Sensitivity analysis development and applications program at ORNL

The cross-section sensitivity analysis program at ORNL is reviewed with emphasis on present computer code capabilities and fast successful applications in the radiation shielding area. The FORSS sensitivity code system is discussed in regard to objectives, methodology, and code specifications. Examples of past shielding applications of FORSS emphasize the success of fine energy grid sensitivity studies and group structure selection, the use of evaluated error file and problem uncertainty estimation, two-dimensional shield sensitivity analysis and integral experiment design for fast reactors, data studies for the LMFBR program related to sodium and iron evaluations and iron data problems in CTR shielding design. Conclusions are drawn about the adequacy of present ENDF/B data files for sodium and iron and the general applicability of sensitivity studies in future design and analysis. 16 figures, 3 tables (auth

Neural Network Modeling of Weld Pool Shape in Pulsed-Laser Aluminum Welds

A neural network model was developed to predict the weld pool shape for pulsed-laser aluminum welds. Several different network architectures were examined and the optimum architecture was identified. The neural network was then trained and, in spite of the small size of the training data set, the network accurately predicted the weld pool shape profiles. The neural network output was in the form of four weld pool shape parameters (depth, width, half-width, and area) and these were converted into predicted weld pool profiles with the use of the actual experimental poo1 profiles as templates. It was also shown that the neural network model could reliably predict the change from conduction-mode type shapes to keyhole-mode shapes

Accuracy estimation for supervised learning algorithms

This paper illustrates the relative merits of three methods - k-fold Cross Validation, Error Bounds, and Incremental Halting Test - to estimate the accuracy of a supervised learning algorithm. For each of the three methods we point out the problem they address, some of the important assumptions that are based on, and illustrate them through an example. Finally, we discuss the relative advantages and disadvantages of each method

Complex Network Approach for Recurrence Analysis of Time Series

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potentials of these complex network measures for detecting dynamical transitions. Finally we apply the proposed approach to a marine palaeo-climate record and identify subtle changes of the climate regime.Comment: 23 pages, 7 figure

Long Tailed Maps as a Representation of Mixed Mode Oscillatory Systems

Mixed mode oscillatory (MMO) systems are known to exhibit some generic features such as the reversal of period doubling sequences and crossover to period adding sequences as bifurcation parameters are varied. In addition, they exhibit a nearly one dimensional unimodal Poincare map with a longtail. We recover these common features from a general class of two parameter family of one dimensional maps with a unique critical point that satisfy a few general constraints that determine the nature of the map. We derive scaling laws that determine the parameter widths of the dominant windows of periodic orbits sandwiched between two successive states of RL^k sequence. An example of a two parameter map with a unique critical point is introduced to verify the analytical results.Comment: 13 pages and 8 figure

Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data

The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias

N-learners problem: Fusion of concepts

We are given N learners each capable of learning concepts (subsets) of a domain set X in the sense of Valiant, i.e. for any c {element of} C {improper subset} 2{sup X}, given a finite set of examples of the form ; ;...; generated according to an unknown probability distribution P{sub X} on X, each learner produces a close approximation to c with a high probability. We are interested in combining the N learners using a single fuser or consolidator. We consider the paradigm of passive fusion, where each learner is first trained with the sample without the influence of the consolidator. The composite system is constituted by the fuser and the individual learners. We consider two cases: open and closed fusion. In open fusion the fuser is given the sample and the hypotheses of the individual learners; we show that the fusion rule can be obtained by formulating this problem as another learning problem. For the case all individual learners are trained with the same sample, we show sufficiency conditions that ensure the composite system to be better than the best of the individual: the hypothesis space of the consolidator (a) satisfies the isolation property of degree at least N, and (b) has Vapnik-Chervonenkis dimension less than or equal to that of every individual learner. If individual learners are trained by independently generated samples, we obtain a much weaker bound on the VC-dimension of the hypothesis space of the fuser. Second, in closed fusion the fuser does not have an access to either the training sample or the hypotheses of the individual learners. By suitable designing a linear threshold function of the outputs of individual learners, we show that the composite system can be made better than the best of the learners

A review of techniques for parameter sensitivity analysis of environmental models

Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a ‘sensitivity analysis’. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42691/1/10661_2004_Article_BF00547132.pd

Evaluation of the mathematical and economic basis for conversion processes in the LEAP energy-economy model

AbstractAn evaluation was made of the mathematical and economic basis for conversion processes in the LEAP energy-economy model. Conversion processes are the main modelling subunit in LEAP used to represent energy conversion industries and are supposedly based on the classical economic theory of the firm. The study arose out of questions about the uniqueness and existence of LEAP solutions and their relation to classical equilibrium economic theory. An analysis of classical theory and LEAP model equations was made to determine their exact relationship. The conclusions drawn from this analysis were that LEAP theory is not consistent with the classical theory of the firm. Specifically, the capacity for factor formalism used by LEAP does not support a classical interpretation in terms of a technological production function for energy conversion processes. The economic implications of this inconsistency are suboptimal process operation and short term negative profits in years where plant operation should be terminated. A new capacity factor formalism, which retains the behavioural features of the original model, is proposed to resolve these discrepancies