Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

A robust and efficient stepwise regression method for building sparse polynomial chaos expansions

Sparse Polynomial Chaos Expansion (PCE) is widely used in various engineering fields to quantitatively analyse the influence of uncertainty, while alleviating the problem of dimensionality curse. However, current sparse PCE techniques focus on choosing features with the largest coefficients, which may ignore uncertainties propagated with high order features. Hence, this paper proposes the idea of selecting polynomial chaos basis based on information entropy, which aims to retain the advantages of existing sparse techniques while considering entropy change as output uncertainty. A novel entropy-based optimization method is proposed to update the state-of-the-art sparse PCE models. This work further develops an entropy-based synthetic sparse model, which has higher computational efficiency. Two benchmark functions and a computational fluid dynamics (CFD) experiment are used to compare the accuracy and efficiency between the proposed method and classical methods. The results show that entropy-based methods can better capture the features of uncertainty propagation, improving accuracy and reducing sparsity while avoiding over-fitting problems.

Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

Efficient computation of global sensitivity indices using sparse polynomial chaos expansions

In this paper a novel improvement to the polynomial chaos (PC) approach for the uncertainty analysis of high speed circuits is presented. The key feature of this work is the development of an alternative hyperbolic truncation scheme to replace the conventional linear truncation scheme used in generation of PC expansions. This hyperbolic truncation scheme results in a sparse PC expansion for marginal loss of accuracy. The computational effort required to evaluate the coefficients of the resultant sparse expansion is only a small fraction of that required for full-blown PC expansions. A greedy adaptive methodology to determine the number of basis terms and evaluate the corresponding coefficients for the sparse expansion is also presented. This approach is validated on a nonlinear radio-frequency (RF) circuit against conventional full-blown PC methods.

Polynomial chaos expansion have received much attention in the past ten years in the domain of computational stochastic mechanics. One keypoint in this context is the problem of the curse of dimensionality. In order to bypass this difficulty, the present paper proposes the use of sparse polynomial chaos basis built from a prior choice of monomials by the so-called hyperbolic q-norms and a selection algorithm known as Least Angle regression. The approach is illustrated by solving a structural reliability problem of a nuclear reactor vessel submitted to a pressurized thermal shock.

In this study, a hybrid metamodel using the orthogonal constraints of radial basis function and sparse polynomial chaos expansions is proposed for the global sensitivity analysis of time-consuming models. Firstly, the orthogonal conditions of radial basis functions (RBF) and polynomial chaos expansions (PCE) were derived to construct the hybrid metamodel. Then, the variance of the metamodel was decoupled into the variances of the RBF and PCE independently by using the orthogonal condition. Furthermore, the analytical formulations of Sobol indices for the hybrid metamodel were derived according to the orthogonal decomposition. Thus, the interaction items of radial basis function and polynomial chaos expansions were eliminated, which significantly simplifies the Sobol indices. Two analytical cases were employed to investigate the influence of the number of the polynomial chaos expansions items, and several analytical and engineering cases were tested to demonstrate the accuracy and efficiency of the proposed method. In the engineering cases, the proposed method yielded significant improvements in terms of both accuracy and efficiency comparing with the existing global sensitivity analysis approaches, which indicates that the proposed method is more appropriate to the global sensitivity analysis of time-consuming engineering problems.

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.

A sequential sparse polynomial chaos expansion using Voronoi exploration and local linear approximation exploitation for slope reliability analysis

Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression

Multi-scale stochastic dynamic response analysis of offshore risers with lognormal uncertainties

Novel data-driven sparse polynomial chaos and analysis of covariance for aerodynamics of compressor cascades with dependent geometric uncertainties

Neumann enriched polynomial chaos approach for stochastic finite element problems

Global sensitivity analysis for multivariate outputs using generalized RBF-PCE metamodel enhanced by variance-based sequential sampling