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

Adjoint neutron flux calculations with Tripoli-4®: Verification and comparison to deterministic codes

The iterated fission probability (IFP) is a quantity proportional to the asymptotic power level originated by a neutron introduced to a reactor. The effective delayed neutron fraction βeff can be accurately calculated by the continuous-energy Monte Carlo method using IFP if a sufficiently large number of generations is considered to obtain the asymptotic state. In order to deterministically quantify the required number of generations in the IFP-based βeff calculations, the concept of the generation-dependent importance functions is introduced to βeff calculations. Furthermore, the most appropriate reactor property used in the IFP calculations, which reduces the required number of generations, is theoretically derived. Through numerical calculations, it is shown that several generations are required in the IFP-based βeff calculations and that the use of the appropriate reactor property can reduce the required number of generations. An efficient procedure for the IFP-based βeff calculations by the Monte Carlo method is also proposed.

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.

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

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.

In order to improve the safety and economy of nuclear reactors, it is necessary to analyze the sensitivity and uncertainty (S/U) of the nuclear data. The capabilities of S/U analysis has been developed in the Reactor Monte Carlo code RMC, using the iterated fission probability (IFP) method and the superhistory method. In this paper, the S/U capabilities of RMC are applied to a typical PWR benchmark B&W’s Core XI, and compared with the multigroup and continuous-energy S/U capabilities in the SCALE code system. The S/U results of the RMC-IFP method and the RMC-superhistory method are compared with TSUNAMI-CE/MG in SCALE. The sensitivity results and the uncertainty results of major nuclides that contribute a lot to the uncertainties in keff are in good agreement in both RMC and SCALE. The RMC-superhistory method has the same precision as the IFP method, but it reduces the memory footprint by more than 95% and only doubles the running time. The superhistory method has obvious advantages when there are many nuclides and reaction types to be analyzed. In addition, the total uncertainties in the keff of the first-order uncertainty quantification method are compared with the stochastic sampling method, and the maximum relative deviation of total uncertainties in the keff is 8.53%. Verification shows that the capabilities of S/U analysis developed in the RMC code has good accuracy.

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.

To estimate the uncertainty of the neutronic parameters it is required to calculate sensitivity coefficients to cross section changes. The sensitivity coefficients are usually calculated based on the diffusion theory. However, the accuracy of the sensitivity coefficients becomes doubtful because of the use of diffusion theory. The purpose of this paper is to derive the generalized perturbation theory using the transport theory, and to evaluate transport effect on the sensitivity coefficients. Sensitivity calculations were performed in 70 energy groups. The calculated sensitivity coefficients were compared with those obtained from direct transport calculations to check the accuracy of the present method, and those obtained from the generalized perturbation calculation based on the diffusion theory to investigate the transport effect on sensitivity coefficients. From the comparison, the difference was remarkably large for the neutronic parameters such as reaction rate distribution, reaction rate ratio, and reactivity worth. For example, the sensitivity coefficient of the 238U capture to 239Pu fission rate ratio in the lower core region of the under-moderated LWR core was large in the energy range 17.6–22.6 eV, and the sensitivity to 238U capture cross section calculated by the transport theory was 20% larger than that by the diffusion theory.

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

Monte Carlo analysis of the CROCUS benchmark on kinetics parameters calculation

Sensitivity analysis of CHF parameters under flow instability by using a neural network method

Calculation of effective point kinetics parameters in the Serpent 2 Monte Carlo code

Statistical and experimental methods in sensitivity analysis

Memory-efficient calculations of adjoint-weighted tallies by the Monte Carlo Wielandt method

Behavior of Emergency Core Cooling System (ECCS) during the early stage of Loss of Coolant Accident (LOCA) for APR 1400 with Flownex software