Related papers: Global Sensitivity Analysis via Multi-Fidelity Pol…
Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…
The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables…
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…
Explainable machine learning techniques have gained increasing attention in engineering applications, especially in aerospace design and analysis, where understanding how input variables influence data-driven models is essential. Partial…
Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a…
Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the…
Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a…
Global sensitivity analysis (GSA) aims at quantifying the contribution of input variables over the variability of model outputs. In the frame of functional outputs, a common goal is to compute sensitivity maps (SM), i.e sensitivity indices…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising measure-consistent multivariate orthonormal polynomials in dependent random variables. Unlike existing PCEs, whether classical or generalized, no…
The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…
Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully…
Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the…
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…
Global Sensitivity Analysis (GSA) is the study of the influence of any given inputs on the outputs of a model. In the context of engineering design, GSA has been widely used to understand both individual and collective contributions of…
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…
Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the…
Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in…