Dimension reduction in stochastic modeling of coupled problems

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced-dimensional representation and, in particular, by an adaptation of the Karhunen-Loeve decomposition. The effectiveness of the proposed dimension-reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering

Utilizing Gauss-Hermite Quadrature to Evaluate Uncertainty in Dynamic System Response

Probabilistic uncertainty is a phenomenon that occurs to a certain degree in many engineering!~ applications. The effects that the uncertainty has upon a given system response is a matter of some concern. Techniques which provide insight to these effects will be required as modeling and prediction become a more vital tool in the engineering design process. As might be expected, this is a difficult proposition and the focus of many research efforts. The purpose of this paper is to outline a procedure to evaluate uncertainty in dynamic system response exploiting Gauss-Hermite numerical quadrature. Specifically numerical integration techniques are utilized in conjunction with the Advanced Mean Value method to efficiently and accurately estimate moments of the response process. A numerical example illustrating the use of this analytical tool in a practical framework is presented

Numerical Techniques to Evaluate Moments of Dynamic System Response

Probabilistic uncertainty is a phenomenon that occurs to a certain degree in many engineering applications. The effects that this uncertainty has upon a given system response are a matter of some concern. Techniques which provide insight to these effects will be required as modeling and prediction becomes a more vital tool in the engineering design process. The purpose of this paper is to outline a procedure to evaluate uncertainty in dynamic system response exploiting various numerical methods. Specifically, the goal is to attain the statistics of the response with minimal computational effort. Numerical interpolation and integration techniques are utilized in conjunction with the iterative form of the Advanced Mean Value (AMV+) method to efficiently and accurately estimate statistical moments of the response random process. A numerical example illustrating the use of this analytical tool in a practical framework is presented

Elements of a function analytic approach to probability.

We first provide a detailed motivation for using probability theory as a mathematical context in which to analyze engineering and scientific systems that possess uncertainties. We then present introductory notes on the function analytic approach to probabilistic analysis, emphasizing the connections to various classical deterministic mathematical analysis elements. Lastly, we describe how to use the approach as a means to augment deterministic analysis methods in a particular Hilbert space context, and thus enable a rigorous framework for commingling deterministic and probabilistic analysis tools in an application setting

Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).

Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback

Computational thermal, chemical, fluid, and solid mechanics for geosystems management.

This document summarizes research performed under the SNL LDRD entitled - Computational Mechanics for Geosystems Management to Support the Energy and Natural Resources Mission. The main accomplishment was development of a foundational SNL capability for computational thermal, chemical, fluid, and solid mechanics analysis of geosystems. The code was developed within the SNL Sierra software system. This report summarizes the capabilities of the simulation code and the supporting research and development conducted under this LDRD. The main goal of this project was the development of a foundational capability for coupled thermal, hydrological, mechanical, chemical (THMC) simulation of heterogeneous geosystems utilizing massively parallel processing. To solve these complex issues, this project integrated research in numerical mathematics and algorithms for chemically reactive multiphase systems with computer science research in adaptive coupled solution control and framework architecture. This report summarizes and demonstrates the capabilities that were developed together with the supporting research underlying the models. Key accomplishments are: (1) General capability for modeling nonisothermal, multiphase, multicomponent flow in heterogeneous porous geologic materials; (2) General capability to model multiphase reactive transport of species in heterogeneous porous media; (3) Constitutive models for describing real, general geomaterials under multiphase conditions utilizing laboratory data; (4) General capability to couple nonisothermal reactive flow with geomechanics (THMC); (5) Phase behavior thermodynamics for the CO2-H2O-NaCl system. General implementation enables modeling of other fluid mixtures. Adaptive look-up tables enable thermodynamic capability to other simulators; (6) Capability for statistical modeling of heterogeneity in geologic materials; and (7) Simulator utilizes unstructured grids on parallel processing computers

Research with American Indian communities: The value of authentic partnerships

Developing evidence for practice is particularly difficult when attempting to accurately capture the experiences of diverse communities. In American Indian communities, the lack of communication between researchers and their subjects has been increasingly recognized. Recent adjustments to research methods, such as community-based participatory research (CBPR) have attempted to emphasize the importance of recognizing the needs and wishes of those studied. Yet, perhaps due to imperfect application, they may fall short in promoting participation and yielding accurate results. A number of fallacies can hinder successful use of the model including the assumption that 'cultural sensitivity' or even locating a project in the community of interest will open the door to successful engagement. Reality-based research was conceived to address these potential deficiencies. It builds on CBPR and is proposed as a means to more effectively develop a connection between American Indians who might benefit from the research relationship and the researchers themselves. An example of a reality-based research project on tobacco use is provided and steps for adopting this approach in child welfare are outlined. These steps set this article apart from other works seeking to address this issue and provide concrete practical assistance to researchers in the field.Child welfare Community-based research Reality-based research Evidence-based practice Cultural competence

Commentary: Cultural Perspectives on Research among American Indians

Recent initiatives implemented by the Indian Health Service target health promotion and disease prevention as service goals for the 1990s. In partial support of these initiatives, the Indian Health Service sponsored a research planning meeting in September 1988. The meeting was intended to initiate thought on research priorities consistent with the initiatives, to identify a cadre of American Indian scholars interested in health promotion and disease prevention, and to frame a research training agenda for a follow-up meeting with the identified scholars. Budget constraints led to cancellation of the second meeting as originally planned. However, in collaboration with the National Institute for Drug Abuse, the Indian Health Service sponsored an alternative meeting in September 1989. Unfortunately, the focus of the meeting shifted from priorities in health promotion and disease prevention to training for research careers in the field of drug abuse. At first glance, one cannot argue with the change in focus. Drug abuse is certainly a vital research concern. Little is known or written about its extent and impact in Indian communities. Dr. Joseph Trimble, an American Indian psychologist, noted that through September 1989 only fifteen research articles had been published on American Indian drug abuse and that nine of these were reviews of literature. Dr. Trimble built a compelling case supporting a need for drug abuse research. However, few of the presentations were as culturally germane and enlightening as Dr. Trimble’s. Most presenters harped on application procedures in efforts to hone individual skills for writing research grants. While useful, this approach did not satisfy the aspirations of the visiting scholars. Midway through the meeting, in a polite and refreshing manner, American Indians objected to research paradigms that failed to account for unalterable cultural factors which are essential conditions overlooked by most research. While this diversion did little to influence the direction of research at the National Institute for Drug Abuse, it does serve as important commentary for health-related research