اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGeneralized Sobol sensitivity indices for dependent variables: numerical methods
81
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X_1,..., X_p are assumed to be dependent, this decomposition is unique if components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y=f(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y with respect to the dependent inputs X. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sensitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem.
قيم البحث
اقرأ أيضاً
The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis.
In this frame, we revisit the computation of the Sobol indices and give general lower bounds for these indices. The case of the eigenfunctions system associated with a Poincar{e} differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.
This paper addresses sensitivity analysis for dynamic models, linking dependent inputs to observed outputs. The usual method to estimate Sobol indices are based on the independence of input variables. We present a method to overpass this constraint w
hen inputs are Gaussian processes of high dimension in a time related framework. Our proposition leads to a generalization of Sobol indices when inputs are both dependant and dynamic. The method of estimation is a modification of the Pick and Freeze simulation scheme. First we study the general Gaussian cases and secondly we detail the case of stationary models. We then apply the results to an example of heat exchanges inside a building.
Uncertainties exist in both physics-based and data-driven models. Variance-based sensitivity analysis characterizes how the variance of a model output is propagated from the model inputs. The Sobol index is one of the most widely used sensitivity ind
ices for models with independent inputs. For models with dependent inputs, different approaches have been explored to obtain sensitivity indices in the literature. Typical approaches are based on procedures of transforming the dependent inputs into independent inputs. However, such transformation requires additional information about the inputs, such as the dependency structure or the conditional probability density functions. In this paper, data-driven sensitivity indices are proposed for models with dependent inputs. We first construct ordered partitions of linearly independent polynomials of the inputs. The modified Gram-Schmidt algorithm is then applied to the ordered partitions to generate orthogonal polynomials with respect to the empirical measure based on observed data of model inputs and outputs. Using the polynomial chaos expansion with the orthogonal polynomials, we obtain the proposed data-driven sensitivity indices. The sensitivity indices provide intuitive interpretations of how the dependent inputs affect the variance of the output without a priori knowledge on the dependence structure of the inputs. Three numerical examples are used to validate the proposed approach.
In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol indices. One reason of the popularity of Sobols approach relies on the simplicity of the statisti
cal estimation of these indices using the so-called Pick and Freeze method. In this work we propose and study sensitivity indices for the case where the output lies on a Riemannian manifold. These indices are based on a Cramer von Mises like criterion that takes into account the geometry of the output support. We propose a Pick-Freeze like estimator of these indices based on an $U$--statistic. The asymptotic properties of these estimators are studied. Further, we provide and discuss some interesting numerical examples.
A proper set of indices characterizing the polarimetric purity of light and material media is defined from the eigenvalues of the corresponding coherency matrix. A simple and generalizable relation of these indices with the current parameters charact
erizing the global purity is obtained. A general definition for systems characterized by nxn positive semidefinite Hermitian matrices is introduced in terms of the corresponding eigenvalues and diagonal Gell-Mann matrices. The set of n-1 indices of purity has a nested structure and provide complete information about the statistical purity of the system.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
