Global sensitivity analysis is widely used in many areas of science, biology, sociology and policy planning. The variance-based methods also known as Sobol' sensitivity indices has become the method of choice among practitioners due to its efficiency and ease of interpretation. For complex practical problems, estimation of Sobol' sensitivity indices generally requires a large number of function...

A novel theoretical and numerical framework for the estimation of Sobol ’ sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical methods, namely the quadrature integration method which may be very efficient for problems of low dimensionality and the MC/QMC estimators based on the acceptanc...

Critical probability estimation is of major interest in safety and reliability applications. In this article, we focus on a black-box model with multidimensional random input X and one random output Y. We consider the estimation of probability P that Y exceeds a threshold S. We assume that the random input X follows a multidimensional parametric density with parameters d and thus the probabilit...

Sobol’ indices measure the dependence of a high dimensional function on groups of variables defined on the unit cube [0, 1]. They are based on the ANOVA decomposition of functions, which is an L decomposition. In this paper we discuss generalizations of Sobol’ indices which yield L measures of the dependence of f on subsets of variables. Our interest is in values p > 2 because then variable imp...

The mechanisms leading to thermodynamic chaos in the Baxter-Wu model is considered. We compare the Baxter-Wu model with triangular antiferromagnets and discuss the difficulties related to the modeling of thermodynamic chaos by disordered models. We also discuss how to overcome the problem of infinitely many order parameters. Then we consider the Baxter-Wu model in a complex magnetic field and s...

In this paper, variability analysis was performed on the model calibration methodology between a multi-camera system and a LiDAR laser sensor (Light Detection and Ranging). Both sensors are used to digitize urban environments. A practical and complete methodology is presented to predict the error propagation inside the LiDAR-camera calibration. We perform a sensitivity analysis in a local and g...

The present paper deals with a new method of global sensitivity analysis of nonlinear models. This is based on a measure of importance to calculate the fractional contribution of the input parameters to the variance of the model prediction. Measures of importance in sensitivity analysis have been suggested by several authors, whose work is reviewed in this article. More emphasis is given to the...

We try to understand the various components affecting the stability of tunneling and wellbore operations. We use a series of advanced finite element (FE) simulations to obtain a dataset which contains the stress response of the soil during drilling operations as a function of 12 input parameters. Using Multivariate Adaptive Regression Splines (MARS), we create a simplified model of the simulati...

Sensitivity analysis is a crucial tool in the development and evaluation of complex mathematical models. Sobol’s method is a variance-based global sensitivity analysis technique that has been applied to computational models to assess the relative importance of input parameters on the output. This paper introduces new notation that describes the Sobol indices in terms of the Pearson correlation ...

This paper presents an efficient sampling-based algorithm for the estimation of the upper bounds of the total sensitivity indices. These upper bounds, introduced by Sobol’, are based on the integration of the classical (local) gradient sensitivity analysis within the whole parameter space of the inputs. Hence, in this work the idea is to repeat the estimation of the local sensitivity analysis a...