Sensitivity and perturbation analysis of alpha-eigenvalue with time-dependent Monte Carlo perturbation techniques

Time dependent Monte Carlo (TDMC) simulations are performed to determine the effects of a variety of H reactions at a diamond {001}(2×1) surface exposed to gaseous atomic and molecular hydrogen under chemical vapor deposition conditions. The simulation time in the TDMC method is the same as the real time measured in experiments because all of the considered reactions are allowed to occur with probabilities which are the product of the TDMC time step and the corresponding reaction rates. The reaction rates are either explicitly calculated via molecular dynamics or transition state theory methods, or taken from experimental measurements. The simulation takes into account H adsorption, H abstraction, H2 desorption, H diffusion, and the reverse of these reactions. The relative values of the calculated rates and how they affect the surface radical density and distribution, as well as the effect of CH3 on radical site diffusion are discussed.

The correlated sampling method is applied to the continuous Markov-chain Monte-Carlo (CMMC) method to efficiently perform sensitivity analysis of input parameters such as the failure rate of safety components. In the correlated sampling method, the original and the perturbed samples are assumed to trace an identical accident sequence, but the weight of the perturbed sample is adjusted to incorporate the variation of input data. The present method is applied to the sensitivity analysis of the safety evaluation of spent fuel pools. The result indicates that the sensitivity analysis for the CMMC coupling method can be efficiently carried out using the correlated sampling method.

The long-term application of inorganic fertilizer and animal manure to agricultural fields has resulted in soil test P (STP) concentrations that greatly exceed the agronomic critical level in many areas of the world. This build-up of soil P, often referred to as legacy P, can increase the risk of P being mobilized during runoff and leaching events, even years or decades after P inputs have decreased or ceased. If this mobilized P reaches P-limited surface waters, eutrophication can result, leading to serious water quality problems that can adversely impact the environment, human health, and recreational activities. Due to the cost and effort involved in soil, manure, and runoff sampling and testing, as well as implementation of best management practices, nutrient management policies and strategies are often guided by computer model predictions. However, computer model predictions are inherently uncertain, thus it is important to account for this uncertainty when interpreting modeling data and using modeling results to guide decision makingIn this study we conducted a sensitivity and uncertainty analysis using the Annual P Loss Estimator (APLE) model focusing on model predictions of STP. We calculated and evaluated the sensitivity coefficients of predicted STP and changes in STP using 1- and 10-yr simulations with and without P application. We also compared two methods for estimating prediction uncertainties: first-order variance approximation (FOVA) and Monte Carlo simulation (MCS). Finally, we compared uncertainties in APLE-predicted STP to uncertainties in measured STP collected from multiple sites in Maryland under different manuring and cropping treatments. Results from our sensitivity analysis showed that predicted STP and changes in STP for 1-yr simulations without P inputs were most sensitive to initial STP whereas model STP predictions were most sensitive to manure and fertilizer application rates when sensitivity analyses included P inputs. For the 10-yr simulations without P application inputs, the range in sensitivity coefficients for crop uptake and precipitation were much greater than for the 1-yr simulations. Prediction uncertainties from FOVA were comparable to those from MCS for model input uncertainties up to 50%. Using FOVA to calculate APLE STP prediction uncertainties using the Maryland data set, the mean measured STP for nearly all site years fell within the 95% confidence intervals of the STP prediction uncertainties. Our results provide users of APLE insight into what model inputs require the most careful measurement when using the model to predict changes in STP under conditions of P drawdown (i.e., no P application) or P buildup. Our results also demonstrate the importance of including model prediction uncertainties when estimating long-term drawdown of STP in agricultural fields.

For next generation reactor designs, which are attempting wide variations of assembly configurations, the flexibility Monte Carlo method holds is attractive, but still costly for repetitive design study works. This paper presents an advanced correlated sampling (ACS) method which was developed to speed up Monte Carlo lattice burnup calculations. The ACS method is the combination of the correlated sampling method and a pseudo-scattering technique. All burnup steps are considered as consecutive perturbed problems using the same neutron collision history, which is pre-calculated based on a selected unperturbed problem. Since neutron weights can be adjusted on every collision point, rather than along paths between them, the perturbed calculation is very fast and the neutron collision history is light enough to be stored in memory or physical storage, which is an indispensable feature for consecutive perturbed calculations. The presented theory shows that the ACS method has good potential to work for a wide range of neutron absorption variations, the dominant perturbation in the lattice burnup. In an example calculation on a BWR lattice, the ACS calculation results of 600,000 neutrons/step agree well with the independent Monte Carlo runs of 20,000,000 neutrons/step within 0.1%dk/k in terms of kœ throughout 95 steps (~50GWd/t). Average calculation time of neutron tracking with the former method is 3.4 s/step with 600,000 neutron histories on a single processor of an Alpha21164-600 MHz, and the speed-up factor against the Monte Carlo calculation turns out to be about 100.

In recent years, cone-beam computed tomography (CBCT) has played an important role in medical imaging. However, the applications of CBCT are limited due to the severe scatter contamination. Conventional Monte Carlo (MC) simulation can provide accurate scatter estimation for scatter correction, but the expensive computational cost has always been the bottleneck of MC method in clinical application. In this work, an MC simulation method combined with a variance reduction technique called correlated sampling is proposed for fast iterative scatter correction. Correlated sampling exploits correlation between similar simulation systems to reduce the variance of interest quantities. Specifically, conventional MC simulation is first performed on the scatter-contaminated CBCT to generate the initial scatter signal. In the subsequent correction iterations, scatter estimation is then updated by applying correlated MC sampling to the latest corrected CBCT images by reusing the random number sequences of the task-related photons in conventional MC. Afterward, the corrected projections obtained by subtracting the scatter estimation from raw projections are utilized for FDK reconstruction. These steps are repeated until an adequate scatter correction is obtained. The performance of the proposed framework is evaluated by the accuracy of the scatter estimation, the quality of corrected CBCT images and efficiency. Overall, the difference in mean absolute percentage error between scatter estimation with and without correlated sampling is 0.25% for full-fan case and 0.34% for half-fan case, respectively. In simulation studies, scatter artifacts are substantially eliminated, where the mean absolute error value is reduced from 15 to 2HU in full-fan case and from 53 to 13HU in half-fan case. Scatter-to-primary ratio is reduced to 0.02 for full-fan and 0.04 for half-fan, respectively. In phantom study, the contrast-to-noise ratio (CNR) is increased by a factor of 1.63, and the contrast is increased by a factor of 1.77. As for clinical studies, the CNR is improved by 11% and 14% for half-fan and full-fan, respectively. The contrast after correction is increased by 19% for half-fan and 44% for full-fan. Furthermore, root mean square error is also effectively reduced, especially from 78 to 4HU for full-fan. Experimental results demonstrate that the figure of merit is improved between 23 and 43 folds when using correlated sampling. The proposed method takes less than 25s for the whole iterative scatter correction process. The proposed correlated sampling-based MC simulation method can achieve fast and accurate scatter correction for CBCT, making it suitable for real-time clinical use.

Two-step Monte Carlo sensitivity analysis of alpha- and gamma-eigenvalues with the differential operator sampling method

This paper presents a sensitivity and reliability analysis of a self-anchored suspension bridge by applying a new hybrid method proposed by the authors based on integration of the Latin hypercube sampling technique (LHS), artificial neural network (ANN), first-order reliability method (FORM), Pearson's linear correlation coefficient (PLCC), and Monte Carlo simulation with important sampling technique (MCS-IS). The framework consists of three stages of analysis: (1) selection of training, validation, and test datasets for establishing an ANN model by the LHS technique; (2) formulation of a performance function from the well-trained ANN model; and (3) sensitivity analysis using PLCC, identification of the most probabilistic failure point based on FORM, and estimation of the failure probability using the MCS-IS technique. Upon demonstration of its efficiency through analysis of a 12-story frame structure, the method is applied to sensitivity and reliability analysis of the Jiangxinzhou Bridge, a five-span self-anchored suspension bridge, in which both structural parameters and external loads are considered as random variables. The analysis identified a number of structural parameters, as well as external loads, that have a significant influence on structural serviceability and safety.

In robust biological systems, wide deviations from highly controlled normal behavior may be rare, yet they may result in catastrophic complications. While in silico analysis has gained an appreciation as a tool to offer insights into system-level properties of biological systems, analysis of such rare events provides a particularly challenging computational problem. This paper proposes an efficient stochastic simulation method to analyze rare events in biochemical systems. Our new approach can substantially increase the frequency of the rare events of interest by appropriately manipulating the underlying probability measure of the system, allowing high-precision results to be obtained with substantially fewer simulation runs than the conventional direct Monte Carlo simulation. Here, we show the algorithm of our new approach, and we apply it to the analysis of rare deviant transitions of two systems, resulting in several orders of magnitude speedup in generating high-precision estimates compared with the conventional Monte Carlo simulation.

Design sensitivity analysis of structures deals with the calculation of the response derivatives with respect to the design variables. These derivatives, called the sensitivity coefficients, are used in the solution of various problems. In design optimization, the sensitivity coefficients are often required to select a search direction. These coefficients are used also in generating approximations for the response of a modified system. In addition, the sensitivities are required for assessing the effects of uncertainties in the structural properties on the system response. Calculation of the sensitivities involves much computational effort, particularly in large structural systems with many design variables. As a result, there has been much interest in efficient procedures for calculating the sensitivity coefficients. Developments in methods for sensitivity analysis are discussed in many studies (e.g. Haug et. al. 1986; Haftka and Adelman, 1989; Haftka and Gurdal, 1993; van Keulen et. al. in press). Methods of sensitivity analysis for discretized systems can be divided into the following classes: a. Finite-difference methods, which are easy to implement but might involve numerous repeated analyses and high computational cost, particularly in problems with many design or response variables. In addition, finite-difference approximations might have accuracy problems. The efficiency can be improved by using fast reanalysis techniques. b. Analytical methods, which provide exact solutions but might not be easy to implement in some problems such as shape optimization. c. "Semi-analytical" methods, which are based on a compromise between finite-difference methods and analytical methods. These methods use finite-difference evaluation of the right-hand-side vector. They are easy to implement but might provide inaccurate results. In general, the following factors are considered in choosing a suitable sensitivity analysis method for a specific application: the accuracy of the calculations, the computational effort involved and the ease-of-implementation. The implementation effort is weighted against the performance of the algorithms as reflected in their computational efficiency and accuracy. The quality of the results and efficiency of the calculations are usually two conflicting factors. That is, higher accuracy is often achieved at the expense of more computational effort. Dynamic sensitivity analysis has been demonstrated by several authors. Using the mode superposition approach and assuming harmonic loading, the response sensitivities were evaluated by direct differentiation of the equations of motion in the generalized coordinates (Kramer and Grierson, 1989). In cases of earthquake loading the ground acceleration is usually given in discrete time steps, thus the loading is not given analytically. In several studies (Kim and Choi, 2000; van Keulen et. al, in press) the unconditionally stable implicit numerical equation was directly derived. It was found that the analysis equations and the sensitivity equations have the same left-hand side expression. Thus, it was possible to use the available factorized coefficient matrix. A numerical procedure was applied for calculation of the sensitivity of the response.

GIS multicriteria decision analysis (MCDA) methods are increasingly being used in landslide susceptibility mapping for the prediction of future hazards, decision making, as well as hazard mitigation plans. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are prone to multiple types of uncertainty. In this paper, the spatiality explicitly method is employed to assess the uncertainty associated with two methods of GIS-MCDA namely, Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA). Our methodology consists of three stages. The first-stage analysis makes use of the AHP matrix weights for GIS-MCDA based landslide susceptibility mapping. This phase is based on a multicriteria evaluation which assesses the susceptibility areas and the landslide hazard potentiality by considering causal and diagnostic criteria. In the second stage the sensitivity and uncertainty analysis of the AHP weights is performed using Monte Carlo Simulation (MCS) and Global Sensitive Analysis (GSA). Finally, validation of results was performed using the existing landslide inventory. This paper carried out a GIS-MCDA uncertainty analysis and demonstrates a solution for the uncertainty modelling. Through the validation exercise with known existing landslides, the AHP clearly performed best. Results of this research demonstrate that further improvement of the accuracy of GIS-based MCDA can be achieved by employing the spatiality explicitly method and accordingly applying MCS and GSA for sensitivity analysis of the AHP weights.

This paper reviews five related types of analysis, namely (i) sensitivity or what-if analysis, (ii) uncertainty or risk analysis, (iii) screening, (iv) validation, and (v) optimization. The main questions are: when should which type of analysis be applied; which statistical techniques may then be used? This paper claims that the proper sequence to follow in the evaluation of simulation models is as follows. 1) Validation, in which the availability of data on the real system determines which type of statistical technique to use for validation. 2) Screening: in the simulation‘s pilot phase the really important inputs can be identified through a novel technique, called sequential bifurcation, which uses aggregation and sequential experimentation. 3) Sensitivity analysis: the really important inputs should be subjected to a more detailed analysis, which includes interactions between these inputs; relevant statistical techniques are design of experiments (DOE) and regression analysis. 4) Uncertainty analysis: the important environmental inputs may have values that are not precisely known, so the uncertainties of the model outputs that result from the uncertainties in these model inputs should be quantified; relevant techniques are the Monte Carlo method and Latin hypercube sampling. 5) Optimization: the policy variables should be controlled; a relevant technique is Response Surface Methodology (RSM), which combines DOE, regression analysis, and steepest-ascent hill-climbing. The recommended sequence implies that sensitivity analysis procede uncertainty analysis. Several case studies for each phase are briefly discussed in this paper.

Sensitivity and uncertainty analysis within a methodology for evaluating environmental restoration technologies

Improved generalized perturbation theory method for sensitivity analysis of generalized response function

The response and operation of a heat flux gage is studied using sensitivity analysis. Sensitivity analysis is the process by which one determines the sensitivity of a model output to changes in the model parameters. This process uses sensitivity coefficients, which are defined as partial derivatives of field variables (e.g. temperature) with respect to model parameters (e.g. thermal properties and boundary conditions). Computing sensitivity coefficients, in addition to the response of a heat flux gage, aids in identifying model parameters that significantly impact the temperature response. A control volume finite element based code is used to implement numerical sensitivity coefficient calculations, allowing general problems to be studied. Sensitivity coefficients are discussed for the well known Gardon gage.

Nuclear data sensitivity/uncertainty analysis for XT-ADS