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Results for “Stochastic numerical methods”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗
NASA NTRS1997

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure.

Deavours, Daniel D.↗
NASA NTRS1990

Advances and trends in computational structures technology

The major goals of computational structures technology (CST) are outlined, and recent advances in CST are examined. These include computational material modeling, stochastic-based modeling, computational methods for articulated structural dynamics, strategies and numerical algorithms for new computing systems, multidisciplinary analysis and optimization. The role of CST in the future development of structures technology and the multidisciplinary design of future flight vehicles is addressed, and the future directions of CST research in the prediction of failures of structural components, the solution of large-scale structural problems, and quality assessment and control of numerical simulations are discussed.

Noor, A. K.↗
NASA NTRS1992

Computational fluid dynamics combustion analysis evaluation

This study involves the development of numerical modelling in spray combustion. These modelling efforts are mainly motivated to improve the computational efficiency in the stochastic particle tracking method as well as to incorporate the physical submodels of turbulence, combustion, vaporization, and dense spray effects. The present mathematical formulation and numerical methodologies can be casted in any time-marching pressure correction methodologies (PCM) such as FDNS code and MAST code. A sequence of validation cases involving steady burning sprays and transient evaporating sprays will be included.

Kim, Y. M.↗
NASA NTRS1992

Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow

For the numerical simulation of inhomogeneous turbulent flows, a method is developed for generating stochastic inflow boundary conditions with a prescribed power spectrum. Turbulence statistics from spatial simulations using this method with a low fluctuation Mach number are in excellent agreement with the experimental data, which validates the procedure. Turbulence statistics from spatial simulations are also compared to those from temporal simulations using Taylor's hypothesis. Statistics such as turbulence intensity, vorticity, and velocity derivative skewness compare favorably with the temporal simulation. However, the statistics of dilatation show a significant departure from those obtained in the temporal simulation. To directly check the applicability of Taylor's hypothesis, space-time correlations of fluctuations in velocity, vorticity, and dilatation are investigated. Convection velocities based on vorticity and velocity fluctuations are computed as functions of the spatial and temporal separations. The profile of the space-time correlation of dilatation fluctuations is explained via a wave propagation model.

Lee, Sangsan↗
NASA NTRS1994

Stochastic solution to quantum dynamics

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

John, Sarah↗
NASA NTRS1983

Tradeoff studies in multiobjective insensitive design of airplane control systems

A computer aided design method for multiobjective parameter-insensitive design of airplane control systems is described. Methods are presented for trading off nominal values of design objectives against sensitivities of the design objectives to parameter uncertainties, together with guidelines for designer utilization of the methods. The methods are illustrated by application to the design of a lateral stability augmentation system for two supersonic flight conditions of the Shuttle Orbiter. Objective functions are conventional handling quality measures and peak magnitudes of control deflections and rates. The uncertain parameters are assumed Gaussian, and numerical approximations of the stochastic behavior of the objectives are described. Results of applying the tradeoff methods to this example show that stochastic-insensitive designs are distinctly different from deterministic multiobjective designs. The main penalty for achieving significant decrease in sensitivity is decreased speed of response for the nominal system.

Schy, A. A.↗
NASA NTRS1988

A forward method for optimal stochastic nonlinear and adaptive control

A computational approach is taken to solve the optimal nonlinear stochastic control problem. The approach is to systematically solve the stochastic dynamic programming equations forward in time, using a nested stochastic approximation technique. Although computationally intensive, this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual dimensionality problem associated with solving the dynamic programming equations backward in time. It is shown that the cost degrades monotonically as the complexity of the algorithm is reduced. This provides a strategy for suboptimal control with clear performance/computation tradeoffs. A numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method.

Bayard, David S.↗
NASA NTRS1998

Stochastic Methods for Aircraft Design

The global stochastic optimization method, simulated annealing (SA), was adapted and applied to various problems in aircraft design. The research was aimed at overcoming the problem of finding an optimal design in a space with multiple minima and roughness ubiquitous to numerically generated nonlinear objective functions. SA was modified to reduce the number of objective function evaluations for an optimal design, historically the main criticism of stochastic methods. SA was applied to many CFD/MDO problems including: low sonic-boom bodies, minimum drag on supersonic fore-bodies, minimum drag on supersonic aeroelastic fore-bodies, minimum drag on HSCT aeroelastic wings, FLOPS preliminary design code, another preliminary aircraft design study with vortex lattice aerodynamics, HSR complete aircraft aerodynamics. In every case, SA provided a simple, robust and reliable optimization method which found optimal designs in order 100 objective function evaluations. Perhaps most importantly, from this academic/industrial project, technology has been successfully transferred; this method is the method of choice for optimization problems at Northrop Grumman.

Pelz, Richard B.↗
NASA NTRS1995

Implementation of probabilistic design methodology at Tennessee State University

The fact that Deterministic Design Method no longer satisfies most design needs calls for methods that will cope with the high trend in technology. The advance in computer technology has reduced the rigors that normally accompany many design analysis methods that account for uncertainties in design parameters. Probabilistic Design Methodology (PDM) is beginning to make impact in engineering design. This method is gaining more recognition in industries than in educational institutions. Some of the reasons for the limited use of the PDM at the moment are that many are unaware of its potentials, and most of the software developed for PDM are very recent. The central goal of the PDM project at Tennessee State University is to introduce engineering students to this method. The students participating in the project learn about PDM and the computer codes that are available to the design engineer. The software being used for this project is NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) developed under NASA probabilistic structural analysis program. NESSUS has three different modules which make it a very comprehensive computer code for PDM. Since this method is new to the students, its introduction into the engineering curriculum is to be in stages. These range from the introduction of PDM and its software to the applications. While this program is being developed for its eventual inclusion into the engineering curriculum, some graduate and undergraduate students are already carrying out some projects using this method. As the students are increasing their understanding on PDM, they are at the same time applying it to some common design problems. The areas this method is being applied at the moment include, Design of Gears (spur and worm); Design of Brakes; Design of Heat Exchangers Design of Helical Springs; and Design of Shock Absorbers. Some of the current results of these projects are presented.

Onwubiko, Chinyere↗
NASA NTRS1982

Random element method for numerical modeling of diffusional processes

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Ghoniem, A. F.↗
NASA NTRS1993

Further studies using matched filter theory and stochastic simulation for gust loads prediction

This paper describes two analysis methods - one deterministic, the other stochastic - for computing maximized and time-correlated gust loads for aircraft with nonlinear control systems. The first method is based on matched filter theory; the second is based on stochastic simulation. The paper summarizes the methods, discusses the selection of gust intensity for each method and presents numerical results. A strong similarity between the results from the two methods is seen to exist for both linear and nonlinear configurations.

Scott, Robert C.↗
NASA NTRS1993

Further studies using matched filter theory and stochastic simulation for gust loads prediction

This paper describes two analysis methods -- one deterministic, the other stochastic -- for computing maximized and time-correlated gust loads for aircraft with nonlinear control systems. The first method is based on matched filter theory; the second is based on stochastic simulation. The paper summarizes the methods, discusses the selection of gust intensity for each method and presents numerical results. A strong similarity between the results from the two methods is seen to exist for both linear and nonlinear configurations.

Scott, Robert C.↗
NASA NTRS1991

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system components, part 2

The technical effort and computer code enhancements performed during the sixth year of the Probabilistic Structural Analysis Methods program are summarized. Various capabilities are described to probabilistically combine structural response and structural resistance to compute component reliability. A library of structural resistance models is implemented in the Numerical Evaluations of Stochastic Structures Under Stress (NESSUS) code that included fatigue, fracture, creep, multi-factor interaction, and other important effects. In addition, a user interface was developed for user-defined resistance models. An accurate and efficient reliability method was developed and was successfully implemented in the NESSUS code to compute component reliability based on user-selected response and resistance models. A risk module was developed to compute component risk with respect to cost, performance, or user-defined criteria. The new component risk assessment capabilities were validated and demonstrated using several examples. Various supporting methodologies were also developed in support of component risk assessment.

Source record↗
NASA NTRS1981

Optimal interpolation and the Kalman filter

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Cohn, S.↗
NASA NTRS1990

Global optimization methods for engineering design

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

Arora, Jasbir S.↗
NASA NTRS1996

Implementation of Probabilistic Design Methodology at Tennessee State University

Engineering Design is one of the most important areas in engineering education. Deterministic Design Methodology (DDM) is the only design method that is taught in most engineering schools. This method does not give a direct account of uncertainties in design parameters. Hence, it is impossible to quantify the uncertainties in the response and the actual safety margin remains unknown. The desire for a design methodology tha can identify the primitive (random) variables that affect the structural behavior has led to a growing interest on Probabilistic Design Methodology (PDM). This method is gaining more recognition in industries than in educational institutions. Some of the reasons for the limited use of the PDM at the moment are that many are unaware of its potentials, and most of the software developed for PDM are very recent. The central goal of the PDM project at Tennessee State University is to introduce engineering students to the method. The students participating in the project learn about PDM and the computer codes that are available to the design engineer. The software being used of this project is NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) developed under NASA probabilistic structural analysis program. NESSUS has three different modules which make it a very comprehensive computer code for PDM. A research in technology transfer through course offering in PDM is in effect a Tennessee State University. The aim is to familiarize students with the problem of uncertainties in engineering design. Included in the paper are some projects on PDM carried out by some students and faculty. The areas this method is being applied at the moment include, Design of Gears (spur and worm); Design of Shafts; Design of Statistically Indeterminate Frame Structures; Design of Helical Springs; and Design of Shock Absorbers. Some of the current results of these projects are presented.

Onwubiko, Chinyere↗
NASA NTRS1978

Linear stochastic control using the UDU matrix factorization

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.

Thornton, C. L.↗