. One of the challenges in developing the NESSUS system is the development of the probabilistic algorithms that provide both efficiency and accuracy. The main probability algorithms developed and implemented in the NESSUS system are efficient, but approximate in nature. In the last six years, the algorithms have improved very significantly.
NASA has funded several major programs (the Probabilistic Structural Analysis Methods Project is an example) to develop probabilistic structural analysis methods and tools for engineers to apply in the design and assessment of aerospace hardware. A probabilistic finite element software code, known as Numerical Evaluation of Stochastic Structures Under Stress, is used to determine the reliability of a critical weld of the Space Shuttle solid rocket booster aft skirt. An external bracket modification to the aft skirt provides a comparison basis for examining the details of the probabilistic analysis and its contributions to the design process. Also, analysis findings are compared with measured Space Shuttle flight data.
The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible, investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. In this paper, we apply the SCEQ algorithm (Cai and Judd, 2023) to solve a large-scale dynamic stochastic global land resource use problem with stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters and bounded shocks, the range of land conversion is considerably smaller for the dynamic stochastic model than for deterministic scenario analysis.
The gap in explicit resolution of phenomena between global climate models and cloud resolving models is shrinking at a steady pace with global integrations of several km in resolution now practical for at least some time scales. In moving toward finer resolution the long standing problem of convective parameterization is being examined along with the assumption of convective quasi-equilibrium and how this can be reconciled with the stochastic and intermittent nature of convection. In this context we examine the nature of parameterized convection in the NASA Goddard Earth Observing System (GEOS-5) Atmospheric General Circulation Model. Our analysis uses both coarse (2.5 degree) and fine scale 0.25 degree spatial resolution integrations. Two basic formulations are compared: the default option is the Relaxed Arakawa-Schubert (RAS) scheme which invokes a sequence of linearly entraining plumes and quasi-equilibrium closure. An optional modification of this method (the "Stochastic Tokioka" constraint) places a random lower limit on plume entrainment. An alternative representation is the Kain-Fritsch parameterization which was originally developed for mesoscale numerical modeling strategies. Here entrainment is determined by a crude buoyancy sorting approach that allows the plume spectrum to be more responsive to ambient vertical stratification of moisture. Diagnostics of the model behavior are referenced to recent observational evidence of continuous phase transition behavior. In particular we examine the relationship between column water vapor and probablility of convective presence and intensity. Sensitivity of the statistics of convective behavior to parcel mixing/entrainment formulations and parcel initial thermodynamics are considered. Observational statistics from A-Train and TRMM sensors provide validation of the model integrations.
A plan was initiated in 1988 to commercialize the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) probabilistic structural analysis software. The goal of the on-going commercialization effort is to begin the transfer of Probabilistic Structural Analysis Method (PSAM) developed technology into industry and to develop additional funding resources in the general area of structural reliability. The commercialization effort is summarized. The SwRI NESSUS Software System is a general purpose probabilistic finite element computer program using state of the art methods for predicting stochastic structural response due to random loads, material properties, part geometry, and boundary conditions. NESSUS can be used to assess structural reliability, to compute probability of failure, to rank the input random variables by importance, and to provide a more cost effective design than traditional methods. The goal is to develop a general probabilistic structural analysis methodology to assist in the certification of critical components in the next generation Space Shuttle Main Engine.
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.
The one point probability density function (PDF) method is examined in light of its use in actual engineering problems. The PDF method, although relatively complicated, appears to be the only format available to handle the nonlinear stochastic difficulties caused by typical reaction kinetics. Turbulence modeling, if it is to play a central role in combustion modeling, has to be integrated with the chemistry in a way which produces accurate numerical solutions to combustion problems. It is questionable whether the development of turbulent models in isolation from the peculiar statistics of reactant concentrations is a fruitful line of development as far as propulsion is concerned. There are three issues for which additional viewgraphs are prepared: the one point pdf method; the amplitude mapping closure; and a hybrid strategy for replacing a full two point pdf treatment of reacting flows by a single point pdf and correlation functions. An appeal is made for the establishment of an adequate data base for compressible flow with reactions for Mach numbers of unity or higher.
The research effort in the Center for the Advancement of Computational Mechanics at Georgia Tech has two main thrusts. The first of these is the development of special approaches for the numerical stress analysis of solids and structures whose material and geometric properties are uncertain. The second seeks to develop and implement high-efficiency plate and shell elements. The stochastic element method, currently being implemented, will be able to more accurately portray the probabilistic nature of stress, strain, and displacement in actual structures. Current research has provided a hybrid-stress shell element whose behavior is acceptable for aspect ratios as high as 30 to 1. Thus, substantially more complex analyses will be practicable as soon as this element is fully implemented. An additional advantage of the hybrid approach is that it permits more accurate stress-recovery at the upper and lower surfaces of the shell, an important consideration in high thickness-gradient applications. The software associated with the above research is being implemented in the form of extensions to the Nessus code. The hybrid shell element has been successfully tested in several small-deformation elastic analyses. The theoretical formulation of the stochastic elements is essentially complete; its implementation is just beginning.
Derived from matrix methods of structural analysis and finite element methods developed over the last three decades, computational structures technology (CST) blends computer science, numerical analysis, and approximation theory into structural analysis and synthesis. Recent significant advances in CST include stochastic-based modeling, strategies for performing large-scale structural calculations on new computing systems, and the integration of CST with other disciplinary modules for multidisciplinary analysis and design. New methodologies have been developed at NASA for integrated fluid-thermal structural analysis and integrated aerodynamic-structure-control design. The need for multiple views of data for different modules also led to the development of a number of sophisticated data-base management systems. For CST to play a role in the future development of structures technology and in the multidisciplinary design of future flight vehicles, major advances and computational tools are needed in a number of key areas.
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (O.L.F.O.) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first order systems are presented.
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with uncertain or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (OLFO) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.
The question of how random, or unconstrained, paleobiologic models should be is examined with a case study: Signor's (1982, 1985) inverse calculation of levels of marine species diversity through the Phanerozoic. His calculation involved an ingenious model that estimated species numbers and species abundances in the world oceans of the past by correcting known numbers of fossil species for variations in sedimentary rocks available for sampling and in effort paleontologists might devote to sampling. The model proves robust to changes in possible shapes of species-abundance distributions, but it is sensitive to alterations in the assumption that paleontologists collect fossils at random. If it is assumed that ease of collecting varies with age of sediment (with the Cenozoic offering easy sampling) or that paleontologists tend to seek out rarer fossils, results of the inverse calculation change. In particular, the magnitude of the calculated Cenozoic diversity increase always declines from the factor of about seven as originally reported to something considerably smaller. This leaves open the problem of the magnitude of Cenozoic increase in marine species diversity, awaiting better empirical data and, perhaps, more exacting models, random or otherwise.
This paper presents a noniterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully interacting combination of Eulerian fluid and Lagrangian particle calculations. The interaction calculations between the two phases are formulated on a pressure-velocity-coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data as well as efficiency assessments are given for some sprays typical of spray combustion applications.