General Sciences Abstracts:

Analysis of Mixture Experiments Using Slack Variable and Mixture Approaches. SAMANTHA LANDMESSER (University of Tennessee, Knoxville, TN, 37916) GREG F. PIEPEL (Pacific Northwest National Laboratory, Richland, WA, 99352)

In a mixture experiment, the response variable depends on the proportions of the components, which must sum to one. Because of this constraint, standard polynomial models cannot be used to analyze mixture experiment data. To get around this, some researchers ignore one of the components and use standard polynomial models in the remaining components. Because the component proportions must sum to one, the ignored component (referred to as the "slack variable" (SV)) makes up the remaining proportion of the mixture. In the literature, there have been many examples of researchers using the SV approach instead of a mixture approach. We have analyzed several of these examples using both approaches. For screening examples, we fit full linear models and identified which components were important using both approaches. In six screening examples, the mixture approach revealed that the SV had a significant effect on the response. For the quadratic examples, we used stepwise regression to develop reduced quadratic models for the SV approach, and partial quadratic mixture (PQM) models for the mixture approach. In three examples, the PQM models identified the SV and/or one of its quadratic blending terms as having a significant effect on the response variable. Hence, by completely ignoring a component’s effect on the response, SV analysis carries an inherent risk of wrong conclusions. There are fewer possible reduced quadratic SV models than possible PQM models because the reduced quadratic models are a subset of the class of PQM models. As a result, the PQM models will always fit the data as well as, or better than, the best reduced quadratic SV model. Our research concludes that it is better to analyze mixture experiments using methods specifically developed for them instead of using standard methods with the SV approach.

High Order Network Analysis in Power and Pulsed Power of the AGS Main Magnet System. GRACE KING (University of California, Los Angeles, Los Angeles, CA, 90024) ARLENE ZHANG (Brookhaven National Laboratory, Upton, NY, 11973)

Particle accelerator systems like the Brookhaven’s Alternating Gradient System (AGS) function on the basis of a high-order network complex of dipole magnets. Comprehensive analysis of this network is essential to the continual success of main magnet system operations. Until now, the limits of current processing technologies have hindered the effective examination of the magnet system’s behavior, whose ladder-style characterization can reach hundreds of degrees in its equivalent polynomial form. Previous analysis, which involved the simplification of the circuit system, failed to reflect the nature of its true complexity. Frequency decomposition, aided by the circuit simulation software, Microcap VIII, is a new approach that is able to take advantage of present computer processing capabilities. Presently, distinct circuit models have been simulated and various transient analysis runs have been conducted successfully. Further analysis with the application of transmission-line and ladder-network theory on simulated data should demonstrate the effectiveness of frequency decomposition. The development of this method has greatly facilitated the investigation of present magnet network properties as well as the exploration of new phenomena that may arise from future simulation studies.

Planning for the Future: Updating Energy Forecasting Techniques. CATHERINE SAMPSON (Western Washington University, Bellingham, WA, 98225) TODD SAMUEL (Pacific Northwest National Laboratory, Richland, WA, 99352)

Every year the Energy Information Administration publishes a document known as the Annual Energy Outlook (AEO), which provides analysis and forecasts of world energy markets through the year 2025. The results of this publication are used in the decision making processes of policy makers and public and private investors alike, and are the most comprehensive energy forecasts currently available. However, the National Energy Modeling System (NEMS), the program used to produce these forecasts, is riddled with minor flaws that may have major impacts on the applications of the AEO results. Though built using a detailed, modular structure, NEMS can only be run deterministically on a scenario by scenario basis. Further, NEMS models display an asymmetric loss function, making the results ambiguous to users whose loss function is not identical to that of modelers’. That is why the Department of Energy and the National Renewable Energy Laboratory are commissioning a new model for forecasting energy use. Known as the Stochastic Energy Deployment System (SEDS), this model will improve on current energy modeling mechanisms by providing for full probabilistic treatment of uncertainties. SEDS is in development under experts from several national laboratories, and will be designed on Analytica, a commercially available software package offering a user-friendly format. Hopefully, SEDS will be able to provide forecasts with better representations of the various possible futures of energy markets than are currently available.

Testing the Multiwavelet Representation of Functions. OWEN WORLEY (Dartmouth College, Hanover, NH, 3755) GEORGE FANN (Oak Ridge National Laboratory, Oak Ridge, TN, 37831)

The multiwavelet transformation of functions is one of the most promising methods for analyzing and performing operations on them. The multiwavelet expansion represents functions in terms of a basis of discontinuous multiwavelet functions, which are nonzero over a unit domain. In particular, representations of the Green’s function of operators of partial differential equations, constructed in multiwavelet bases, can be proven, in many cases, to be sparse and nearly diagonal. Thus, the computational complexity of the application of these operators is linear or nearly linear with respect to the problem size, and so is very attractive as a method of solution. As in the development of any complex software, testing must be done to assure that the transformed function behaves correctly with respect to basic algebraic and calculus operations. This testing is done by creating and inputting a variety of functions into a program, calculating the multiwavelet representation of these functions, applying a number of operators to both the original and transformed functions, and comparing the results, demonstrating that operating on the multiwavelet representation is numerically stable and achieves the required accuracy. Said testing demonstrated that the transformed functions do behave correctly with respect to the algebra and calculus operations tested to a high degree of accuracy. Also, as the tests were scaled to higher numbers of processors, the completion times decreased in a smooth log curve. These results were expected, but in obtaining them, debugging was performed and problems were identified and worked around. Further testing should be performed on functions represented with a higher wavelet order, and testing should generally be done as the code is modified and improved. The Joule program, written by George Fann and Robert Harrison, performs the multiwavelet transformation which is tested. The paper, Adaptive Solution of Partial Differential Equations in Multiwavelet Bases, by B. Alpert et al, provides background on multiwavelet transformations.