Carlo Perturbation Research Articles

Improved Monte Carlo-perturbation method for estimation of control rod worths in a research reactor

A hybrid method dedicated to improve the experimental technique for estimation of control rod worths in a research reactor is presented. The method uses a combination of Monte Carlo technique and perturbation theory. Perturbation method is used to obtain the equation for the relative efficiency of control rod insertion. A series of coefficients, describing the axial absorption profile are used to correct the equation for a composite rod, having a complicated burn-up irradiation history. These coefficients have to be determined – by experiment or by using some theoretical/numerical method. In the present paper they are derived from the macroscopic absorption cross-sections, obtained from detailed Monte Carlo calculations by MCNPX 2.6.F of the axial burn-up profile during control rod life. The method is validated on measurements of control rod worths at the BR2 reactor. Comparison with direct MCNPX evaluations of control rod worths is also presented.

UNCERTAINTIES ANALYSIS FOR THE PLUTONIUM DOSIMETRY MODEL, DOSES-2005, USING MAYAK BIOASSAY DATA

The Doses-2005 model is a combination of the International Commission on Radiological Protection (ICRP) models modified using data from the Mayak Production Association cohort. Surrogate doses from inhaled plutonium can be assigned to approximately 29% of the Mayak workers using their urine bioassay measurements and other history records. The purpose of this study was to quantify and qualify the uncertainties in the estimates for radiation doses calculated with the Doses-2005 model by using Monte Carlo methods and perturbation theory. The average uncertainty in the yearly dose estimates for most organs was approximately 100% regardless of the transportability classification. The relative source of the uncertainties comes from three main sources: 45% from the urine bioassay measurements, 29% from the Doses-2005 model parameters, and 26% from the reference masses for the organs. The most significant reduction in the overall dose uncertainties would result from improved methods in bioassay measurement with additional improvements generated through further model refinement. Additional uncertainties were determined for dose estimates resulting from changes in the transportability classification and the smoking toggle. A comparison was performed to determine the effect of using the model with data from either urine bioassay or autopsy data; no direct correlation could be established. Analysis of the model using autopsy data and incorporation of results from other research efforts that have utilized plutonium ICRP models could improve the Doses-2005 model and reduce the overall uncertainty in the dose estimates.

Stochastic Sensitivity of 3D-Elastodynamic Response Subjected to Random Ground Excitation

The present study deals with structural sensitivity of dynamic response having uncertainties in design parameters subjected to random earthquake loading. Earthquake is modeled as stationary random process defined by Kanai–Tajimi power spectral density. The uncertain design parameters are modeled as homogeneous Gaussian process and discretized through 3D local averaging. Subsequently the Cholesky decomposition of respective co-variance matrix is used to simulate random values of design parameters. The Neumann expansion blended with Monte Carlo simulation (NE-MCS) is explored for computing response sensitivity in frequency domain. Application examples related to a building frame and a gravity dam are presented serving to validate the NE-MCS technique in terms of its accuracy and effectiveness compared to direct Monte Carlo simulation and perturbation method.

NE-MCS technique for stochastic structural response sensitivity

In structural sensitivity analysis deterministic procedure is insufficient to provide complete information. Stochastic analysis is a holistic approach for computing response sensitivity considering uncertainties in structural parameters. Present study focuses an efficient stochastic finite element method for random response sensitivity analysis. Randomness of design variables is modeled through local averaging technique followed by Cholesky decomposition for digital simulation. Neumann expansion blended with Monte Carlo simulation (NE-MCS) has been employed in finite element solution for response sensitivity. Numerical examples are presented to illustrate the NE-MCS technique. Solution employing direct Monte Carlo simulation and perturbation are also presented to show the efficiency and accuracy of the proposed technique.

Sensitivity Statistics of 3D Structures under Parametric Uncertainty

Determination of sensitivity gradient is a major prerequisite for structural optimization, reliability assessment, and parameter identification. As the conventional deterministic sensitivity analysis cannot provide complete information, stochastic analysis is needed to tackle the uncertainties in structural parameters. This study focuses on the utility of the stochastic finite-element method for random response sensitivity analysis. The stochastic modeling of a random parameter is based on a commonly used 2D local averaging method generalized for a 3D case. The Choleski decomposition technique is then employed for digital simulation. The Neumann expansion based finite-element simulation method is extended for stochastic sensitivity analysis. This technique leads to a considerable saving of computational time. Example problems are used to compare the accuracy of this method to the direct Monte Carlo simulation and perturbation method in terms of varying stochasticity and efficiency in CPU time.

Monte Carlo methods and perturbation theory

Monte Carlo methods and perturbation theory