Stochastic hydrodynamics of sediment transport
Three dimensional unsteady and steady sediment distribution obtained by Monte Carlo simulation method, using stochastic hydrodynamics model for transport
Chen, K.-C.↗
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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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Assimilating partial observation to enhance feedback control of stochastic dynamical systems
Here, in this paper, we present a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage partial observation of the state process, a common occurrence in practical scenarios. Traditional stochastic optimal control methods assume full state observation, which is often not feasible in real-world fluid dynamics control problems. Our approach underscores the significance of utilizing observational data to inform control policy design. Specifically, we introduce a kernel learning backward stochastic differential equation (SDE) filter to enhance data assimilation efficiency and propose a sample-wise stochastic optimization method within the stochastic maximum principle framework. We demonstrate the efficacy and accuracy of our method in the control of advection-diffusion-reaction flow problem and the Dubins airplane maneuvering problem with model uncertainty.
data driven↗
Thermodynamically consistent incorporation of the Langmuir adsorption model into compressible fluctuating hydrodynamics
For a gas–solid interfacial system where chemical species undergo reversible adsorption, we develop a mesoscopic stochastic modeling method that simulates both gas-phase hydrodynamics and surface coverage dynamics by coupling the Langmuir adsorption model with compressible fluctuating hydrodynamics. To this end, we derive a thermodynamically consistent mass–energy update scheme that accounts for how the mass and energy variables in the gas and surface subsystems should be updated according to the changes in the number of molecules of each species in each subsystem due to adsorption and desorption events. By performing a stochastic analysis for the ideal Langmuir model and the full hydrodynamic system, we analytically confirm that our mass–energy update scheme captures thermodynamic equilibrium predicted by equilibrium statistical mechanics. We find that an internal energy correction term is needed, which is attributed to the difference in the mean kinetic energy of gas molecules colliding with the surface from that computed from the Maxwell–Boltzmann distribution. By performing an equilibrium simulation study for an ideal gas mixture of CO and Ar, with CO undergoing reversible adsorption, we validate our overall simulation method and implementation.
Adsorption↗
Approximations to optimal non-linear filters
Signal and noise problem as solution to nonlinear stochastic differential equations
DIFFERENTIAL EQUATION↗
On the evaluation of expected performance cost for partially observed closed-loop stochastic systems
New methods are presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.
Bayard, D. S.↗
Planning to fail: mission design for modular repairable robot teams
This paper presents a method using stochastic simulation to evaluate the reliability of robot teams consisting of modular robots. For an example planetary exploration mission we use this method to compare the performance of a repairable robot team with spare modules versus nonrepairable robot teams.
mission planning↗
STUDIES IN THE ASYMPTOTIC THEORY OF CONTROL SYSTEMS, I. STOCHASTIC AND DETERMINISTIC N-STAGE PROCESSES
Asymptotic theory of control - stochastic and deterministic n-stage processes
N-STAGE PROCESS↗
Numerical methods for the solution of the degenerate non-linear elliptic equations arising in optimal stochastic control theory.
Iterative method for optimal control problems for Markov chains, discussing degenerate nonlinear elliptic equations solution in optimal stochastic control theory
Kleinman, A.↗
A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus
This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.
stochastic calculus↗
Estimation of correlation functions by stochastic approximation.
Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.
Habibi, A.↗
A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus
This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.
Corbetta, M.↗
A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering
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.
Deepak, A.↗
Supercomputer optimizations for stochastic optimal control applications
Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.
Chung, Siu-Leung↗
Efficient Parameterization of Density Functional Tight-Binding for 5 f -Elements: A Th–O Case Study
Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th–O system, which was subsequently applied to the study of ThO 2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO 2 . Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Determining design gust loads for nonlinear aircraft similarity between methods based on matched filter theory and on stochastic simulation
This is a work-in-progress paper. It explores the similarity between the results from two different analysis methods - one deterministic, the other stochastic - for computing maximized and time-correlated gust loads for nonlinear aircraft. To date, numerical studies have been performed using two different nonlinear aircraft configurations. These studies demonstrate that results from the deterministic analysis method are realizable in the stochastic analysis method.
Scott, Robert C.↗
Stochastic parametric skeletal dosimetry model for humans: Pediatric and adult computational skeleton phantoms for internal bone marrow dosimetry
Currently, computational phantoms that simulate skeletal tissues are used in active red bone marrow (AM) internal dosimetry. Up-to-date reference computational phantoms recommended by the ICRP are based on the analysis of CT-images of cadavers. Such phantoms have significant disadvantages. One disadvantage is that the assessment of uncertainty due to the population variability of skeleton dimensions and microstructure results from the limited availability of autopsy material. Another disadvantage is the simplified modelling of cortical layer and bone microarchitecture. A method of stochastic parametric skeletal dosimetry modelling of the bone structures – SPSD modelling – has been developed as an alternative to the ICRP reference phantoms. In the framework of this approach, skeletal phantom parameters are evaluated based on extensively reviewed results of published measurements of real bones. The SPSD approach allows for the assessment of both population-average values and their variability. SPSD-phantoms of the skeleton are modelled in voxel representation. They consist of smaller phantoms of the bone sites – segments – described by simple geometric shapes with uniform microarchitecture parameters. Such segmentation makes it possible to account for non-homogeneous skeletal microarchitecture and to model the bone structure with the required voxel resolution to elaborate suitable skeletal phantoms. The current study presents the parameters of the SPSD skeletal phantoms for the following age-groups: newborn, 1-year-old, 5-year-old, 10-year-old, 15-year-old (male and female), and adult (male and female). This skeletal phantom can be used for dosimetry as an alternative to available reference phantoms for bone-seeking radionuclides. The above-mentioned age- and sex-specific skeletal phantoms are comprised of 289 unique segments. The characteristics of the SPSD phantoms do not contradict published data and are in good agreement with the measurement results of real bones.
Science & Technology - Other Topics↗
Alternative Representations of Convective Processes in the NASA GEOS-5 AGCM
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.
Robertson, Franklin↗
Cosmic Ray Propagation through the Magnetic Fields of the Galaxy with Extended Halo
In this project we perform theoretical studies of 3-dimensional cosmic ray propagation in magnetic field configurations of the Galaxy with an extended halo. We employ our newly developed Markov stochastic process methods to solve the diffusive cosmic ray transport equation. We seek to understand observations of cosmic ray spectra, composition under the constraints of the observations of diffuse gamma ray and radio emission from the Galaxy. The model parameters are directly are related to properties of our Galaxy, such as the size of the Galactic halo, particle transport in Galactic magnetic fields, distribution of interstellar gas, primary cosmic ray source distribution and their confinement in the Galaxy. The core of this investigation is the development of software for cosmic ray propagation models with the Markov stochastic process approach. Values of important model parameters for the halo diffusion model are examined in comparison with observations of cosmic ray spectra, composition and the diffuse gamma-ray background. This report summarizes our achievement in the grant period at the Florida Institute of Technology. Work at the co-investigator's institution, the University of New Hampshire, under a companion grant, will be covered in detail by a separate report.
Zhang, Ming↗