Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty

Three applications of sampling-based sensitivity analysis in conjunction with evidence theory representations for epistemic uncertainty in model inputs are described: (i) an initial exploratory analysis to assess model behavior and provide insights for additional analysis; (ii) a stepwise analysis showing the incremental effects of uncertain variables on complementary cumulative belief functions and complementary cumulative plausibility functions; and (iii) a summary analysis showing a spectrum of variance-based sensitivity analysis results that derive from probability spaces that are consistent with the evidence space under consideration.     

Vandermonde and resultant matrices: An abstract approach

We propose an abstract approach to the problems of common divisors and common multiples of rational matrix functions which (in the case of matrix polynomials) have been studied before using Vandermonde and resultant matrices.Supported in part by the Office of Naval Research, Air Force Office of Scientific Research, and the National Science Foundation.The work of this author was partially supported by an NSF grant and was carried out while visiting the University of California, San Diego.     

Frequency response algorithms for H∞optimization with time domain constraints

A very broad framework for control system design is considered that encompasses frequency-response methodologies for H_∞ optimization that solve various aspects of the control design problem and that are less well known that state-space methods. The focus is on linear programming, Lawson's algorithm, and Trefethen's algorithm. A modified Lawson's algorithm is proposed and related to Trefethan's method. The modified algorithm is shown to be significantly faster than linear programming and Lawson's algorithm. It is also shown how to extend the modified Lawson's algorithm so as to handle time-domain constraints in addition to frequency-domain specifications, which distinguishes it from other H_∞ optimization methods. Some steps are taken toward dealing with time domain constraints within an H_∞ optimization framework     

Vandermonde and resultant matrices: An abstract approach

Vandermonde and resultant matrices: An abstract approach     

Bias in bacteriophage morphological classification by transmission electron microscopy due to breakage or loss of tail structures

Virtually every study that has used transmission electron microscopy (TEM) to estimate viral diversity has acknowledged that loss of phage tails during sample preparation may have biased the results. However, the magnitude of this potential bias has yet to be constrained. To characterize biases in virus morphological diversity due to tail loss, six phage strains representing the order Caudovirales were inoculated into sterile sediments and soils. Phage particles were then extracted using standard methods. Morphologies of extracted phage particles were compared to those of unmanipulated control samples to determine the extent of tail breakage incurred by extraction procedures. Podoviruses exhibited the smallest frequency of tail loss during extraction (1.2-14%), myoviruses were moderately susceptible to tail breakage (15-40%), and siphoviruses were highly susceptible (32-76%). Thus, TEM assessments of viral diversity in soils or sediments by distribution of tail morphologies may be biased toward podoviruses and virions lacking tails, while simultaneously underestimating the abundance of siphoviruses. However, since the majority of viral capsids observed under TEM were intact, estimates of viral diversity based on the distribution of capsid diameters may provide a more reliable basis for morphological comparisons within and across ecosystems.     

Dissipative control systems synthesis with full state feedback

In this paper we present a general framework for synthesizing state feedback controllers to achieve any desired closed loop dissipative behavior. Special cases include positive real andH _∞ controller synthesis. We show that the solution to this dissipative controller synthesis problem is equivalent to the existence of a solution to a partial differential inequality (nonlinear systems case) or an algebraic Riccati inequality (linear systems case). Stability results can be obtained under appropriate detectability assumptions, and a generalization of the strict bounded real lemma is given. We also present an application of the results to a robust stabilization problem. This work was supported by the Cooperative Research Centre for Robert and Adaptive Systems (CRASys), Australia.     

Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty

In 2001, the National Nuclear Security Administration (NNSA) of the U.S. Department of Energy (DOE) in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories) initiated development of a process designated quantification of margins and uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. A previous presentation, “Quantification of Margins and Uncertainties: Conceptual and Computational Basis,” describes the basic ideas that underlie QMU and illustrates these ideas with two notional examples. The basic ideas and challenges that underlie NNSA's mandate for QMU are present, and have been successfully addressed, in a number of past analyses for complex systems. To provide perspective on the implementation of a requirement for QMU in the analysis of a complex system, three past analyses are presented as examples: (i) the probabilistic risk assessment carried out for the Surry Nuclear Power Station as part of the U.S. Nuclear Regulatory Commission's (NRC's) reassessment of the risk from commercial nuclear power in the United States (i.e., the NUREG-1150 study), (ii) the performance assessment for the Waste Isolation Pilot Plant carried out by the DOE in support of a successful compliance certification application to the U.S. Environmental Agency, and (iii) the performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada, carried out by the DOE in support of a license application to the NRC. Each of the preceding analyses involved a detailed treatment of uncertainty and produced results used to establish compliance with specific numerical requirements on the performance of the system under study. As a result, these studies illustrate the determination of both margins and the uncertainty in margins in real analyses.     

Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models

The analysis of many physical and engineering problems involves running complex computational models (simulation models, computer codes). With problems of this type, it is important to understand the relationships between the input variables (whose values are often imprecisely known) and the output. The goal of sensitivity analysis (SA) is to study this relationship and identify the most significant factors or variables affecting the results of the model. In this presentation, an improvement on existing methods for SA of complex computer models is described for use when the model is too computationally expensive for a standard Monte-Carlo analysis. In these situations, a meta-model or surrogate model can be used to estimate the necessary sensitivity index for each input. A sensitivity index is a measure of the variance in the response that is due to the uncertainty in an input. Most existing approaches to this problem either do not work well with a large number of input variables and/or they ignore the error involved in estimating a sensitivity index. Here, a new approach to sensitivity index estimation using meta-models and bootstrap confidence intervals is described that provides solutions to these drawbacks. Further, an efficient yet effective approach to incorporate this methodology into an actual SA is presented. Several simulated and real examples illustrate the utility of this approach. This framework can be extended to uncertainty analysis as well.     

Parameters effect on proton conductivity to obtain chitosan membranes for use as electrolytes in PEMFC

The chitosan biopolymer can be used as a proton‐conducting membrane in proton‐exchange membrane fuel cell. In the forms that they have normally obtained and tested, chitosan membranes typically show poor performance in conduction of protons, requiring modifications in the structure of the biopolymer or blending with other polymers to increase its proton conductivity. The present work investigates the individual properties of chitosan and relates them to the proton conductivity performance of membranes composed of this polymer. Evaluation was made of the effects of variables such as the degree of deacetylation (DD) and the molar mass (Mv) of chitosan membranes without addition of any other polymer. The DD and Mv values of the chitosan used to produce membranes determined the proton conduction, with lower DD and higher Mv resulting in higher conductivity. The thicker membranes presented greater crystallinity, with conductivity between 2.0 × 10^?4 and 1.8 × 10^?3 S cm^?1. The characteristic stages of degradation of the chitosan membranes were in the ranges 200 to 300°C and 500 to 600°C, indicating good thermal stability of the material.