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Results for “stochastic collocation method”

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 NTRS2003

A Stochastic Collocation Algorithm for Uncertainty Analysis

This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.

Mathelin, Lionel↗
NASA NTRS2003

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Zang, Thomas A.↗
NASA NTRS2012

Image Mapping and Visual Attention on the Sensory Ego-Sphere

The Sensory Ego-Sphere (SES) is a short-term memory for a robot in the form of an egocentric, tessellated, spherical, sensory-motor map of the robot s locale. Visual attention enables fast alignment of overlapping images without warping or position optimization, since an attentional point (AP) on the composite typically corresponds to one on each of the collocated regions in the images. Such alignment speeds analysis of the multiple images of the area. Compositing and attention were performed two ways and compared: (1) APs were computed directly on the composite and not on the full-resolution images until the time of retrieval; and (2) the attentional operator was applied to all incoming imagery. It was found that although the second method was slower, it produced consistent and, thereby, more useful APs. The SES is an integral part of a control system that will enable a robot to learn new behaviors based on its previous experiences, and that will enable it to recombine its known behaviors in such a way as to solve related, but novel, task problems with apparent creativity. The approach is to combine sensory-motor data association and dimensionality reduction to learn navigation and manipulation tasks as sequences of basic behaviors that can be implemented with a small set of closed-loop controllers. Over time, the aggregate of behaviors and their transition probabilities form a stochastic network. Then given a task, the robot finds a path in the network that leads from its current state to the goal. The SES provides a short-term memory for the cognitive functions of the robot, association of sensory and motor data via spatio-temporal coincidence, direction of the attention of the robot, navigation through spatial localization with respect to known or discovered landmarks, and structured data sharing between the robot and human team members, the individuals in multi-robot teams, or with a C3 center.

Fleming, Katherine Achim↗