This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Reliability Engineering and System Safety

Dose calculation methods for photon beams are reviewed in the context of radiation therapy treatment planning. Following introductory summaries on photon beam characteristics and clinical requirements on dose calculations, calculation methods are described in order of increasing explicitness of particle transport. The simplest are dose ratio factorizations limited to point dose estimates useful for checking other more general, but also more complex, approaches. Some methods incorporate detailed modelling of scatter dose through differentiation of measured data combined with various integration techniques. State-of-the-art methods based on point or pencil kernels, which are derived through Monte Carlo simulations, to characterize secondary particle transport are presented in some detail. Explicit particle transport methods, such as Monte Carlo, are briefly summarized. The extensive literature on beam characterization and handling of treatment head scatter is reviewed in the context of providing phase space data for kernel based and/or direct Monte Carlo dose calculations. Finally, a brief overview of inverse methods for optimization and dose reconstruction is provided.

https://iopscience.iop.org/article/10.1088/0031-9155/44/11/201/pdf

Dose calculations for external photon beams in radiotherapy

1 From the Departments of Epidemiology and Health, and of Experimental Medicine, McGill University, and from the Department of Medicine, Royal Victoria Hospital, Montreal, Quebec, Canada. 2 Requests for reprints should l.>e addressed to Department of Epidemiology and Health, McGill University, 3775 University Street, Montreal, Quebec, Canada. 3 Associate of the Medical Research Council of Canada. Pathology Pathogenesis Clinical Features Radiographic Changes Lung Function Diagnosis Prognosis, Complications, and Medical Management

Asbestos-related diseases of the lung and other organs: their epidemiology and implications for clinical practice.

Fusion materials research started in the early 1970s following the observation of the degradation of irradiated materials used in the first commercial fission reactors. The technological challenges of fusion energy are intimately linked with the availability of suitable materials capable of reliably withstanding the extremely severe operational conditions of fusion reactors. Although fission and fusion materials exhibit common features, fusion materials research is broader. The harder mono-energetic spectrum associated with the deuterium–tritium fusion neutrons (14.1 MeV compared to <2 MeV on average for fission neutrons) releases significant amounts of hydrogen and helium as transmutation products that might lead to a (at present undetermined) degradation of structural materials after a few years of operation. Overcoming the historical lack of a fusion-relevant neutron source for materials testing is an essential pending step in fusion roadmaps. Structural materials development, together with research on functional materials capable of sustaining unprecedented power densities during plasma operation in a fusion reactor, have been the subject of decades of worldwide research efforts underpinning the present maturity of the fusion materials research programme. For achieving proper safety and efficiency of future fusion power plants, low-activation materials able to withstand the extreme fusion conditions are needed. Here, the irradiation physics at play and fusion materials research is reviewed.

/pdf/materials-research-for-fusion-3cn3itrgpo.pdf

Materials research for fusion

CAD-based Monte Carlo program for integrated simulation of nuclear system SuperMC

Although the Monte Carlo method is considered to be the most accurate method available for solving radiation transport problems, its applicability is limited by its computational expense. Thus, bia...

Automated variance reduction of Monte Carlo shielding calculations using the discrete ordinates adjoint function

Monte carlo variance reduction with deterministic importance functions

The primary objective of ADVANTG is to reduce both the user effort and the computational time required to obtain accurate and precise tally estimates across a broad range of challenging transport applications. ADVANTG has been applied to simulations of real-world radiation shielding, detection, and neutron activation problems. Examples of shielding applications include material damage and dose rate analyses of the Oak Ridge National Laboratory (ORNL) Spallation Neutron Source and High Flux Isotope Reactor (Risner and Blakeman 2013) and the ITER Tokamak (Ibrahim et al. 2011). ADVANTG has been applied to a suite of radiation detection, safeguards, and special nuclear material movement detection test problems (Shaver et al. 2011). ADVANTG has also been used in the prediction of activation rates within light water reactor facilities (Pantelias and Mosher 2013). In these projects, ADVANTG was demonstrated to significantly increase the tally figure of merit (FOM) relative to an analog MCNP simulation. The ADVANTG-generated parameters were also shown to be more effective than manually generated geometry splitting parameters.

/pdf/advantg-an-automated-variance-reduction-parameter-generator-ynp85r0b42.pdf

ADVANTG An Automated Variance Reduction Parameter Generator

This paper presents a hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh talli...

/pdf/fw-cadis-method-for-global-and-regional-variance-reduction-3xqeh3v7el.pdf

FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations

Recent applications’ needs/desires have motivated efforts to develop approaches for optimizing Monte Carlo calculations for global distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as response at multiple localized detectors and spectra. Recent efforts at Oak Ridge National Laboratory (ORNL) have led to the development of a variation on the Consistent Adjoint Driven Importance Sampling (CADIS) method for effective global variance reduction. This method, referred to as Forward-Weighted CADIS (FW-CADIS), and an example of its application are presented in this paper. To the authors’ knowledge, this is a new method and novel use of the adjoint methodology for biasing Monte Carlo simulations. It has long been recognized that the adjoint function (i.e., the solution to the adjoint form of the Boltzmann transport equation) has physical significance [1] as a measure of the importance of a particle to some objective function (e.g., the response of a detector) and that this physical interpretation makes the adjoint function well suited for biasing Monte Carlo simulations. Accordingly, recent trends in Monte Carlo code development have reflected a recognition of the benefits of using deterministic adjoint (importance) functions for Monte Carlo variance reduction.[2] The CADIS methodology [2,3], which has been incorporated into codes such as ADVANTG [4] (based on MCNP) and the MAVRIC [5] sequence of SCALE, is being routinely used at ORNL for three-dimensional (3-D) Monte Carlo simulations of real applications. Although the CADIS methodology has proven to be very effective for automated optimization of localized quantities, until very recently, efforts to optimize global distributions have not been nearly as successful. A number of heuristic approaches, such as specification of the adjoint source (response function) throughout the problem phase space, have been tested and found to be ineffective. Specification of the adjoint source at the outer boundaries of a problem in an attempt to encourage particles to move outward through the entire system was found to be reasonably effective. Previous work by Cooper and Larsen, which used the inverted forward flux as the importance function (no adjoint calculation) in an attempt to distribute particles uniformly throughout the system has demonstrated some benefit [6]. While this approach does encourage particles toward regions of lower flux and discourage particles from moving toward regions of higher flux, the forward flux does not represent the expected contribution to the desired response, which is uniform particle density (or response) throughout the system. When applied to a large realistic application, this method was not found to be effective. Hence, a need has remained for an effective method for global variance reduction of Monte Carlo simulations.

/pdf/forward-weighted-cadis-method-for-global-variance-reduction-113o1nugek.pdf

John C. Wagner

Papers

Automated variance reduction of Monte Carlo shielding calculations using the discrete ordinates adjoint function

Monte carlo variance reduction with deterministic importance functions

ADVANTG An Automated Variance Reduction Parameter Generator

FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations

Forward-weighted CADIS method for global variance reduction