Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.
For licensing purposes, safety cases of nuclear power plants (NPPs) must be presented at the Regulatory Authority with the necessary confidence on the outcomes of the models used to analyze the plant safety behavior. In the present work, we consider the problem of providing a quantitative indication of the confidence in the safety margin estimation by a model with uncertain inputs giving in output the maximum outlet water temperature of the residual heat removal system (RHRs) in accident scenarios of the high temperature reactor-pebble modular (HTR-PM). The quantitative evaluation is carried out by means of a computational procedure of literature, based on order statistics (OS). The procedure is analyzed with respect to some of its key parameters defining the sample size and the number of uncertain inputs.
The first recorded usage of the word reliability dates back to the 1800s, albeit referred to a person and not a technical system. Since then, the concept of reliability has become a pervasive attribute worth of both qualitative and quantitative connotations. In particular, the revolutionary social, cultural and technological changes that have occurred from the 1800s to the 2000s have contributed to the need for a rational framework and quantitative treatment of the reliability of engineered systems and plants. This has led to the rise of reliability engineering as a scientific discipline. In this paper, some considerations are shared with respect to a number of problems and challenges which researchers and practitioners in reliability engineering are facing when analyzing today's complex systems. The focus will be on the contribution of reliability to system safety and on its role within system risk analysis.
Today, the quantification of the quality of a dynamic structural model remains a major issue, and the number of methods being devised in order to validate a model by comparison with an experimental reference keeps increasing. This paper presents a theory based on the concept of lack of knowledge, which consists in globalizing the various sources of errors on the substructure level by means of a scalar internal variable, called the LOK variable, defined over an interval whose upper and lower bounds follow probabilistic laws. These intervals, which are defined for each substructure, are then propagated rigorously throughout the mechanical model in order to determine intervals with stochastic bounds within which lies a given quantity of interest defined over the whole structure. Then, a general strategy for the reduction of the lack of knowledge is discussed and applied to academic examples as well as industrial cases.
Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.
For licensing purposes, safety cases of nuclear power plants (NPPs) must be presented at the Regulatory Authority with the necessary confidence on the outcomes of the models used to analyze the plant safety behavior. In the present work, we consider the problem of providing a quantitative indication of the confidence in the safety margin estimation by a model with uncertain inputs giving in output the maximum outlet water temperature of the residual heat removal system (RHRs) in accident scenarios of the high temperature reactor-pebble modular (HTR-PM). The quantitative evaluation is carried out by means of a computational procedure of literature, based on order statistics (OS). The procedure is analyzed with respect to some of its key parameters defining the sample size and the number of uncertain inputs.
