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

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.

Rockwell hardness testing is a widely used hardness test, and there are many scales depending on the indenter shape and test force for corresponding to various materials. The common Rockwell indenters are the diamond sphero-conical indenter and the tungsten carbide ball indenter. The influence of indenter shape error on Rockwell hardness has been acknowledged, as this shape impacts test results. To accurately estimate this uncertainty, it is essential to understand the sensitivity coefficient, which delineates the relationship between indenter shape and Rockwell hardness. Traditionally, this coefficient has been derived experimentally, but this approach faces challenges that are attributable to the nonuniformity of hardness test blocks and indenter shape measurement errors. This study introduces the estimation of sensitivity coefficients for Rockwell indenters using finite element analysis (FEA). The FEA method offers the advantage of being unaffected by the nonuniformity of test blocks and indenter shape measurement errors. We calculated the sensitivity coefficients by assessing the influence of variations in indenter angle and tip radius for diamond indenters, and indenter diameter for ball indenters, on hardness results through FEA. The sensitivity coefficients obtained via FEA for specific scales aligned with those from previous experimental studies, affirming the validity of FEA-derived coefficients for other scales. This study demonstrates that FEA is a useful tool for estimating the sensitivity coefficients of Rockwell indenters.

Perturbation mapping method for sensitivity analysis of three-dimensional cracks near a free surface

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.

Efficient sensitivity analysis method for chaotic dynamical systems

Sensitivity coefficients are calculated, for the simple thickness modes of quartz plates, due to perturbations of the elastic, piezoelectric, and dielectric material values. These are given in tabular form for various cuts of practical and analytic interest. Also shown are a number of sensitivity coefficient surfaces using the two plate orientational angles as variables.

To materialize actual designs in computer-aided design, we presented a method to determine structural dimensions in order to make all design requirements accomplish their respective objective values, using the attainability and simultaneous equations with several unknowns. However, most of the designs have no theoretical design formula or sensitivity coefficients. This paper presents an approximation method to identify sensitivity coefficients by trial production evaluations of the designs. The coefficient matrix is specified between k th revised values of the attainabilities and k th revised values of the design variables, and made into a square or a triangular matrix by neglecting insignificant variables. The matrix is solved iteratively until all coefficients converge. This paper also presents a multiobjective satisfactory design using the identified coefficients to prove the effectiveness of the identification, comparing the identified coefficients with the theoretical ones.

The standardized FAO56 Penman-Monteith model, which has been the most reasonable method in both humid and arid climatic conditions, provides reference evapotranspiration (ETo) estimates for planning and efficient use of agricultural water resources. And sensitivity analysis is important in understanding the relative importance of climatic variables to the variation of reference evapotranspiration. In this study, a non-dimensional relative sensitivity coefficient was employed to predict responses of ETo to perturbations of four climatic variables in the Ejina oasis northwest China. A 20-year historical dataset of daily air temperature, wind speed, relative humidity and daily sunshine duration in the Ejina oasis was used in the analysis. Results have shown that daily sensitivity coefficients exhibited large fluctuations during the growing season, and shortwave radiation was the most sensitive variable in general for the Ejina oasis, followed by air temperature, wind speed and relative humidity. According to this study, the response of ETo can be preferably predicted under perturbation of air temperature, wind speed, relative humidity and shortwave radiation by their sensitivity coefficients.

Dependence of sensitivity coefficient of a nude-type Bayard–Alpert gauge on the diameter of an envelope

In naturally fractured reservoirs, the fracture intensity (density) control the fracture permeability and the dimensions of matrix blocks, and hence govern the reservoir production performance and oil recovery process. In the last decade, great progress has been made in the characterization of natural fracture system of naturally fracture reservoirs. The statistical fracture intensity model can be constructed by integrating the direct local data, such as core and image log data, and field scale data derived from seismic attributes, fault-related-strain-field, structural information (curvature), etc. The static fracture model must be converted into flow simulation model for dynamic simulation, and must be adjusted to honor the production history to perform production performance prediction and optimal development planning.This paper discusses the development of a novel method of conditioning the fracture intensity model to the production data. This is achieved by making the sensitivity coefficients available of production data with respect to fracture intensity through the building of correlations between fracture intensity and fracture permeability and fracture/matrix coupling factor.Gradient simulator and adjoint methods are used to calculate the sensitivity coefficients of production data to the parameters of fracture and matrix blocks. Both two methods usually involve solving of a great number of matrix equations. Sparse LU decomposition is used to solve the matrix equations to improve the computational efficiency of sensitivity coefficient. To the best of our knowledge, the particular implementation of the sparse LU direct methods in automatic history matching is new to the petroleum engineering literature.The proposed method and developed software is validated by applying to a giant Middle East carbonate naturally fracture reservoir.

Spatiotemporal interactions between soil moisture and water availability across the Yellow River Basin, China

Changing the value of the porosity or the horizontal or vertical permeability in any grid cell in a reservoir simulator by a small amount often results in a small change in the value of a property predicted by the simulator. The ratio of change in prediction to change in reservoir property is called the sensitivity coefficient. In this paper, we describe the use of the adjoint system of equations to compute the sensitivity of wellbore pressure, water-oil ratio, and gas-oil ratio to changes in gridblock permeability and porosity. Unlike some other methods of computing sensitivity coefficients, this method is applicable for problems with large numbers of model parameters and for problems in which cross-flow and compressibility are significant. Although the adjoint system has previously been used to compute the gradient of an objective function for three-phase flow data with respect to model parameters, the sensitivity coefficients are significantly more powerful as they enable the use of Newton-like methods with quadratic convergence, i.e., estimation of the covariance of model estimates based on the inverse of the Hessian, and they provide insight into the information content of data. We use several three-phase flow examples with solution-gas drive, gas injection, and gravity segregation to illustrate these ideas.

The interaction of angular and linear stimuli produces a complex alignment of spatial orientation and the VOR. This phenomenon was studied by measuring three dimensional eye movements in 6 squirrel monkeys during centrifugation in the dark. The axis of eye rotation was always aligned with gravity and with the spinal axis of the upright monkeys. The erect monkeys were oriented such that they were either facing toward the direction of motion or were facing away from the motion. Angular velocity trapezoids were utilized as the motion stimuli with a ramp acceleration of 10 degrees/s2 to a constant velocity of 200 degrees/s. This yields a final centripetal acceleration of 1 g. The orientation of centripetal acceleration dramatically altered the VOR by changing the axis of eye rotation, the peak value of slow phase eye velocity, and the time constant of per-rotary decay. The axis of eye rotation always tended to align with gravito-inertial force, the peak value of slow phase eye velocity was greater when the monkey faced the motion than when it faced away from the motion, and the time constant of decay was smaller when the monkey faced the motion than when it faced away from the motion. These findings were statistically significant (p less than 0.05) and were consistent across all monkeys. The data also indicate that the VOR may be separated into two reflexes, a linear reflex and a rotational reflex. The linear reflex decays as the axis of eye rotation aligns with gravito-inertial force (GIF). These results indicate that GIF is resolved into two components: one representing an internal estimate of linear acceleration and one representing an internal estimate of gravity.

A simple and efficient computational method for Sensitivity Coefficient calculation is presented. Sensitivity analysis are carried out for a simple one-dimensional heat conduction problem with respect to two parameters: thermal conductivity (k) and volumetric heat capacity (c). Results obtained by finite difference and complex step differentiation are compared with analytical solution in non-dimensional form. With an arbitrary small step-size, the complex differentiation method can achieve near analytical accuracy in languages that support complex arithmetic. Further implementation of complex step differentiation in Matlab environment is explained with some precautions.

The correct data or information from the building sensing networks plays a vital role in the operation algorithms. The sensor errors usually show a negative effect on the performance of control, diagnosis, and optimization of building energy systems. Thus, the physical working sensors periodically need to be removed to be calibrated by the reference sensors, which will disrupt the normal operation of building systems from time to time. The virtual in situ sensor calibration (VIC), based on the Bayesian inference and Markov chain Monte Carlo methods (MCMC), is an effective approach to handle the systematic and random errors of various working sensors simultaneously. This technology uses the distance function and system models to estimate the true measurements and addresses most of the practical problems in a traditional calibration process. However, the sensitivity coefficient in the definition of distance function is one of the determining factors in the calibration accuracy and how to define it still remains uncertain. Therefore, this study employed the genetic algorithm (GA) to optimize this parameter in a LiBr–H2O absorption refrigeration system. The results revealed that the systematic and random errors of temperature and mass flow rate were reduced considerably with the help of optimized sensitivity coefficients and most of the measurements approached to their true values after the calibration.