Efficiency of the averaged rank-based estimator for first order Sobol index inference

Among the many estimators of first order Sobol indices that have been proposed in the literature, the so-called rank-based estimator is arguably the simplest to implement. This estimator can be viewed as the empirical auto-correlation of the response variable sample obtained upon reordering the data by increasing values of the inputs. This simple idea can be extended to higher lags of autocorrelation, thus providing several competing estimators of the same parameter. We show that these estimators can be combined in a simple manner to achieve the theoretical variance efficiency bound asymptotically

Uncertainty analysis of PKL SBLOCA G7.1 test simulation using TRACE with Wilks and GAM surrogate methods

[EN] The Nuclear Energy Agency auspices simulation of experiments in different facilities under several programs. One on them consisted of performing a counterpart test between ROSA/LSTF and PKL facilities, with the main objective of determining the effectiveness of late accident management actions in a small break loss of coolant accident. The results obtained by TRACE code for PKL experiment SBLOCA G7.1 (a scaled model of Konvoi reactor) were in good agreement with the experiments. However, in the simulation process, uncertainty was not accounted. Uncertainty, analysis, following the principles of Best Estimate Plus Uncertainty (BEPU) approach, must be performed to measure the effect of uncertainties on the evolution of safety variables of interest, such as the maximum of the Peak Cladding Temperature (PCTmax) in the experiment. In this paper we present a comparison between two uncertainty analysis techniques. The first technique is based on order statistics that makes use of Wilks' formula. The second technique is based on a Generalized Additive Model (GAM) that substitutes the thermal-hydraulic code, without and with consideration of errors in adjusting the GAM model. The comparison of the uncertainty analysis results makes use of several performance metrics such as coverage, Coefficient of Variation and conservativeness. Based on the results of these metrics it can be concluded that the GAMPE (GAM Plus Error) provides the best performance, in particular, when using small sample size, i.e. n = 59, 93. For larger sample sizes, i.e. n = 124, 153, GAMPE and Wilks' results presents similar performance.This work has been developed partially with the support of Programa de Apoyo a la Investigacion y Desarrollo of UPV (PAID). Authors are grateful to Spanish CSN (Consejo de Seguridad Nuclear) for the financial support of these researches: (Research Project SIN/4078/2013/640; MASA Project) and (Research Project STN/4524/2015/640; CAMP Project).Sánchez Sáez, F.; Carlos Alberola, S.; Villanueva López, JF.; Sánchez Galdón, AI.; Martorell Alsina, SS. (2017). Uncertainty analysis of PKL SBLOCA G7.1 test simulation using TRACE with Wilks and GAM surrogate methods. Nuclear Engineering and Design. 319:61-72. https://doi.org/10.1016/j.nucengdes.2017.04.037S617231

A Bootstrapped Modularised method of Global Sensitivity Analysis applied to Probabilistic Seismic Hazard Assessment

Probabilistic Seismic Hazard Assessment (PSHA) evaluates the probability of exceedance of a given earthquake intensity threshold like the Peak Ground Acceleration, at a target site for a given exposure time. The stochasticity of the occurrence of seismic events is modelled by stochastic processes and the propagation of the earthquake wave in the soil is typically evaluated by empirical relationships called Ground Motion Prediction Equations. The large uncertainty affecting PSHA is quantified by defining alternative model settings and/or model parametri-zations. In this work, we propose a novel Bootstrapped Modularised Global Sensitivity Analysis (BMGSA) method for identifying the model parameters most important for the uncertainty in PSHA, that consists in generating alternative artificial datasets by bootstrapping an available input-output dataset and aggregating the individual rankings obtained with the modularized method from each of those.The proposed method is tested on a realistic PSHA case study in Italy. The results are compared with a standard variance-based Global Sensitivity Analysis (GSA) method of literature. The novelty and strength of the proposed BMGSA method are both in the fact that its application only requires input-output data and not the use of a PSHA code for repeated calculations

Sensitivity of carbon anode baking model outputs to kinetic parameters describing pitch pyrolysis

Carbon anode blocks, used in aluminum electrolysis cells, are usually baked in furnaces for several days, during which they release volatiles due to pitch pyrolysis. Therefore, numerical modeling of anode baking furnaces has to include some representation of pitch pyrolysis via a set of kinetic parameters. These kinetic parameters can vary with raw materials and baking parameters and are tedious to determine experimentally. In this work, we studied how the main outputs of an anode baking model are affected by the variance of the kinetic parameters. Results show that certain model outputs are not considerably influenced by changes in the kinetic parameters (e.g., spatial variation of anode porosity, maximum heating value from volatiles), while others are significantly affected (e.g., time evolution of anode porosity, time of maximum heating value of volatiles, internal pressure of anode), in particular by activation energy variability

Virtual process for evaluating the influence of real combined module variations on the overall performance of an aircraft engine

The effects of real combined variances in components and modules of aero engines, due to production tolerances or deterioration, on the performance of an aircraft engine are analysed in a knowledge-based process. For this purpose, an aero-thermodynamic virtual evaluation process that combines physical and probabilistic models to determine the sensitivities in the local module aerodynamics and the global overall performance is developed. Therefore, an automatic process that digitises, parameterises, reconstructs and analyses the geometry automatically using the example of a real turbofan high-pressure turbine blade is developed. The influence on the local aerodynamics of the reconstructed blade is investigated via a computational fluid dynamics (CFD) simulations. The results of the high-pressure turbine (HPT) CFD as well as of a Gas-Path-Analysis for further modules, such as the com-pressors and the low-pressure turbine, are transferred into a simulation of the performance of the whole aircraft engine to evaluate the overall performance. All results are used to train, validate and test several deep learning architectures. These metamodels are utilised for a global sensitivity analysis that is able to evaluate the sensitivities and interactions. On the one hand, the results show that the aerodynamics (especially the efficiency ηHPT and capacity _mHPT)are particularly driven by the variation of the stagger angle. On the other hand, ηHPT is significantly related to exhaust gas temperature (Tt5), while specific fuel consumption (SFC) and mass flow _mHPT are related to HPC exit temperature (Tt3). However, it can be seen that the high-pressure compressor has the most significant impact on the overall performance. This novel knowledge-based approach can accurately determine the impact of component variances on overall performance and complement experience-based approaches